Based on the theoretical analysis of nonlinear random response of structure, for the engineering practical problem, that is, the large deformation of industry cooling tower shell structure under the action of strong w...Based on the theoretical analysis of nonlinear random response of structure, for the engineering practical problem, that is, the large deformation of industry cooling tower shell structure under the action of strong wind loads, the statistic perturbation method is also used to analyze some statistic characteristics of the nonlinear random response of rotational shell with geometric nonlinearity and stationary strong wind load considered. Through computation, some average values of nornal displacements and the nonlinear effect factor of the cooling tower shell are given.展开更多
Aimed at the large deformation problem of industry cooling tower shell, the mathematical model for the random response of rotational shell under the external random excitation is established by statistic perturbation ...Aimed at the large deformation problem of industry cooling tower shell, the mathematical model for the random response of rotational shell under the external random excitation is established by statistic perturbation method. The effect of nonlinear geometric behavior on the response of rotational shell is analyzed.展开更多
A novel vibration isolation device called the nonlinear energy sink(NES)with NiTiNOL-steel wire ropes(NiTi-ST)is applied to a whole-spacecraft system.The NiTi-ST is used to describe the damping of the NES,which is cou...A novel vibration isolation device called the nonlinear energy sink(NES)with NiTiNOL-steel wire ropes(NiTi-ST)is applied to a whole-spacecraft system.The NiTi-ST is used to describe the damping of the NES,which is coupled with the modified Bouc-Wen model of hysteresis.The NES with NiTi-ST vibration reduction principle uses the irreversibility of targeted energy transfer(TET)to concentrate the energy locally on the nonlinear oscillator,and then dissipates it through damping in the NES with NiTi-ST.The generalized vibration transmissibility,obtained by the root mean square treatment of the harmonic response of the nonlinear output frequency response functions(NOFRFs),is first used as the evaluation index to analyze the whole-spacecraft system in the future.An optimization analysis of the impact of system responses is performed using different parameters of NES with NiTi-ST based on the transmissibility of NOFRFs.Finally,the effects of vibration suppression by varying the parameters of NiTi-ST are analyzed from the perspective of energy absorption.The results indicate that NES with NiTi-ST can reduce excessive vibration of the whole-spacecraft system,without changing its natural frequency.Moreover,the NES with NiTi-ST can be directly used in practical engineering applications.展开更多
To provide appropriate uses of nonlinear ground response analysis for engineering practice, a three-dimensional soil column with a distributed mass system and a time domain numerical analysis were implemented on the O...To provide appropriate uses of nonlinear ground response analysis for engineering practice, a three-dimensional soil column with a distributed mass system and a time domain numerical analysis were implemented on the Open Sees simulation platform. The standard mesh of a three-dimensional soil column was suggested to be satisfied with the specified maximum frequency. The layered soil column was divided into multiple sub-soils with a different viscous damping matrix according to the shear velocities as the soil properties were significantly different. It was necessary to use a combination of other one-dimensional or three-dimensional nonlinear seismic ground analysis programs to confirm the applicability of nonlinear seismic ground motion response analysis procedures in soft soil or for strong earthquakes. The accuracy of the three-dimensional soil column finite element method was verified by dynamic centrifuge model testing under different peak accelerations of the earthquake. As a result, nonlinear seismic ground motion response analysis procedures were improved in this study. The accuracy and efficiency of the three-dimensional seismic ground response analysis can be adapted to the requirements of engineering practice.展开更多
This article proposes a diffused hepatitis B virus （HBV） model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical ...This article proposes a diffused hepatitis B virus （HBV） model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.展开更多
Based on the Schapery three-dimensional viscoelastic constitutive relationship with growing damage, a damage model with transverse matrix cracks for the unidirectional ?bre rein- forced viscoelastic composite ...Based on the Schapery three-dimensional viscoelastic constitutive relationship with growing damage, a damage model with transverse matrix cracks for the unidirectional ?bre rein- forced viscoelastic composite plates is developed. By using Karman theory, the nonlinear dynamic governing equations of the viscoelastic composite plates under transverse periodic loading are es- tablished. By applying the ?nite di?erence method in spatial domain and the Newton-Newmark method in time domain, and using the iterative procedure, the integral-partial di?erential gov- erning equations are solved. Some examples are given and the results are compared with available data.展开更多
In this study, we investigate the nonlinear cou- pling magneto-electric （ME） effect of a giant magnetostric- tive/piezoelectric composite cylinder. The nonlinear consti- tutive relations of the ME material are taken...In this study, we investigate the nonlinear cou- pling magneto-electric （ME） effect of a giant magnetostric- tive/piezoelectric composite cylinder. The nonlinear consti- tutive relations of the ME material are taken into account, and the influences of the nonlinear material properties on the ME effect are investigated for the static and dynamic cases, respectively. The influences of different constraint conditions on the ME effect are discussed. In the dynamic case considering nonlinear material properties, the double frequency ME response （The response frequency is twice the applied magnetic frequency） is obtained and discussed, which can be used to explain the experiment phenomenon in which the input signal with frequency f is converted to the output signal with 2f in ME laminated structures. Some calculations on nonlinear ME effect are conducted. The obtained results indicate that the nonlinear material properties affect not only the magnitude of the ME effect in the static case but also the ME response frequency in the dynamic case展开更多
This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of...This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.展开更多
Many studies have been done on the heave-pitch unstable coupling response for a spar platform by a 2-DOF model.In fact,in addition to the heave and pitch which are in one plane,the nonlinear unstable motion will also ...Many studies have been done on the heave-pitch unstable coupling response for a spar platform by a 2-DOF model.In fact,in addition to the heave and pitch which are in one plane,the nonlinear unstable motion will also occur in roll.From the results of the experiments,the unstable roll motion plays a dominant role in the motion of a spar platform which is much stronger than that of pitch.The objective of this paper is to study 3-DOF coupling response performance of spar platform under wave and vortex-induced force.The nonlinear coupled equations in heave,roll and pitch are established by considering time-varying wet surface and coupling.The first order steady-state response is solved by multi-scales method when the incident wave frequency approaches the heave natural frequency.Numerical integration of the motion equations has been performed to verify the first-order perturbation solution.The results are confirmed by model test.There is a saturation phenomenon associated with heave mode in 3-DOF systems and all extra energy is transferred to roll and pitch.It is observed that sub-harmonic response occurs in roll and pitch when the wave force exceeds a certain value.The energy distribution in roll and pitch is determined by the initial value and damping characteristics of roll and pitch.The energy transfers from heave to pitch and then transfers from pitch to roll.Due to the influence of the low-frequency vortex-excited force,the response of roll is more complicated than that of pitch.展开更多
The response of subsoil strata subjected to seismic excitations plays an important role in governing the response of the overlying superstructures at any site. Ground response analysis(GRA) helps to assess the influen...The response of subsoil strata subjected to seismic excitations plays an important role in governing the response of the overlying superstructures at any site. Ground response analysis(GRA) helps to assess the influence of soil characteristics on the propagating seismic stress waves from the bedrock level to the ground surface during an earthquake. For the northeastern region of India, located in the highest seismic zone in the country, conducting an extensive GRA study is of prime importance. Conventionally, most of the GRA studies are carried out using the equivalent linear method, which, being a simplistic approach, cannot capture the nonlinear behavior of soil during seismic shaking. This paper presents the outcomes of a one-dimensional effective stress based nonlinear GRA conducted for Guwahati city(located in northeast India) incorporating the non-Masing load/unload/reload characteristics. The various ground response parameters evaluated from this study help in assessing the ground shaking, soil amplification, and site responses expected in this region. 2D contour maps, which are representative of the distribution of some of these parameters throughout Guwahati city, are also developed. The results presented herein can serve as guidelines for the design of foundations and superstructures in this region.展开更多
Components of mechanical product are assembled by structural joints,such as bolting,riveting,welding,etc.Structural joints introduce nonlinearity to some engineering structures,and the nonlinearity need to be modeled ...Components of mechanical product are assembled by structural joints,such as bolting,riveting,welding,etc.Structural joints introduce nonlinearity to some engineering structures,and the nonlinearity need to be modeled precisely.To meet serious quality requirements,it is necessary to detect and identify nonlinearity of mechanical products for structural optimization.Modal test to acquire a dynamic response has been applied for decades,which provides reliable results for finite element(FE)model updating.Here response control vibration test for identification of nonlinearity is presented.A nonlinear system can be regarded as linearity for particular steady state response,and classical linear analysis tool is applicable to extract modal data for particular response.First,its applicability is illustrated by some numerical simulations.Subsequently,it is implemented on experimental setup with structural joints by shaking table.The stiffness and damping function dependent of relative displacement are fitted to describe its inherent nonlinearity.The spring and damping forces are identified by harmonic balance method(HBM)to predict output response.Based on the identified results,the procedure is recommended that it allows a reliable measurement of nonlinearity with a certain accuracy.展开更多
According to theoretical analysis, a general characteristic of the ground vibration induced by high dam flood discharge is that the dominant frequency ranges over several narrow frequency bands, which is verified by o...According to theoretical analysis, a general characteristic of the ground vibration induced by high dam flood discharge is that the dominant frequency ranges over several narrow frequency bands, which is verified by observations from the Xiangjiaba Hydropower Station. Nonlinear base isolation is used to reduce the structure vibration under ground excitation and the advantage of the isolation application is that the low-frequency resonance problem does not need to be considered due to its excitation characteristics, which significantly facilitate the isolation design. In order to obtain the response probabilistic distribution of a nonlinear system, the state space split technique is modified. As only a few degrees of freedom are subjected to the random noise, the probabilistic distribution of the response without involving stochastic excitation is represented by the δ function. Then, the sampling property of the δ function is employed to reduce the dimension of the Fokker-Planck-Kolmogorov （FPK） equation and the low-dimensional FPK equation is solvable with existing methods. Numerical results indicate that the proposed approach is effective and accurate. Moreover, the response probabilistic distributions are more reasonable and scientific than the peak responses calculated by conventional time and frequency domain methods.展开更多
This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochas...This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.展开更多
By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the gener...By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general sixdegrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.展开更多
An effective nonlinear response of a nonlinear composite with spherical coated inclusions randomly embedded in a host medium under the action of an external AC electric field, Ea= E1 sin（wt） ＋ E3 sin（3wt）, is inv...An effective nonlinear response of a nonlinear composite with spherical coated inclusions randomly embedded in a host medium under the action of an external AC electric field, Ea= E1 sin（wt） ＋ E3 sin（3wt）, is investigated using a perturbation method. The local potentials of the composite at higher harmonics are given both in the region of local inclusion particles and in the local host region under the external AC electric field. All effective nonlinear responses of the composite and the relationship between the effective nonlinear responses at the fundamental frequency and third harmonics are also studied for spherical coated inclusion in a dilute limit.展开更多
The effect of oil film force nonlinearity on unbalance response of Jeffcot rotor elliptical bearing system is studied. Linear analysis is done by linearizing the bearing oil film dynamic forces and expressing them wi...The effect of oil film force nonlinearity on unbalance response of Jeffcot rotor elliptical bearing system is studied. Linear analysis is done by linearizing the bearing oil film dynamic forces and expressing them with stiffness and damping constants. Nonlinear dynamic simulation is done by taking the nonlinearity of bearing oil film dynamic force into full consideration, with the latter being expressed by a special database which is generated beforehand, and based on non stationary Reynolds equation and Reynolds boundary condition of film rupture. The linear and nonlinear unbalance responses of a Jeffcot rotor supported on a pair of elliptical bearings is studied. The resulting dynamic characteristics and rotor and journal whirling orbits are compared. While good consistancy between nonlinear and linear predictions is found under very small unbalance, significant or even drastic differences are found whenever the unbalance is not small, indicating the necessity of including the nonlinearity of oil film dynamic forces, especially when response to large unbalance is to be predicted.展开更多
The nonlinear behavior of a soil-foundation system may alter the seismic response of a structure by providing additional flexibility to the system and dissipating hysteretic energy at the soil-foundation interface. Ho...The nonlinear behavior of a soil-foundation system may alter the seismic response of a structure by providing additional flexibility to the system and dissipating hysteretic energy at the soil-foundation interface. However, the current design practice is still reluctant to consider the nonlinearity of the soil-foundation system, primarily due to lack of reliable modeling techniques. This study is motivated towards evaluating the effect of nonlinear soil-structure interaction （SSI） on the seismic responses of low-rise steel moment resisting frame （SMRF） structures. In order to achieve this, a Winkler- based approach is adopted, where the soil beneath the foundation is assumed to be a system of closely-spaced, independent, nonlinear spring elements. Static pushover analysis and nonlinear dynamic analyses are performed on a 3-story SMRF building and the performance of the structure is evaluated through a variety of force and displacement demand parameters. It is observed that incorporation of nonlinear SSI leads to an increase in story displacement demand and a significant reduction in base moment, base shear and inter-story drift demands, indicating the importance of its consideration towards achieving an economic, yet safe seismic design.展开更多
The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear...The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.展开更多
Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application. Two categories of the tension-dominant and curvaturedominant nonlinearities are analyzed. The dynamic non...Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application. Two categories of the tension-dominant and curvaturedominant nonlinearities are analyzed. The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach. The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity, its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects. However, for the nanomechanical resonator of the curvature-dominant nonlinearity, its dynamic nonlinearity is only dependent on axial loading. Compared with the tension-dominant nonlinearity, the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity展开更多
The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution ...The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.展开更多
文摘Based on the theoretical analysis of nonlinear random response of structure, for the engineering practical problem, that is, the large deformation of industry cooling tower shell structure under the action of strong wind loads, the statistic perturbation method is also used to analyze some statistic characteristics of the nonlinear random response of rotational shell with geometric nonlinearity and stationary strong wind load considered. Through computation, some average values of nornal displacements and the nonlinear effect factor of the cooling tower shell are given.
文摘Aimed at the large deformation problem of industry cooling tower shell, the mathematical model for the random response of rotational shell under the external random excitation is established by statistic perturbation method. The effect of nonlinear geometric behavior on the response of rotational shell is analyzed.
基金Project supported by the National Natural Science Foundation of China(No.11772205)the Scientific Research Fund of Liaoning Provincial Education Department(No.L201703)+1 种基金the Liaoning Revitalization Talent Program(No.XLYC1807172)the Training Project of Liaoning Higher Education Institutions in Domestic and Overseas(No.2018LNGXGJWPY-YB008)
文摘A novel vibration isolation device called the nonlinear energy sink(NES)with NiTiNOL-steel wire ropes(NiTi-ST)is applied to a whole-spacecraft system.The NiTi-ST is used to describe the damping of the NES,which is coupled with the modified Bouc-Wen model of hysteresis.The NES with NiTi-ST vibration reduction principle uses the irreversibility of targeted energy transfer(TET)to concentrate the energy locally on the nonlinear oscillator,and then dissipates it through damping in the NES with NiTi-ST.The generalized vibration transmissibility,obtained by the root mean square treatment of the harmonic response of the nonlinear output frequency response functions(NOFRFs),is first used as the evaluation index to analyze the whole-spacecraft system in the future.An optimization analysis of the impact of system responses is performed using different parameters of NES with NiTi-ST based on the transmissibility of NOFRFs.Finally,the effects of vibration suppression by varying the parameters of NiTi-ST are analyzed from the perspective of energy absorption.The results indicate that NES with NiTi-ST can reduce excessive vibration of the whole-spacecraft system,without changing its natural frequency.Moreover,the NES with NiTi-ST can be directly used in practical engineering applications.
基金National Natural Science Foundation of China under Grant No.41672266
文摘To provide appropriate uses of nonlinear ground response analysis for engineering practice, a three-dimensional soil column with a distributed mass system and a time domain numerical analysis were implemented on the Open Sees simulation platform. The standard mesh of a three-dimensional soil column was suggested to be satisfied with the specified maximum frequency. The layered soil column was divided into multiple sub-soils with a different viscous damping matrix according to the shear velocities as the soil properties were significantly different. It was necessary to use a combination of other one-dimensional or three-dimensional nonlinear seismic ground analysis programs to confirm the applicability of nonlinear seismic ground motion response analysis procedures in soft soil or for strong earthquakes. The accuracy of the three-dimensional soil column finite element method was verified by dynamic centrifuge model testing under different peak accelerations of the earthquake. As a result, nonlinear seismic ground motion response analysis procedures were improved in this study. The accuracy and efficiency of the three-dimensional seismic ground response analysis can be adapted to the requirements of engineering practice.
基金supported by the National Natural Science Foundation of China(10971166,10901131)the National High Technology Research and Development Program of China(863 Program,2009AA01A135)the Natural Science Foundation of Xinjiang Province(2010211B04)
文摘This article proposes a diffused hepatitis B virus （HBV） model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.
基金Project supported by the National Natural Science Foundation of China (No.10272024).
文摘Based on the Schapery three-dimensional viscoelastic constitutive relationship with growing damage, a damage model with transverse matrix cracks for the unidirectional ?bre rein- forced viscoelastic composite plates is developed. By using Karman theory, the nonlinear dynamic governing equations of the viscoelastic composite plates under transverse periodic loading are es- tablished. By applying the ?nite di?erence method in spatial domain and the Newton-Newmark method in time domain, and using the iterative procedure, the integral-partial di?erential gov- erning equations are solved. Some examples are given and the results are compared with available data.
基金supported by the National Natural Science Foundation of China (11072093)the State Key Program of National Natural Science of China (11032006)the Fundamental Research Funds for the Central Universities (lzujbky-2012-k05)
文摘In this study, we investigate the nonlinear cou- pling magneto-electric （ME） effect of a giant magnetostric- tive/piezoelectric composite cylinder. The nonlinear consti- tutive relations of the ME material are taken into account, and the influences of the nonlinear material properties on the ME effect are investigated for the static and dynamic cases, respectively. The influences of different constraint conditions on the ME effect are discussed. In the dynamic case considering nonlinear material properties, the double frequency ME response （The response frequency is twice the applied magnetic frequency） is obtained and discussed, which can be used to explain the experiment phenomenon in which the input signal with frequency f is converted to the output signal with 2f in ME laminated structures. Some calculations on nonlinear ME effect are conducted. The obtained results indicate that the nonlinear material properties affect not only the magnitude of the ME effect in the static case but also the ME response frequency in the dynamic case
文摘This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.
基金supported by the National Natural Science Foundation of China(Grant No.51279130)
文摘Many studies have been done on the heave-pitch unstable coupling response for a spar platform by a 2-DOF model.In fact,in addition to the heave and pitch which are in one plane,the nonlinear unstable motion will also occur in roll.From the results of the experiments,the unstable roll motion plays a dominant role in the motion of a spar platform which is much stronger than that of pitch.The objective of this paper is to study 3-DOF coupling response performance of spar platform under wave and vortex-induced force.The nonlinear coupled equations in heave,roll and pitch are established by considering time-varying wet surface and coupling.The first order steady-state response is solved by multi-scales method when the incident wave frequency approaches the heave natural frequency.Numerical integration of the motion equations has been performed to verify the first-order perturbation solution.The results are confirmed by model test.There is a saturation phenomenon associated with heave mode in 3-DOF systems and all extra energy is transferred to roll and pitch.It is observed that sub-harmonic response occurs in roll and pitch when the wave force exceeds a certain value.The energy distribution in roll and pitch is determined by the initial value and damping characteristics of roll and pitch.The energy transfers from heave to pitch and then transfers from pitch to roll.Due to the influence of the low-frequency vortex-excited force,the response of roll is more complicated than that of pitch.
文摘The response of subsoil strata subjected to seismic excitations plays an important role in governing the response of the overlying superstructures at any site. Ground response analysis(GRA) helps to assess the influence of soil characteristics on the propagating seismic stress waves from the bedrock level to the ground surface during an earthquake. For the northeastern region of India, located in the highest seismic zone in the country, conducting an extensive GRA study is of prime importance. Conventionally, most of the GRA studies are carried out using the equivalent linear method, which, being a simplistic approach, cannot capture the nonlinear behavior of soil during seismic shaking. This paper presents the outcomes of a one-dimensional effective stress based nonlinear GRA conducted for Guwahati city(located in northeast India) incorporating the non-Masing load/unload/reload characteristics. The various ground response parameters evaluated from this study help in assessing the ground shaking, soil amplification, and site responses expected in this region. 2D contour maps, which are representative of the distribution of some of these parameters throughout Guwahati city, are also developed. The results presented herein can serve as guidelines for the design of foundations and superstructures in this region.
文摘Components of mechanical product are assembled by structural joints,such as bolting,riveting,welding,etc.Structural joints introduce nonlinearity to some engineering structures,and the nonlinearity need to be modeled precisely.To meet serious quality requirements,it is necessary to detect and identify nonlinearity of mechanical products for structural optimization.Modal test to acquire a dynamic response has been applied for decades,which provides reliable results for finite element(FE)model updating.Here response control vibration test for identification of nonlinearity is presented.A nonlinear system can be regarded as linearity for particular steady state response,and classical linear analysis tool is applicable to extract modal data for particular response.First,its applicability is illustrated by some numerical simulations.Subsequently,it is implemented on experimental setup with structural joints by shaking table.The stiffness and damping function dependent of relative displacement are fitted to describe its inherent nonlinearity.The spring and damping forces are identified by harmonic balance method(HBM)to predict output response.Based on the identified results,the procedure is recommended that it allows a reliable measurement of nonlinearity with a certain accuracy.
基金National Key R&D Program of China under Grant No.2016YFC0401705Science Fund for Creative Research Groups of the National Natural Science Foundation of China Grant No.51621092+3 种基金the National Natural Science Foundation of China Grant No.51579173,No.51379140,No.51309177 and No.51509180the Fund for Key Research Area Innovation Groups of China Ministry of Science and Technology Grant No.2014RA4031the Program of Introducing Talents of Discipline to Universities Grant No.B14012the Tianjin Innovation Team Foundation of Key Research Areas Grant No.2014TDA001
文摘According to theoretical analysis, a general characteristic of the ground vibration induced by high dam flood discharge is that the dominant frequency ranges over several narrow frequency bands, which is verified by observations from the Xiangjiaba Hydropower Station. Nonlinear base isolation is used to reduce the structure vibration under ground excitation and the advantage of the isolation application is that the low-frequency resonance problem does not need to be considered due to its excitation characteristics, which significantly facilitate the isolation design. In order to obtain the response probabilistic distribution of a nonlinear system, the state space split technique is modified. As only a few degrees of freedom are subjected to the random noise, the probabilistic distribution of the response without involving stochastic excitation is represented by the δ function. Then, the sampling property of the δ function is employed to reduce the dimension of the Fokker-Planck-Kolmogorov （FPK） equation and the low-dimensional FPK equation is solvable with existing methods. Numerical results indicate that the proposed approach is effective and accurate. Moreover, the response probabilistic distributions are more reasonable and scientific than the peak responses calculated by conventional time and frequency domain methods.
基金National Natural Science Foundation of China for Innovative Research Groups Under Grant No.50321803 & 50621062National Natural Science Foundation of China Under Grant No.50808113 & 10872148
文摘This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.
基金the National Natural Science Foundation of China (10572049)Hunan Provincial Natural Science Foundation of China (07JJ3009)National 985 Special Foundation of China
文摘By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general sixdegrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.
基金Project supported by the Natural Science Foundation of Inner Mongolia,China (Grant No.200711020116)the Open Fund of the Key Laboratory of Ocean Circulation and Waves,Chinese Academy of Sciences (Grant No.KLOCAW0805)+1 种基金the Research Fund of Higher Education of Inner Mongolia,China (Grant No.NJ09066)the National Natural Science Foundation for Young Scientists of China (Grant No.40806008)
文摘An effective nonlinear response of a nonlinear composite with spherical coated inclusions randomly embedded in a host medium under the action of an external AC electric field, Ea= E1 sin（wt） ＋ E3 sin（3wt）, is investigated using a perturbation method. The local potentials of the composite at higher harmonics are given both in the region of local inclusion particles and in the local host region under the external AC electric field. All effective nonlinear responses of the composite and the relationship between the effective nonlinear responses at the fundamental frequency and third harmonics are also studied for spherical coated inclusion in a dilute limit.
文摘The effect of oil film force nonlinearity on unbalance response of Jeffcot rotor elliptical bearing system is studied. Linear analysis is done by linearizing the bearing oil film dynamic forces and expressing them with stiffness and damping constants. Nonlinear dynamic simulation is done by taking the nonlinearity of bearing oil film dynamic force into full consideration, with the latter being expressed by a special database which is generated beforehand, and based on non stationary Reynolds equation and Reynolds boundary condition of film rupture. The linear and nonlinear unbalance responses of a Jeffcot rotor supported on a pair of elliptical bearings is studied. The resulting dynamic characteristics and rotor and journal whirling orbits are compared. While good consistancy between nonlinear and linear predictions is found under very small unbalance, significant or even drastic differences are found whenever the unbalance is not small, indicating the necessity of including the nonlinearity of oil film dynamic forces, especially when response to large unbalance is to be predicted.
文摘The nonlinear behavior of a soil-foundation system may alter the seismic response of a structure by providing additional flexibility to the system and dissipating hysteretic energy at the soil-foundation interface. However, the current design practice is still reluctant to consider the nonlinearity of the soil-foundation system, primarily due to lack of reliable modeling techniques. This study is motivated towards evaluating the effect of nonlinear soil-structure interaction （SSI） on the seismic responses of low-rise steel moment resisting frame （SMRF） structures. In order to achieve this, a Winkler- based approach is adopted, where the soil beneath the foundation is assumed to be a system of closely-spaced, independent, nonlinear spring elements. Static pushover analysis and nonlinear dynamic analyses are performed on a 3-story SMRF building and the performance of the structure is evaluated through a variety of force and displacement demand parameters. It is observed that incorporation of nonlinear SSI leads to an increase in story displacement demand and a significant reduction in base moment, base shear and inter-story drift demands, indicating the importance of its consideration towards achieving an economic, yet safe seismic design.
文摘The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.
基金supported by the National Natural Science Foundation of China (10721202 and 11023001)the Chinese Academy of Sciences (KJCX2-EW-L03)
文摘Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application. Two categories of the tension-dominant and curvaturedominant nonlinearities are analyzed. The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach. The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity, its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects. However, for the nanomechanical resonator of the curvature-dominant nonlinearity, its dynamic nonlinearity is only dependent on axial loading. Compared with the tension-dominant nonlinearity, the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity
基金the National Natural Science Foundation of Chinafor Innovative Research Groups Under Grant No.50621062the National Natural Science Foundation of China forYoung Scholars Under Grant No.10402030
文摘The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.
