A novel approach for analyzing coupled vibrations between vehicles and bridges is presented,taking into account spatiotemporal effects and mechanical phenomena resulting fromvehicle braking.Efficient modeling and solu...A novel approach for analyzing coupled vibrations between vehicles and bridges is presented,taking into account spatiotemporal effects and mechanical phenomena resulting fromvehicle braking.Efficient modeling and solution of bridge vibrations induced by vehicle deceleration are realized using this method.The method’s validity and reliability are substantiated through numerical examples.A simply supported beam bridge with a corrugated steel web is taken as an example and the effects of parameters such as the initial vehicle speed,braking acceleration,braking location,and road surface roughness on the mid-span displacement and impact factor of the bridge are analyzed.The results show that vehicle braking significantly amplifies mid-span displacement and impact factor responses in comparison to uniform vehicular motion across the bridge.Notably,the influence of wheelto-bridge friction forces is of particular significance and cannot be overlooked.When the vehicle initiates braking near the middle of the span,both the mid-span displacement and impact factor of the bridge exhibit substantial increases,further escalating with higher braking acceleration.Under favorable road surface conditions,the midspan displacement and the impact factor during vehicle braking may exceed the design values stipulated by codes.It is important to note that road surface roughness exerts a more pronounced effect on the impact factor of the bridge in comparison to the effects of vehicle braking.展开更多
Effects of system size,coupling strength,and noise on vibrational resonance(VR)of globally coupled bistable systems are investigated.The power spectral amplifications obtained by the three methods all show that the VR...Effects of system size,coupling strength,and noise on vibrational resonance(VR)of globally coupled bistable systems are investigated.The power spectral amplifications obtained by the three methods all show that the VR exists over a wide range of parameter values.The increase in system size induces and enhances the VR,while the increase in noise intensity suppresses and eventually eliminates the VR.Both the stochastic resonance and the system size resonance can coexist with the VR in different parameter regions.This research has potential applications to the weak signal detection process in stochastic multi-body systems.展开更多
By applying the sinusoidal wave mode to simulate the rugged surface of bridge deck,accounting for vehicle-bridge interaction and using Euler-Bernoulli beam theory, a coupling vibration model of vehicle-bridge system w...By applying the sinusoidal wave mode to simulate the rugged surface of bridge deck,accounting for vehicle-bridge interaction and using Euler-Bernoulli beam theory, a coupling vibration model of vehicle-bridge system was developed. The model was solved by mode analyzing method and Runge-Kutta method, and the dynamic response and the resonance curve of the bridge were obtained. It is found that there are two resonance regions, one represents the main resonance while the other the minor resonance, in the resonance curve. The influence due to the rugged surface, the vibration mode of bridge, and the interaction between vehicle and bridge on vibration of the system were discussed. Numerical results show that the influence due to these parameters is so significant that the effect of roughness of the bridge deck and the mode shape of the bridge can't be ignored and the vehicle velocity should be kept away from the critical speed of the vehicle.展开更多
To numerically evaluate the reinforcement effect on dynamic characteristics of a concrete-filled steel tube arch bridge with vibration problems,a 12-degree-of-freedom sprung-mass dynamic vehicle model and a 3D finite ...To numerically evaluate the reinforcement effect on dynamic characteristics of a concrete-filled steel tube arch bridge with vibration problems,a 12-degree-of-freedom sprung-mass dynamic vehicle model and a 3D finite element bridge model were established.Then,the coupled equations of vehicle-bridge interaction were derived and a computer program was developed using the FORTRAN language.This program can accurately simulate vehicle-bridge coupled vibration considering the bumping effect and road surface irregularity during motion of the vehicle.The simulated results were compared with those of relevant literatures to verify the correctness of the self-developed program.Then,three reinforcement schemes for the bridge(Addition of longitudinal beams,Reinforcement of bridge decks,and Replacement of suspenders)were proposed and numerically simulated,and the vibration reduction effects of the three schemes were evaluated based on the numerical results to find effective ones.It is confirmed that the reinforcement scheme of Addition of longitudinal beams shows the most significant vibration reduction effect.It is recommended in the engineering practice that the combination of the reinforcement schemes of Addition of longitudinal beams and Replacement of bridge deck can be used to solve the excessive vibration problem.展开更多
Potential energy surfaces(PESs), vibrational frequencies, and infrared spectra are calculated for NF_(3)^(+) using ab initio calculations, based on UCCSD(T)/cc-p VTZ combined with vibrational configuration interaction...Potential energy surfaces(PESs), vibrational frequencies, and infrared spectra are calculated for NF_(3)^(+) using ab initio calculations, based on UCCSD(T)/cc-p VTZ combined with vibrational configuration interaction(VCI). Based on an iterative algorithm, the surfaces(SURF) program adds automatic points to the lattice representation of the potential function, the one-dimensional and two-dimensional PESs are calculated after reaching a convergence threshold, finally the smooth image of the potential energy surface is fitted. The PESs accurately account for the interaction between the different modes, with the mode q_(6) symmetrical stretching vibrations having the greatest effect on the potential energy change of the whole system throughout the potential energy surface shift. The anharmonic frequencies are obtained when the VCI matrix is diagonalized. Fundamental frequencies, overtones, and combination bands of NF_(3)^(+) are calculated, which generate the degenerate phenomenon between their frequencies. Finally, the calculated anharmonic frequency is used to plot the infrared spectra.Modal antisymmetric stretching ν_(5) and symmetric stretching ν_(6) exhibit a phenomenon of large-intensity borrowing. This study can provide data to support the characterization in the laboratory.展开更多
A nonlinear model of a low pressure cylinder-generator rotor system is presented to study sub-synchronous resonance and combined resonance. Analytical results are obtained by an averaging method. Transition sets and b...A nonlinear model of a low pressure cylinder-generator rotor system is presented to study sub-synchronous resonance and combined resonance. Analytical results are obtained by an averaging method. Transition sets and bifurcation diagrams are obtained based on the singularity theory for the two-state variable system. The bifurcation characteristics are analyzed to provide a basis for the optimal design and fault diagnosis of the rotor system. Finally, the theoretical results are verified with the numerical results.展开更多
The intramolecular vibrational dynamics due to extremely irrational couplings is demonstrated by contrast to the resonance couplings, for the three-mode case of H2O as an example. The extremely irrational couplings ar...The intramolecular vibrational dynamics due to extremely irrational couplings is demonstrated by contrast to the resonance couplings, for the three-mode case of H2O as an example. The extremely irrational couplings are shown to impose such strong hindrance to intramolecular vibrational relaxation （IVR） that they act as barriers. They restrict the direct action/energy transfer between the two stretching modes, though they allow the transfer between a stretching and a bending modes. In contrast, the resonance is more mediated by the bending mode and leads to chaotic IVR. It is also shown that there is a region in the dynamical space in which resonance and extremely irrational couplings coexist.展开更多
The objective of this study is to investigate the effects of earthquakes on road vehicle-bridge coupling vibration systems. A two-axle highway freight vehicle is treated as a 13 degree-of-freedom system composed of se...The objective of this study is to investigate the effects of earthquakes on road vehicle-bridge coupling vibration systems. A two-axle highway freight vehicle is treated as a 13 degree-of-freedom system composed of several rigid bodies, which are connected by a series of springs and dampers. The framework of the earthquake-vehicle-bridge dynamic analysis system is then established using an earthquake as the extemal excitation. The equivalent lateral contact force serves as the judgment criteria for sideslip accidents according to reliability theory. The entire process of the vehicle crossing the bridge is considered for a very high pier continuous rigid frame bridge. The response characteristics of the vehicle and the bridge are discussed in terms of various parameters such as earthquake ground motion, PGA value of the earthquake, incident angle, pier height, vehicle speed and mass. It is found that seismic excitation is the most influential factor in the responses of the vehicle-bridge system and that the safety of vehicles crossing the bridge is seriously impacted by the dual excitations of earthquake and bridge vibration.展开更多
Numerical analyses of the coupled vibrations of vehicle-bridge system and the effects of different types of cable stayed bridges on the coupled vibration responses have been presented in this paper using ANSYS. The br...Numerical analyses of the coupled vibrations of vehicle-bridge system and the effects of different types of cable stayed bridges on the coupled vibration responses have been presented in this paper using ANSYS. The bridge model and vehicle model were independently built which have no internal relationship in the ANSYS. The vehicle-bridge coupled vibration relationship was obtained by using the APDL program which subsequently imposed on the vehicle and bridge models during the numerical analysis. The proposed model was validated through a field measurements and literature data. The judging method, possibility, and criterion of the vehicle-bridge resonance （coupled vibrations） of cable stayed bridges （both the floating system and half floating system） under traffic flows were presented. The results indicated that the interval time between vehicles is the main influence factor on the resonance excitation frequency under the condition of equally spaced traffic flows. Compared to other types of cable stayed bridges, the floating bridge system has relatively high possibility to cause vehicle-bridge resonance.展开更多
The 3D characteristic diagram of acoustically induced surface vibration was employed to study the influence of different buried landmines on the acoustic detection signal. By using the vehicular experimental system fo...The 3D characteristic diagram of acoustically induced surface vibration was employed to study the influence of different buried landmines on the acoustic detection signal. By using the vehicular experimental system for acoustic landmine detection and the method of scanning detection, the 3D characteristic diagrams of surface vibration were measured when different objects were buried underground, including big plastic landmine, small plastic landmine, big metal landmine and bricks. The results show that, under the given conditions, the surface vibration amplitudes of big plastic landmine, big metal landmine, small plastic landmine and bricks decrease in turn. The 3D characteristic diagrams of surface vibration can be used to further identify the locations of buried landmines.展开更多
To systematically study the vehicle-bridge coupled dynamic response and its change rule with different parameters, a vehicle model with seven degrees of freedom was built and the total potential energy of vehicle spac...To systematically study the vehicle-bridge coupled dynamic response and its change rule with different parameters, a vehicle model with seven degrees of freedom was built and the total potential energy of vehicle space vibration system was deduced. Considering the stimulation of road roughness, the dynamic response equation of vehicle-bridge coupled system was established in accordance with the elastic system principle of total potential energy with stationary value and the ＂set-in-right-position＂ rule. On the basis of the self-compiled Fortran program and bridge engineering, the dynamic response of long- span continuous girder bridge under vehicle load was studied. This study also included the calculation of vehicle impact coefficient, evaluation of vibration comfort, and analysis of dynamic response parameters. Results show the impact coefficient changes with lane number and is larger than the value calculated by the ＂general code for design of highway bridges and culverts （China）＂. The Dieckmann index of bridge vibration is also related to lane number, and the vibration comfort evaluation is good in normal conditions. The relevant conclusions from parametric analyses have practical significance to dynamic design and daily operation of long-span continuous girder bridges in expressways. Safety and comfort are expected to improve significantly with further control of the vibration of vehicle-bridge system.展开更多
The nonlinear modal coupling in a T-shaped piezoelectric resonator,when the former two natural frequencies are away from 1:2,is studied.Experimentally sweeping up the exciting frequency shows that the horizontal beam ...The nonlinear modal coupling in a T-shaped piezoelectric resonator,when the former two natural frequencies are away from 1:2,is studied.Experimentally sweeping up the exciting frequency shows that the horizontal beam exhibits a nonlinear hardening behavior.The first primary resonance of the vertical beam,owing to modal coupling,exhibits an abrupt amplitude increase,namely the Hopf bifurcation.The frequency comb phenomenon induced by modal coupling is measured experimentally.A Duffing-Mathieu coupled model is theoretically introduced to derive the conditions of the modal coupling and frequency comb phenomenon.The results demonstrate that the modal coupling results from nonlinear stiffness hardening and is strictly dependent on the loading range and sweeping form of the driving voltage and the frequency of the piezoelectric patches.展开更多
Because of propeller hydrodynamic influence, the shafting vibration is a coupled vibration which includes torsional, longitudinal and whirling vibrations. It is unsuitable to analyze different vibrations of propulsive...Because of propeller hydrodynamic influence, the shafting vibration is a coupled vibration which includes torsional, longitudinal and whirling vibrations. It is unsuitable to analyze different vibrations of propulsive shafting systems with development of shipbuilding technologies. To overcome the shortages of traditional marine standards, we establish a new numerical model of the shafting coupled vibration. And we put forward shafting coupled vibration calculation to ensure better reliability of main propulsion system. The shafting system is modeled into two sub-systems, a continuous one and a discrete one. Wave approach and transit matrix method are used to investigate displacement and stress fields in continuous and discrete sub-systems, respectively. And vibrations of different modes in both sub-systems are coupled by using dynamic equilibrium and continuity condition to deduce the global equations governing the motion of shafting. The coupling calculation is then used to research the reason of a very large crude carrier(VLCC) stern hull vibration. It is shown by the comparison of the results from both coupling and dependent vibration calculations that vibration in deferent directions will cause deformation in the same mode, which leads to extra stress and displacements on shafting, especially as the resonant frequencies of different vibration modes match each other. This is helpful to prevent ship stern vibration due to poor shafting vibration calculation.展开更多
基金supported by the Henan Provincial Science and Technology Research Project under Grant(152102310295).
文摘A novel approach for analyzing coupled vibrations between vehicles and bridges is presented,taking into account spatiotemporal effects and mechanical phenomena resulting fromvehicle braking.Efficient modeling and solution of bridge vibrations induced by vehicle deceleration are realized using this method.The method’s validity and reliability are substantiated through numerical examples.A simply supported beam bridge with a corrugated steel web is taken as an example and the effects of parameters such as the initial vehicle speed,braking acceleration,braking location,and road surface roughness on the mid-span displacement and impact factor of the bridge are analyzed.The results show that vehicle braking significantly amplifies mid-span displacement and impact factor responses in comparison to uniform vehicular motion across the bridge.Notably,the influence of wheelto-bridge friction forces is of particular significance and cannot be overlooked.When the vehicle initiates braking near the middle of the span,both the mid-span displacement and impact factor of the bridge exhibit substantial increases,further escalating with higher braking acceleration.Under favorable road surface conditions,the midspan displacement and the impact factor during vehicle braking may exceed the design values stipulated by codes.It is important to note that road surface roughness exerts a more pronounced effect on the impact factor of the bridge in comparison to the effects of vehicle braking.
基金Project supported by the Xing Dian Talents Support Project of Yunnan Province(Grant No.YNWR-QNBJ-2018-0040)the Youth Project of Applied Basic Research of Yunnan Science(Grant No.202201AU070062)the Yunnan University’s Research Innovation Fund for Graduate Students(Grant No.KC-22221171).
文摘Effects of system size,coupling strength,and noise on vibrational resonance(VR)of globally coupled bistable systems are investigated.The power spectral amplifications obtained by the three methods all show that the VR exists over a wide range of parameter values.The increase in system size induces and enhances the VR,while the increase in noise intensity suppresses and eventually eliminates the VR.Both the stochastic resonance and the system size resonance can coexist with the VR in different parameter regions.This research has potential applications to the weak signal detection process in stochastic multi-body systems.
文摘By applying the sinusoidal wave mode to simulate the rugged surface of bridge deck,accounting for vehicle-bridge interaction and using Euler-Bernoulli beam theory, a coupling vibration model of vehicle-bridge system was developed. The model was solved by mode analyzing method and Runge-Kutta method, and the dynamic response and the resonance curve of the bridge were obtained. It is found that there are two resonance regions, one represents the main resonance while the other the minor resonance, in the resonance curve. The influence due to the rugged surface, the vibration mode of bridge, and the interaction between vehicle and bridge on vibration of the system were discussed. Numerical results show that the influence due to these parameters is so significant that the effect of roughness of the bridge deck and the mode shape of the bridge can't be ignored and the vehicle velocity should be kept away from the critical speed of the vehicle.
基金This work is supported by the Natural Science Foundation Projects of Liaoning Province(2019-ZD-0145).
文摘To numerically evaluate the reinforcement effect on dynamic characteristics of a concrete-filled steel tube arch bridge with vibration problems,a 12-degree-of-freedom sprung-mass dynamic vehicle model and a 3D finite element bridge model were established.Then,the coupled equations of vehicle-bridge interaction were derived and a computer program was developed using the FORTRAN language.This program can accurately simulate vehicle-bridge coupled vibration considering the bumping effect and road surface irregularity during motion of the vehicle.The simulated results were compared with those of relevant literatures to verify the correctness of the self-developed program.Then,three reinforcement schemes for the bridge(Addition of longitudinal beams,Reinforcement of bridge decks,and Replacement of suspenders)were proposed and numerically simulated,and the vibration reduction effects of the three schemes were evaluated based on the numerical results to find effective ones.It is confirmed that the reinforcement scheme of Addition of longitudinal beams shows the most significant vibration reduction effect.It is recommended in the engineering practice that the combination of the reinforcement schemes of Addition of longitudinal beams and Replacement of bridge deck can be used to solve the excessive vibration problem.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.52002318 and 22103061)。
文摘Potential energy surfaces(PESs), vibrational frequencies, and infrared spectra are calculated for NF_(3)^(+) using ab initio calculations, based on UCCSD(T)/cc-p VTZ combined with vibrational configuration interaction(VCI). Based on an iterative algorithm, the surfaces(SURF) program adds automatic points to the lattice representation of the potential function, the one-dimensional and two-dimensional PESs are calculated after reaching a convergence threshold, finally the smooth image of the potential energy surface is fitted. The PESs accurately account for the interaction between the different modes, with the mode q_(6) symmetrical stretching vibrations having the greatest effect on the potential energy change of the whole system throughout the potential energy surface shift. The anharmonic frequencies are obtained when the VCI matrix is diagonalized. Fundamental frequencies, overtones, and combination bands of NF_(3)^(+) are calculated, which generate the degenerate phenomenon between their frequencies. Finally, the calculated anharmonic frequency is used to plot the infrared spectra.Modal antisymmetric stretching ν_(5) and symmetric stretching ν_(6) exhibit a phenomenon of large-intensity borrowing. This study can provide data to support the characterization in the laboratory.
基金Project supported by the National Natural Science Foundation of China(No.10632040)
文摘A nonlinear model of a low pressure cylinder-generator rotor system is presented to study sub-synchronous resonance and combined resonance. Analytical results are obtained by an averaging method. Transition sets and bifurcation diagrams are obtained based on the singularity theory for the two-state variable system. The bifurcation characteristics are analyzed to provide a basis for the optimal design and fault diagnosis of the rotor system. Finally, the theoretical results are verified with the numerical results.
基金Project supported by the National Natural Science Foundation of China （Grant No 20373030） and the Foundation for Key Program of Ministry of Education, China （Grant No 306020） and the Specialized Research Fund for the Doctoral Program of Higher Education of China.
文摘The intramolecular vibrational dynamics due to extremely irrational couplings is demonstrated by contrast to the resonance couplings, for the three-mode case of H2O as an example. The extremely irrational couplings are shown to impose such strong hindrance to intramolecular vibrational relaxation （IVR） that they act as barriers. They restrict the direct action/energy transfer between the two stretching modes, though they allow the transfer between a stretching and a bending modes. In contrast, the resonance is more mediated by the bending mode and leads to chaotic IVR. It is also shown that there is a region in the dynamical space in which resonance and extremely irrational couplings coexist.
基金National Natural Science Foundation of China under Grant NNSF-50508036New Century Excellent Talents in University of China Under Grant NCET-06-0802Outstanding Young Academic Leaders Program of Sichuan Province Under Grant 2009-15-406
文摘The objective of this study is to investigate the effects of earthquakes on road vehicle-bridge coupling vibration systems. A two-axle highway freight vehicle is treated as a 13 degree-of-freedom system composed of several rigid bodies, which are connected by a series of springs and dampers. The framework of the earthquake-vehicle-bridge dynamic analysis system is then established using an earthquake as the extemal excitation. The equivalent lateral contact force serves as the judgment criteria for sideslip accidents according to reliability theory. The entire process of the vehicle crossing the bridge is considered for a very high pier continuous rigid frame bridge. The response characteristics of the vehicle and the bridge are discussed in terms of various parameters such as earthquake ground motion, PGA value of the earthquake, incident angle, pier height, vehicle speed and mass. It is found that seismic excitation is the most influential factor in the responses of the vehicle-bridge system and that the safety of vehicles crossing the bridge is seriously impacted by the dual excitations of earthquake and bridge vibration.
文摘Numerical analyses of the coupled vibrations of vehicle-bridge system and the effects of different types of cable stayed bridges on the coupled vibration responses have been presented in this paper using ANSYS. The bridge model and vehicle model were independently built which have no internal relationship in the ANSYS. The vehicle-bridge coupled vibration relationship was obtained by using the APDL program which subsequently imposed on the vehicle and bridge models during the numerical analysis. The proposed model was validated through a field measurements and literature data. The judging method, possibility, and criterion of the vehicle-bridge resonance （coupled vibrations） of cable stayed bridges （both the floating system and half floating system） under traffic flows were presented. The results indicated that the interval time between vehicles is the main influence factor on the resonance excitation frequency under the condition of equally spaced traffic flows. Compared to other types of cable stayed bridges, the floating bridge system has relatively high possibility to cause vehicle-bridge resonance.
基金Supported by the National Natural Science Foundation of China(No.61575119)Science and Technology on Near-Surface Detection Laboratory(No.TCGZ2015A005)State Key Laboratory of Precision Measuring Technology and Instruments(PIL1402)
文摘The 3D characteristic diagram of acoustically induced surface vibration was employed to study the influence of different buried landmines on the acoustic detection signal. By using the vehicular experimental system for acoustic landmine detection and the method of scanning detection, the 3D characteristic diagrams of surface vibration were measured when different objects were buried underground, including big plastic landmine, small plastic landmine, big metal landmine and bricks. The results show that, under the given conditions, the surface vibration amplitudes of big plastic landmine, big metal landmine, small plastic landmine and bricks decrease in turn. The 3D characteristic diagrams of surface vibration can be used to further identify the locations of buried landmines.
基金provided by the National Natural Science Foundation of China (51378504)Funding Project of Traffic Science and Technology Program of Hunan Province (201022)
文摘To systematically study the vehicle-bridge coupled dynamic response and its change rule with different parameters, a vehicle model with seven degrees of freedom was built and the total potential energy of vehicle space vibration system was deduced. Considering the stimulation of road roughness, the dynamic response equation of vehicle-bridge coupled system was established in accordance with the elastic system principle of total potential energy with stationary value and the ＂set-in-right-position＂ rule. On the basis of the self-compiled Fortran program and bridge engineering, the dynamic response of long- span continuous girder bridge under vehicle load was studied. This study also included the calculation of vehicle impact coefficient, evaluation of vibration comfort, and analysis of dynamic response parameters. Results show the impact coefficient changes with lane number and is larger than the value calculated by the ＂general code for design of highway bridges and culverts （China）＂. The Dieckmann index of bridge vibration is also related to lane number, and the vibration comfort evaluation is good in normal conditions. The relevant conclusions from parametric analyses have practical significance to dynamic design and daily operation of long-span continuous girder bridges in expressways. Safety and comfort are expected to improve significantly with further control of the vibration of vehicle-bridge system.
基金supported by the National Natural Science Foundation of China(No.11902182)the Program of Shanghai Academic/Technology Research Leader of China(No.19XD1421600)+2 种基金the China Postdoctoral Science Foundation(No.2019M651485)the Natural Science Foundation of Shandong Province of China(No.ZR2019BA001)the Natural Science Foundation of Tianjin of China(No.20JCQNJC01070)。
文摘The nonlinear modal coupling in a T-shaped piezoelectric resonator,when the former two natural frequencies are away from 1:2,is studied.Experimentally sweeping up the exciting frequency shows that the horizontal beam exhibits a nonlinear hardening behavior.The first primary resonance of the vertical beam,owing to modal coupling,exhibits an abrupt amplitude increase,namely the Hopf bifurcation.The frequency comb phenomenon induced by modal coupling is measured experimentally.A Duffing-Mathieu coupled model is theoretically introduced to derive the conditions of the modal coupling and frequency comb phenomenon.The results demonstrate that the modal coupling results from nonlinear stiffness hardening and is strictly dependent on the loading range and sweeping form of the driving voltage and the frequency of the piezoelectric patches.
基金the National Natural Science Foundation of China(No.51109131)
文摘Because of propeller hydrodynamic influence, the shafting vibration is a coupled vibration which includes torsional, longitudinal and whirling vibrations. It is unsuitable to analyze different vibrations of propulsive shafting systems with development of shipbuilding technologies. To overcome the shortages of traditional marine standards, we establish a new numerical model of the shafting coupled vibration. And we put forward shafting coupled vibration calculation to ensure better reliability of main propulsion system. The shafting system is modeled into two sub-systems, a continuous one and a discrete one. Wave approach and transit matrix method are used to investigate displacement and stress fields in continuous and discrete sub-systems, respectively. And vibrations of different modes in both sub-systems are coupled by using dynamic equilibrium and continuity condition to deduce the global equations governing the motion of shafting. The coupling calculation is then used to research the reason of a very large crude carrier(VLCC) stern hull vibration. It is shown by the comparison of the results from both coupling and dependent vibration calculations that vibration in deferent directions will cause deformation in the same mode, which leads to extra stress and displacements on shafting, especially as the resonant frequencies of different vibration modes match each other. This is helpful to prevent ship stern vibration due to poor shafting vibration calculation.
