In this paper,vibration analysis of functionally graded porous beams is carried out using the third-order shear deformation theory.The beams have uniform and non-uniform porosity distributions across their thickness a...In this paper,vibration analysis of functionally graded porous beams is carried out using the third-order shear deformation theory.The beams have uniform and non-uniform porosity distributions across their thickness and both ends are supported by rotational and translational springs.The material properties of the beams such as elastic moduli and mass density can be related to the porosity and mass coefficient utilizing the typical mechanical features of open-cell metal foams.The Chebyshev collocation method is applied to solve the governing equations derived from Hamilton's principle,which is used in order to obtain the accurate natural frequencies for the vibration problem of beams with various general and elastic boundary conditions.Based on the numerical experiments,it is revealed that the natural frequencies of the beams with asymmetric and non-uniform porosity distributions are higher than those of other beams with uniform and symmetric porosity distributions.展开更多
In this paper,a new technique for analysing functionally graded material(FGM)beams using the Chebyshev polynomials and Lagrange multipliers with various beam theories is presented.By utilizing the inner products and t...In this paper,a new technique for analysing functionally graded material(FGM)beams using the Chebyshev polynomials and Lagrange multipliers with various beam theories is presented.By utilizing the inner products and the Chebyshev polynomials’orthogonality properties incorporated with Lagrange multipliers,we can combine the governing equation and boundary conditions to yield the matrix equations with explicit weighting coefficients.Numerical examples are provided for vibration analysis of various beam theories and assumptions.Based on numerical evaluations,it is revealed that the proposed technique can efficiently achieve good agreement with those of the references.展开更多
This research work deals with a study on dynamic behavior of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)beams under various types of dynamic loads.Carbon nanotubes(CNTs)are used as the reinforci...This research work deals with a study on dynamic behavior of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)beams under various types of dynamic loads.Carbon nanotubes(CNTs)are used as the reinforcing materials that distribute continuously across the beam thickness.By using third order shear deformable theory(TSDT)in this current study,the straightness and normality of the transverse normal after deformation are unconstrained.The equations of motion based on TSDT are solved by Gram-Schmidt-Ritz method in which the displacement functions are generated via Gram-Schmidt procedure.Additionally,the time-integration of Newmark is also employed to carry out dynamic response of the beams under dynamic loads.Several effects such as material distributions,types of dynamic loads,boundary conditions and so on are taken into account.According to numerical results,it can be revealed that adding small amount of CNTs can reduce considerably the dynamic amplitude of FG-CNTRC beams.Moreover,the dynamic analysis of beam-like structures plays an important role in structural design because mass inertia matrix of the beam being involved in the equations of motion,which yields much larger deflection than that predicted by simple static analysis.展开更多
文摘In this paper,vibration analysis of functionally graded porous beams is carried out using the third-order shear deformation theory.The beams have uniform and non-uniform porosity distributions across their thickness and both ends are supported by rotational and translational springs.The material properties of the beams such as elastic moduli and mass density can be related to the porosity and mass coefficient utilizing the typical mechanical features of open-cell metal foams.The Chebyshev collocation method is applied to solve the governing equations derived from Hamilton's principle,which is used in order to obtain the accurate natural frequencies for the vibration problem of beams with various general and elastic boundary conditions.Based on the numerical experiments,it is revealed that the natural frequencies of the beams with asymmetric and non-uniform porosity distributions are higher than those of other beams with uniform and symmetric porosity distributions.
基金support from King Mongkut’s University of Technology North Bangkok(KMUTNB-60-ART-025).
文摘In this paper,a new technique for analysing functionally graded material(FGM)beams using the Chebyshev polynomials and Lagrange multipliers with various beam theories is presented.By utilizing the inner products and the Chebyshev polynomials’orthogonality properties incorporated with Lagrange multipliers,we can combine the governing equation and boundary conditions to yield the matrix equations with explicit weighting coefficients.Numerical examples are provided for vibration analysis of various beam theories and assumptions.Based on numerical evaluations,it is revealed that the proposed technique can efficiently achieve good agreement with those of the references.
基金supported by the New Strategic Research(P2P)project(phase 2),Walailak University,Thailand.
文摘This research work deals with a study on dynamic behavior of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)beams under various types of dynamic loads.Carbon nanotubes(CNTs)are used as the reinforcing materials that distribute continuously across the beam thickness.By using third order shear deformable theory(TSDT)in this current study,the straightness and normality of the transverse normal after deformation are unconstrained.The equations of motion based on TSDT are solved by Gram-Schmidt-Ritz method in which the displacement functions are generated via Gram-Schmidt procedure.Additionally,the time-integration of Newmark is also employed to carry out dynamic response of the beams under dynamic loads.Several effects such as material distributions,types of dynamic loads,boundary conditions and so on are taken into account.According to numerical results,it can be revealed that adding small amount of CNTs can reduce considerably the dynamic amplitude of FG-CNTRC beams.Moreover,the dynamic analysis of beam-like structures plays an important role in structural design because mass inertia matrix of the beam being involved in the equations of motion,which yields much larger deflection than that predicted by simple static analysis.
