This paper presents a study on nonlinear vibration of inhomogeneous functional plates composed of sigmoid graded metalceramic materials. The material properties vary continuously along the thickness direction accordin...This paper presents a study on nonlinear vibration of inhomogeneous functional plates composed of sigmoid graded metalceramic materials. The material properties vary continuously along the thickness direction according to a sigmoid distribution rule, which is defined by piecewise functions to ensure smooth distribution of stress among all the interfaces. The geometric nonlinearity is considered by adopting the von Kármán geometrical relations. Based on the d'Alembert's principle, the nonlinear out-of-plane equation of motion of the plates is developed. The Galerkin method is employed to discretize the motion equation to a series of ordinary differential ones, which are subsequently analyzed via the use of the method of harmonic balance. Then, the analytical results are validated by the comparison to numerical solutions, which are obtained by using the adaptive step-size fourth-order Runge-Kutta method. The stability of the steady-state response is examined by the perturbation technique. Results show the first and third modes are both activated while the second mode is not activated for the plates under harmonic point excitation. The frequency response relationships of activated modes exhibit very complicated curves due to the nonlinear modal interaction. In addition, influences of key system parameters on nonlinear vibrational characteristics of the present inhomogeneous plates are illustrated.展开更多
Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material （S-FGM） plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along th...Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material （S-FGM） plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along the thickness direction. Based on the D＇Alembert＇s principle, a nonlinear equation of motion is derived for the moving S-FGM plates, where the von K^rm^n nonlinear plate theory is adopted. Utilizing the Galerkin method, the equation of motion is discretized and solved via the method of harmonic bal- ance. The approximate analytical solutions are validated through the adaptive step-size fourth-order Runge-Kutta method. Besides, the stability of the steady-state solutions is examined. The results reveal that the mode interaction behavior can happen between the first two modes of the moving S-FGM plates, leading to a complex nonlinear frequency response. It is further found that the power-law index, the longitudinal speed, the exci- tation amplitude, and the in-plane pretension force can significantly affect the nonlinear frequency-response characteristics of longitudinally traveling S-FGM plates.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11672071,11302046 and 11672072)the Fundamental Research Funds for the Central Universities(Grant No N170504023)
文摘This paper presents a study on nonlinear vibration of inhomogeneous functional plates composed of sigmoid graded metalceramic materials. The material properties vary continuously along the thickness direction according to a sigmoid distribution rule, which is defined by piecewise functions to ensure smooth distribution of stress among all the interfaces. The geometric nonlinearity is considered by adopting the von Kármán geometrical relations. Based on the d'Alembert's principle, the nonlinear out-of-plane equation of motion of the plates is developed. The Galerkin method is employed to discretize the motion equation to a series of ordinary differential ones, which are subsequently analyzed via the use of the method of harmonic balance. Then, the analytical results are validated by the comparison to numerical solutions, which are obtained by using the adaptive step-size fourth-order Runge-Kutta method. The stability of the steady-state response is examined by the perturbation technique. Results show the first and third modes are both activated while the second mode is not activated for the plates under harmonic point excitation. The frequency response relationships of activated modes exhibit very complicated curves due to the nonlinear modal interaction. In addition, influences of key system parameters on nonlinear vibrational characteristics of the present inhomogeneous plates are illustrated.
基金supported by the National Natural Science Foundation of China(Nos.11672071,11302046,and 11672072)the Fundamental Research Funds for the Central Universities(No.N150504003)
文摘Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material （S-FGM） plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along the thickness direction. Based on the D＇Alembert＇s principle, a nonlinear equation of motion is derived for the moving S-FGM plates, where the von K^rm^n nonlinear plate theory is adopted. Utilizing the Galerkin method, the equation of motion is discretized and solved via the method of harmonic bal- ance. The approximate analytical solutions are validated through the adaptive step-size fourth-order Runge-Kutta method. Besides, the stability of the steady-state solutions is examined. The results reveal that the mode interaction behavior can happen between the first two modes of the moving S-FGM plates, leading to a complex nonlinear frequency response. It is further found that the power-law index, the longitudinal speed, the exci- tation amplitude, and the in-plane pretension force can significantly affect the nonlinear frequency-response characteristics of longitudinally traveling S-FGM plates.
