Nonlinear oscillations of sigmoid functionally graded material plates moving in longitudinal direction

doi:10.1007/s10483-017-2277-9

Abstract

Abstract:

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 Kármán nonlinear plate theory is adopted. Utilizing the Galerkin method, the equation of motion is discretized and solved via the method of harmonic balance. 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 excitation amplitude, and the in-plane pretension force can significantly affect the nonlinear frequency-response characteristics of longitudinally traveling S-FGM plates.

Key words: bituminous pavement, temperature field, solar radiation, thermal conduction, moving, frequency response, method of harmonic balance, sigmoid functionally graded material (S-FGM) plate, nonlinear oscillation

2010 MSC Number:

74H45

Yanqing WANG, J. W. ZU. Nonlinear oscillations of sigmoid functionally graded material plates moving in longitudinal direction. Applied Mathematics and Mechanics (English Edition), 2017, 38(11): 1533-1550.

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