TY - JOUR
T1 - Nonlinear oscillations of sigmoid functionally graded material plates moving in longitudinal direction
AU - Wang, Yanqing
AU - Zu, J. W.
N1 - Publisher Copyright:
© 2017, Shanghai University and Springer-Verlag GmbH Germany.
PY - 2017/11/1
Y1 - 2017/11/1
N2 - 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´arm´an 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.
AB - 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´arm´an 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.
KW - frequency response
KW - method of harmonic balance
KW - moving
KW - nonlinear oscillation
KW - sigmoid functionally graded material (S-FGM) plate
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U2 - 10.1007/s10483-017-2277-9
DO - 10.1007/s10483-017-2277-9
M3 - Article
AN - SCOPUS:85028831127
SN - 0253-4827
VL - 38
SP - 1533
EP - 1550
JO - Applied Mathematics and Mechanics (English Edition)
JF - Applied Mathematics and Mechanics (English Edition)
IS - 11
ER -