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

Yanqing Wang, J. W. Zu

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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 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.

Original languageEnglish
Pages (from-to)1533-1550
Number of pages18
JournalApplied Mathematics and Mechanics (English Edition)
Volume38
Issue number11
DOIs
StatePublished - 1 Nov 2017

Keywords

  • frequency response
  • method of harmonic balance
  • moving
  • nonlinear oscillation
  • sigmoid functionally graded material (S-FGM) plate

Fingerprint

Dive into the research topics of 'Nonlinear oscillations of sigmoid functionally graded material plates moving in longitudinal direction'. Together they form a unique fingerprint.

Cite this