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

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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.

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Author information

Authors and Affiliations

  1. Department of Mechanics, Northeastern University, Shenyang, 110819, China

    Yanqing Wang

  2. Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, M5S 3G8, Canada

    J. W. Zu

Authors
  1. Yanqing Wang
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  2. J. W. Zu
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Correspondence to Yanqing Wang.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11672071, 11302046, and 11672072) and the Fundamental Research Funds for the Central Universities (No.N150504003)

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Wang, Y., Zu, J.W. Nonlinear oscillations of sigmoid functionally graded material plates moving in longitudinal direction. Appl. Math. Mech.-Engl. Ed. 38, 1533–1550 (2017). https://doi.org/10.1007/s10483-017-2277-9

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  • DOI: https://doi.org/10.1007/s10483-017-2277-9

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2010 Mathematics Subject Classification

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