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

doi:10.1007/s10483-017-2277-9

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (11): 1533-1550.doi: https://doi.org/10.1007/s10483-017-2277-9

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

Yanqing WANG¹, J. W. ZU²

1. Department of Mechanics, Northeastern University, Shenyang 110819, China;
2. Department of Mechanical and Industrial Engineering, University of Toronto, Toronto M5S 3G8, Canada

收稿日期:2017-02-20 修回日期:2017-05-10 出版日期:2017-11-01 发布日期:2017-11-01
通讯作者: Yanqing WANG,E-mail:wangyanqing@mail.neu.edu.cn E-mail:wangyanqing@mail.neu.edu.cn
基金资助:
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)

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

Yanqing WANG¹, J. W. ZU²

1. Department of Mechanics, Northeastern University, Shenyang 110819, China;
2. Department of Mechanical and Industrial Engineering, University of Toronto, Toronto M5S 3G8, Canada

Received:2017-02-20 Revised:2017-05-10 Online:2017-11-01 Published:2017-11-01
Contact: Yanqing WANG E-mail:wangyanqing@mail.neu.edu.cn
Supported by:
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)

摘要/Abstract

摘要：

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.

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

Abstract:

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

中图分类号:

74H45

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

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

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

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