Dynamic stability of axially accelerating viscoelastic plates with longitudinally varying tensions

doi:10.1007/s10483-016-2146-8

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (12): 1647-1668.doi: https://doi.org/10.1007/s10483-016-2146-8

Dynamic stability of axially accelerating viscoelastic plates with longitudinally varying tensions

Youqi TANG¹, Dengbo ZHANG¹, Mohan RUI², Xin WANG¹, Dicheng ZHU¹

1. School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418, China;
2. Third Maintenance Squadron, People's Liberation Army 93256 Troops, Shenyang 110034, China

收稿日期:2016-03-07 修回日期:2016-05-01 出版日期:2016-12-01 发布日期:2016-12-01
通讯作者: Youqi TANG E-mail:tangyouqi2000@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11672186, 11502147, and 11602146), the Chen Guang Project supported by the Shanghai Municipal Education Commission and the Shanghai Education Development Foundation (No. 14CG57), the Training Scheme for the Youth Teachers of Higher Education of Shanghai (No. ZZyyy12035), and the Alliance Program (No.LM201663)

Dynamic stability of axially accelerating viscoelastic plates with longitudinally varying tensions

Youqi TANG¹, Dengbo ZHANG¹, Mohan RUI², Xin WANG¹, Dicheng ZHU¹

1. School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418, China;
2. Third Maintenance Squadron, People's Liberation Army 93256 Troops, Shenyang 110034, China

Received:2016-03-07 Revised:2016-05-01 Online:2016-12-01 Published:2016-12-01
Contact: Youqi TANG E-mail:tangyouqi2000@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11672186, 11502147, and 11602146), the Chen Guang Project supported by the Shanghai Municipal Education Commission and the Shanghai Education Development Foundation (No. 14CG57), the Training Scheme for the Youth Teachers of Higher Education of Shanghai (No. ZZyyy12035), and the Alliance Program (No.LM201663)

摘要/Abstract

摘要：

The dynamic stability of axially accelerating plates is investigated. Longitudinally varying tensions due to the acceleration and nonhomogeneous boundary conditions are highlighted. A model of the plate combined with viscoelasticity is applied. In the viscoelastic constitutive relationship, the material derivative is used to take the place of the partial time derivative. Analytical and numerical methods are used to investigate summation and principal parametric resonances, respectively. By use of linear models for the transverse behavior in the small displacement regime, the plate is confined by a viscous damping force. The generalized Hamilton principle is used to derive the governing equations, the initial conditions, and the boundary conditions of the coupled planar vibration. The solvability conditions are established by directly using the method of multiple scales. The Routh-Hurwitz criterion is used to obtain the necessary and sufficient condition of the stability. Numerical examples are given to show the effects of related parameters on the stability boundaries. The validity of longitudinally varying tensions and nonhomogeneous boundary conditions is highlighted by comparing the results of the method of multiple scales with those of a differential quadrature scheme.

关键词: longitudinally varying tension, parametric resonance, axially moving plate, nonhomogeneous boundary condition

Abstract:

Key words: nonhomogeneous boundary condition, axially moving plate, longitudinally varying tension, parametric resonance

中图分类号:

70J40

Youqi TANG, Dengbo ZHANG, Mohan RUI, Xin WANG, Dicheng ZHU. Dynamic stability of axially accelerating viscoelastic plates with longitudinally varying tensions[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(12): 1647-1668.

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Dynamic stability of axially accelerating viscoelastic plates with longitudinally varying tensions

Dynamic stability of axially accelerating viscoelastic plates with longitudinally varying tensions

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