Dynamic stability of axially accelerating viscoelastic plates with longitudinally varying tensions  

作　　者：Youqi TANG Dengbo ZHANG Mohan RUI Xin WANG Dicheng ZHU 

机构地区：[1]School of Mechanical Engineering,Shanghai Institute of Technology [2]Third Maintenance Squadron,People's Liberation Army 93256 Troops

出　　处：《Applied Mathematics and Mechanics(English Edition)》2016年第12期1647-1668,共22页应用数学和力学（英文版）

基　　金：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);the Alliance Program(No.LM201663)

摘　　要：The dynamic stability of axially accelerating plates is investigated. Longitudi- nally 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 govern- ing equations, the initial conditions, and the boundary conditions of the coupled planar vibration. The solvability conditions are established by directly using the method of mul- tiple 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.The dynamic stability of axially accelerating plates is investigated. Longitudi- nally 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 govern- ing equations, the initial conditions, and the boundary conditions of the coupled planar vibration. The solvability conditions are established by directly using the method of mul- tiple 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：parametric resonance axially moving plate longitudinally varying tension nonhomogeneous boundary condition 

分 类 号：O343[理学—固体力学]