Effect of rotary inertia on stability of axially accelerating viscoelastic Rayleigh beams  

作　　者：Bo WANG 

机构地区：[1]School of Mechanical Engineering,Shanghai Institute of Technology,Shanghai 201418,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2018年第5期717-732,共16页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11202136,11372195,11502147,and 11602146)

摘　　要：The dynamic stability of axially moving viscoelastic Rayleigh beams is pre- sented. The governing equation and simple support boundary condition are derived with the extended Hamilton＇s principle. The viscoelastic material of the beams is described as the Kelvin constitutive relationship involving the total time derivative. The axial tension is considered to vary longitudinally. The natural frequencies and solvability condition are obtained in the multi-scale process. It is of interest to investigate the summation parametric resonance and principal parametric resonance by using the Routh-Hurwitz criterion to obtain the stability condition. Numerical examples show the effects of viscos- ity coefficients, mean speed, beam stiffness, and rotary inertia factor on the summation parametric resonance and principle parametric resonance. The differential quadrature method （DQM） is used to validate the value of the stability boundary in the principle parametric resonance for the first two modes.The dynamic stability of axially moving viscoelastic Rayleigh beams is pre- sented. The governing equation and simple support boundary condition are derived with the extended Hamilton＇s principle. The viscoelastic material of the beams is described as the Kelvin constitutive relationship involving the total time derivative. The axial tension is considered to vary longitudinally. The natural frequencies and solvability condition are obtained in the multi-scale process. It is of interest to investigate the summation parametric resonance and principal parametric resonance by using the Routh-Hurwitz criterion to obtain the stability condition. Numerical examples show the effects of viscos- ity coefficients, mean speed, beam stiffness, and rotary inertia factor on the summation parametric resonance and principle parametric resonance. The differential quadrature method （DQM） is used to validate the value of the stability boundary in the principle parametric resonance for the first two modes.

关 键 词：axially moving Rayleigh beam extended Hamilton＇s principle parametric resonance differential quadrature method （DQM） 

分 类 号：O342[理学—固体力学]