轴向变速黏弹性Poynting-Thompson梁参数共振稳定性

本文研究了轴向变速黏弹性梁的组合参数共振和主参数共振稳定性．梁的材料黏弹性本构关系由Poynting-Thompson模型描述．使用多尺度法渐近展开求解，导出了其可解性条件．根据Routh-Hurwitz准则给出了组合参数共振和主参数共振稳定性条件．考虑Poynting-Thompson模型退化到Kelvin-Voigt模型的情况．通过数值算例对两个模型进行了失稳边界的比较．

Stability on Parametric Resonance of Axially Accelerating Viscoelastic Poynting-Thompson Beams

This paper investigates the stabilities of axially accelerating viscoelastic beams in summation parametric resonance and principal parametric resonance. The constitutive relation of beam is described by Poynting-Thompson model. The method of multiple scales is used to solve the governing equation. Then, the solvability condition is derived. In view of Routh-Hurwitz criterion, the stability conditions in summation parametric resonance and principal parametric resonance are obtained. The situation of Poynting-Thompson model reduced to Kelvin-Voigt model is discussed. Numerical examples compare the two models in terms of the unstable boundary condition.