轴向变速黏弹性Poynting-Thompson梁参数共振稳定性

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

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.

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.