粘弹性结构动力稳定性分析的谐波平衡法

本文分析了线粘弹性结构的长期动力稳定特性。设材料具积分型本构关系，且其松弛模量能用Prony级数描述，将微分-积分型控制方程化成微分型方程，应用谐波平衡法确定动力稳定区域，着重讨论了材料参数及系统振动频率对动力稳定区域的影响发现该类粘弹性结构具有与一般阻尼系统不同的动力稳定特性。文中也将系统平衡法直接应用于微分-积分型控制方程，忽略卷积积分运算后产生的随时间衰减的非谐波项来得到决定动力稳定边界的特征方程，并对两种应用所得结果进行了比较。

Analysis of Dynamic Stability for Viscoelastic Structures with Harmonic Balance Method

The features of linear dynamic stability for viscoelastic structures under parametric excitations were investigated. Boltzman integral constitutive relationship was used to model the material behavior, and the relaxation modules were described in Prony series. After the conversion of governing equations from differential-integral type to ordinary differential type, the boundary equations to determine the dynamic unstable regions were derived by applying Harmonic Balance Method(HBM) corresponding to standard linear solid and five parametric solid. A detailed discussion for the effects of materials parameters and vibration frequencies on principal dynamic unstable regions was presented, also some features that are different from elastic sysem with damping were observed. A direct HBM application to original governing e-quation was proposed. The direct method was constructed by neglecting non-harmonic items decaying with time's increasing. The results of two types of HBM applications were compared. The latter method is potential to treat the case with multi-items in Prony series since without tedious converting.