粘弹性复合材料层合板壳的动力稳定性分析

Dynamic instability of viscoelastic cross-ply laminated plates and circular cylindrical shells

分析面内周期激励下粘弹性层合平板以及轴向周期荷载作用下粘弹性层合圆柱壳的动力稳定性。设粘弹性复合材料服从Boltzmann积分型本构关系,其松弛模量由Prony-Dirichlet级数表示,基于薄板与薄壳理论,分别得到对称正交铺设层合板与层合圆柱壳的微分-积分型动力学方程,并应用谐波平衡法直接求解,忽略积分运算所产生的衰减项,导出确定动力不稳定区域边界的特征方程。分析结果表明,主要动力不稳定区域的缩小与材料的粘性参数以及结构横向振动的基频密切相关。

In this paper, the dynamic instability for viscoelastic laminated plates subjected to in-plane harmonic excitations, and cylindrical shells under axially harmonic loads are investigated. Boltzmann hereditary constitutive relation is used to model the viscoelastic behavior of fiber-reinforced composite materials and the relaxation modulus are expressed in the form of Prony-Dirichlet series. The integro-differential Mathieu equation of motion is obtained on the basis of the theory of thin plates and thin shells. An approach is developed to determine the boundaries of principal dynamic instable regions by applying directly harmonic balance method to solve the integro-differential equations of motion, meanwhile the time-dependent decay items arisen from the integration manipulation is neglected. This approximate method, that is shown to be very efficient, is then employed to analyze the dynamic stabilities of viscoelastic cross-ply plates and cylindrical shells. The results reveal that the shrink of principal dynamic unstable region is dependent on the magnitude of viscous parameters of materials and the natural frequencies of corresponding elastic laminated structures.