粘弹性复合材料夹芯板稳态响应分析

Steady response analysis for a composite sandwich plate with viscoelastic core layer based on Kelvin model

芯材用Kelvin粘弹性本构模型,推导复合材料夹芯板的动力学方程;运用模态正交原理,以Navier完备解形式求解四边简支正交对称铺层层合板稳态响应;给出固有频率和结构损耗因子的解析解。通过固有频率有限元解对比验证数值计算的可靠性。分析芯材剪切模量与芯材厚度对结构固有频率及损耗因子影响。探讨稳态响应的收敛性,得到结构稳态响应振幅与频率的关系。分析芯材损耗因子对结构稳态响应影响。结果表明,芯材剪切模量存在最佳设计值;结构首阶模态特性主导结构的稳态动态响应。

Considering Kelvin model as viscoelastic core constitutive property, a set of dynamical equations were derived for a rectangular composite sandwich plate, the steady response of a composite sandwich plate with symmetric and orthotropic face layers under simply supported boundary conditions was obtained using Navier complete solution form and the modal orthogonal principle. The analytic solutions to its natural frequencies and modal loss factors were presented, the comparison of the natural frequencies with those using FEM verified the relizbility of the analytic model. The influences of shear modulus and thickness of the core on the dynamic characteristics of the composite sandwich plate were analyzed. The convergence of the steady response solution was discussed, and the relation between the steady response amplitude and frequency was acquired, the effect of the core loss factor on the response was analyzed. Results revealed that there is a design optimal value of the core material shear modulus ; the dynamic characteristics of the first mode of the plate dominate the steady response of the structure.