粘弹性复合材料夹芯板的稳态响应分析

芯材采用Kelvin粘弹性本构模型，推导了复合材料夹芯板的动力学方程，运用模态正交原理，以Navier完备解形式求解了四边简支正交对称铺层层合板的稳态响应，并给出了固有频率和结构损耗因子的解析解。通过固有频率的有限元解对比验证了数值计算的可靠性。分析了芯材剪切模量和芯材厚度对结构固有频率和损耗因子的影响。探讨了稳态响应的收敛性，并得到结构稳态响应振幅与频率的关系，分析了芯材损耗因子对结构稳态响应的影响。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。

The steady state response analysis of the composite sandwich plate with viscoelastic core layer based on Kelvin model

Considering the viscoelastic core constitutive property as Kelvin model, a set of dynamical equations are derived for rectangular composite sandwich plate, the steady state response, for a composite sandwich plate with symmetric and orthotropic face layers under the simple support boundary condition, are obtained using Navier complete solution through the mode orthogonal principle. The analytic solutions of natural frequencies and mode loss factors are presented, the comparison of natural frequencies with FEM validates the analytic model. The influences of the shear modulus and thickness of the core on the dynamic performance of the composite sandwich plate are discussed. The astringency of steady state response of the solution is discussed, and the steady state response amplitudes at various frequency are acquired; the effect of the core loss factor on the response are analyzed. Result reveals that there is an optimal value of the design of the core material shear modulus；the steady state response is mostly determined by characteristics of the first mode.