黏弹夹芯板的有限元建模及实验研究

从有限元分析和数值模拟及实验验证的角度研究了黏弹夹芯板的频率依赖振动特性。夹芯板中间层为黏弹性材料，其刚度和阻尼的频率依赖性行为直接影响系统的模态频率和阻尼，并导致振动模式求解的复杂化。采用三阶七参数Biot模型描述黏弹性材料频率相关的黏弹性行为。开发了三层四节点28自由度的夹芯板单元，基于经典板理论和哈密顿原理建立了黏弹夹芯板的有限元动力学方程。通过引入辅助耗散坐标，将Biot模型和黏弹夹芯板的有限元动力学模型结合起来，并将其转化为常规二阶线性系统形式，极大简化了求解非线性振动特性的过程。对一边固定、另三边自由的黏弹夹芯板进行了前三阶固有频率和损耗因子的预测，并与实验结果对比。数值模拟结果和实验结果吻合良好，说明所提有限元方法是正确有效的。

Finite element modeling and experimental study of viscoelastic sandwich plate

The frequency-dependent viscoelastic characteristics of sandwich plates are investigated from finite element analysis,numerical simulation and experimental validation.The core layer of the sandwich plate is a viscoelastic material.The frequency-dependent behavior of the stiffness and damping directly affects the modal frequency and damping of the plate system,and results in complex vibration modes.A third-order seven-parameter Biot model is used to describe the frequency-dependent viscoelastic behavior of viscoelastic materials.A type of three-layer,four-node,and 28-degree-of-freedom sandwich plate element is developed for the sandwich plate structures.Based on the classical plate theory and the Hamiltonian principle,the finite element dynamic equations of the viscoelastic sandwich plates is established.By introducing auxiliary dissipative coordinates,the Biot model and the finite element dynamics model of the viscoelastic sandwich plate are combined,and then converted into a conventional second-order linear system form,which greatly simplifies the process of solving nonlinear vibration characteristics.The first three orders of natural frequency and loss factor are predicted for a viscoelastic sandwich cantilever plate structure,and the numerical simulation results are compared with the experimental results.The results show that they are very close to each other,which illustrates and proves the computational efficiency and accuracy of the finite element model presented here.