粘弹层合板的稳态振动和层间应力

应用混合分层理论和Ressiner混合变分原理，在板厚方向取二次位移插值函数和三次、四次横向应力插值函数推导出粘弹层合板的动力学方程，得出简支粘弹层合板稳态振动的解。不仅得出与三层弹性板精确的自振频率吻合良好的解，而且对于粘弹层合板，所计算的自振频率和结构损耗因子也与三维结果吻合较好。计算了自由阻尼层合板对应的低阶法向位移响应幅值和层问横向应力的幅值。结果表明，较高的层间横向正应力是低频稳态振动中引起粘弹层合板分层破坏的主要因素，采用适当模量和厚度的粘弹性材料将有效地降低粘弹层合板的层间横向正应力的幅值。

The Steady State Vibration and Interlaminar Stresses of Viscoelastic Laminated Plates

Applying the mixed layerwise theories and Ressiner's mixed variational theorem, adopting quadratic functions for displacement and three-order or four-order functions for transverse stresses in the plate-thickness direction, the dynamics equations of viscoelastic laminated plates are deduced and the numerical solutions for simple-support laminated plates are derived through Navier solutions. The predicted vibration frequency and loss factor show the good agreement with the three-dimensional observations for the laminated plates. Computing the radial displacement max-value and interlaminar transverse stress max-value in the plates corresponding to the lower-rank models and analyzing the viscoelastic layer' influence on the interlaminar transverse stresses, the results show that very high interlaminar transverse normal stresses are the main factor which leads to the break of laminates for the Laminated plates in the low frequency steady state response, moreover, using a viscoelastic layer of proper module and thickness will effectively decrease the max-value of interlaminar transverse normal stresses.