提出了一种计算纤维增强复合材料粘弹性阻尼和能耗的新方法.在层片的层次上,基于各向异性粘弹性理论导出以阻尼矩阵表示的材料能耗计算公式.在层板的层次上由能量等效原理得到有效阻尼矩阵.由此,可由层板的有效应力和有效应变计算出其能量耗散进而得到比阻尼.其中的关键点是有效阻尼矩阵的推导,最终得到的有效阻尼矩阵是各单层阻尼系数、体积分数、刚度系数以及层合板有效刚度系数的函数.用有效阻尼矩阵计算能耗可以适用于任意复合材料的应力应变状态,这对于粘弹性复合材料结构能耗的数值分析尤其重要.最后将该理论应用于几种情况下的复合材料的能耗和比阻尼分析,算例表明与其它的理论预测和试验相比吻合良好,证实了该方法的合理性.
A new method for calculating viscoelastic damping and energy loss of fiber composites is presented. Firstly, on the scale of lamina, the energy dissipation formula is obtained by using a damping matrix and the theory of linear anisotropic viscoelasticity. Then on the scale of laminate, an effective damping(loss) matrix is obtained by using an equivalent energy theory (including stored energy and dissipated energy). In terms of the effective damping matrix, the energy loss and specific damping of the laminate can be calculated by using the effective stress and effective strain. The key point is the derivation of the effective damping matrix, which is a function of damping coefficients, volume fraction, and stiffness coefficients of each lamina and the effective stiffness coefficients of the laminate. In this way, the energy loss of fiber composites under arbitrary loading can be computed, which is very important in the numerical analysis for viscoelastic material and structures. In the end, several numerical examples are given to show the reasonability of the model.
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