基于有效三维损耗矩阵的复合材料层合板模态阻尼预测

为了在复合材料层合板阻尼分析中既考虑层合板厚度方向应力、应变对结构阻尼的贡献，又不增加厚度方向的单元数量，基于复合材料的有效三维阻尼矩阵预报理论，建立了新的高效复合材料结构模态阻尼的三维有限元预测方法。沿层合板厚度方向将原结构分成若干亚层，每一亚层包含若干单层。根据合成理论计算每一亚层的刚度矩阵、柔度矩阵和有效三维阻尼损耗矩阵。对亚层划分单元，进行结构的有限元模态分析。根据模态分析结果，利用有效三维阻尼矩阵求出各个模态对应的模态阻尼。利用该理论，分别计算了单向层合板、对称层合板以及厚板的结构模态阻尼。数值计算结果表明，该方法具有很好的适用性，其优点在于既考虑了板厚方向的阻尼贡献，又减少了厚度方向的单元数，提高了计算的准确性和效率。 

FRP laminates modal damping prediction based on 3-D effective damping matrix

Considering the contribution of out-of-plane stresses and strains to laminate structural modal damping in FEM with fewer elements in the thickness direction，a composite structural modal damping prediction theory is presented based on the 3-D effective damping matrix. The composite structure was divided into several sub laminates along the thickness，and each sub laminate contains many laminas. These sub laminates'stiffness matrices，compliance matrices and 3-D effective damping matrices were calculated by the synthesizing theory. The finite elements were generated with these sub laminates，and a structural modal analysis was executed. Combining the 3-D effective damping matrices and the results of the modal analysis，specific damping capacities for each modal were calculated. The presented method is validated by the calculations for structural specific damping capacities of unidirectional laminates，symmetrical laminates and thick laminates. This method combines the accuracy and efficiency with the consideration of the contribution of out-of-plane stresses and strains.