一种基于谱元法的层合板SEA参数计算方法

A SFEM-based algorithm for computing SEA parameters of laminated plates

针对一般层合板统计能量分析(SEA)参数获取困难问题,建立了一种基于谱元法(SFEM)的SEA参数计算方法。采用三节点二次谱单元在层合板厚度方向进行网格划分,通过刚度矩阵与质量矩阵建立波数的特征方程;根据模态相似原则,利用皮尔逊相关系数对各阶模态的波数进行分类,进而获得层合板的模态密度、辐射效率等SEA参数。对单层薄板和三明治夹芯板进行了数值模拟研究,计算结果与其他理论值或实验值进行对比,验证了该方法的有效性,并以五层碳-碳正交各向异性板为例,考察了经典层合板理论和一阶剪切理论的分析偏差。最后计算了汽车玻璃层合板的内损耗因子,验证了基于SFEM计算层合板内损耗因子的有效性。

Aiming at the problem of difficult to acquire common laminated plates’SEA parameters,an effective algorithm based on the spectral finite element method(SFEM)for SEA parameters computation was proposed.The 3-node quadratic spectral finite element was used to divide grids in thickness direction of a laminated plate,and the characteristic equation of wave number was established by using the plate’s stiffness and mass matrices.According to the modal similarity criterion,Pearson correlation coefficient was used to classify various modes’wave numbers to gain the laminated plate’s SEA parameters,such as,modal densities and radiation efficiencies.Numerical simulation was performed for single-layer thin plates and sandwich ones.The computation results were compared with other theoretical values or test ones to verify the effectiveness of the proposed method.A five-layer C-C orthotropic laminated plate was taken as an example to investigate analysis deviations of the classical laminate plate theory and the first-order shear theory.Finally,the internal loss factor of automobile glass laminated plate was calculated to verify the effectiveness of calculating laminated plate’s internal loss factor based on SFEM.