摘要
论文采用基于Layerwise离散层理论的有限元板单元建模粘弹性阻尼复合结构,发展了一种考虑粘弹性材料的频变特性的复合结构频率响应计算方法.该方法首先计算结构的质量矩阵和各个频率点下的结构复刚度矩阵,然后求解运动方程的若干阶复特征对并由此计算各阶模态的传递函数,最后将各模态传函线性叠加得到近似的总传函.为了提高计算效率,论文采用了一种高效的数值方法,即只计算若干频率点下的特征向量与特征值,并计算这些点处特征向量关于频率的高阶导数,通过泰勒系数展开逼近和Rayleigh商式,可求得附近若干频率点处的特征向量和特征值,从而避免了在各个频率点下求解大自由度结构特征方程的问题,可以极大地提高计算效率.对一端简支的三层约束阻尼梁算例进行了分析,并与文献中的结果作对比,结果验证了方法的有效性和计算效率.
This paper introduces an efficient frequency response analysis method for structures with frequency-dependent viscoelastic layers,making use of the complex mode superposition method.The structures are modeled with layerwsie 4-node shell element.First,the constant mass matrix and frequency-dependent stiffness matrix at each computational frequency are formed.Then,the complex eigenpair for the computational frequency can be determined from the complex eigenproblem,and each modal transfer function can be calculated as well.Finally,the total transfer function can be obtained bythe complex mode superposition method.To avoid the large computational requirements caused by the frequency dependence of the mechanical properties of the viscoelastic materials,the first and higher order eigenderivatives of the eigenvectors atcertain computational frequency are usedto update the complex eigenvalues and eigenvectors of the next several steps,by using Taylor's series and Rayleigh quotient.Finally,a sandwich cantilever beam application is presented,and the validation and the efficiency of the proposed method are discussed.
出处
《固体力学学报》
CAS
CSCD
北大核心
2015年第S1期105-110,共6页
Chinese Journal of Solid Mechanics
