局部缺陷周期简支层合梁结构的波传播特性分析

摘要

Delamination is one of the main types of damage for composite laminated structures .The dynamic stiffness matrix of the undamaged periodic cell of the periodic structure is firstly derived by employing both the Euler‐Bernoulli beam theory and spectral finite element method .Then ,considering the delamination is located in one periodic cell of the periodic beam and neg‐lecting the effect of stress singularity at the delamination tip ,a delamination model is developed with the plain section assump‐tion for the cross‐section of delamination edges .The super‐element dynamic stiffness matrix of delaminated periodic cell is formed by utilizing the continuous condition of displacement and rotation at the edge of each subelement as well as the force bal‐ance condition at the delamination interface .After that ,the transfer matrices of both healthy and delaminated periodic cells are formulated based on transfer matrix method ,and then the global transfer matrix as well as the global dynamic stiffness matrix is formulated .The propagation constants obtained from the transfer matrices are employed to investigate the wave propagation properties of the whole periodic structure .In addition ,for verification purpose ,a set of numerical simulations are carried out for investigating the wave propagation characteristics of a periodically simply‐supported beam under both the healthy and disor‐dered conditions .Furthermore ,the ANSYS software is also utilized to verify the proposed methodology .%脱层是复合材料层合结构最主要的破坏形式之一。基于Euler‐Bernoulli梁理论和谱有限元方法得到周期结构中健康基本周期单元的动刚度矩阵。再考虑脱层位于周期结构的某一基本周期单元中，并假设脱层边缘处横截面变形服从平截面假定，忽略脱层前沿的应力奇异，建立分层模型，根据分层边缘处各子单元位移、转角连续及分层界面处力平衡条件形成含脱层的周期层合梁超单元动刚度矩阵。基于传递矩阵法得到健康及含脱层周期单元的传递矩阵，进而形成含脱层周期层合梁结构的传递矩阵及总体动刚度矩阵，并通过传递矩阵计算获得的波传播常数来分析周期结构的振动与波传播特性。分别对无脱层情况与脱层引起局部失谐情况下一周期简支梁结构的波传播特性进行数值计算研究，并结合ANSYS有限元仿真分析，对方法进行了验证。