含局部脱层的周期层合梁波传播特性研究

摘要

The wave propagation characteristic of a periodic simply-supported delaminated beam is investigated.The dynamic stiff-ness matrix of the undamaged periodic cell is firstly derived by employing Euler-Bernoulli beam theory and spectral finite element method.Then,considering the delamination located in one periodic cell of the periodic beam,a delamination model is developed with the plain section assumption for the cross-section of delamination edges and neglecting the effect of stress singularity at the delamination tip.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 balance condition at the delamination in-terface.After that,the complete model of delaminated periodic beam structures is established.Finally,a set of numerical simula-tions are carried out for investigating the wave propagation characteristic of a periodic simply-supported beam under the harmonic and disordered conditions,results show that the influence of delamination on the dynamic characteristics of periodic structures is significantand with some pattern.In addition,the finite element software ANSYS is utilized to verify the developed theoretical model with a single delamination.%为对含脱层的周期性简支层合梁的波传播特性进行研究，基于欧拉伯努利梁理论和谱有限元方法得到周期结构中完好基本周期单元的动刚度矩阵。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，进而形成含脱层的周期层合梁整体结构模型。分别对谐和条件与脱层引起失谐条件下一周期简支梁结构的波传播特性进行数值仿真研究，结果表明：脱层较显著改变了周期层合梁的动力特性，且具有一定的规律，同时采用ANSYS 有限元数值模型对本文含脱层理论模型进行验证。