Analysis of Wave Propagation in Beams With Transverse and Lateral Cracks Using a Weakly Formulated Spectral Method
Analysis of Wave Propagation in Beams With Transverse and Lateral Cracks Using a Weakly Formulated Spectral Method
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DOI：
10.1115/1.2188015
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
N. Hu;H. Fukunaga;M. Kameyama;D. Mahapatra;S. Gopalakrishnan
中科院分区：
文献类型：
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作者：
N. Hu;H. Fukunaga;M. Kameyama;D. Mahapatra;S. Gopalakrishnan
本文提出了一种新的基于全局-局部混合谱单元(HSE)方法的数值方法，用于研究含有横向和横向裂纹损伤的梁中的波传播。外场或远场区域采用普通谱单元法模拟，而内部含损伤区域采用一种新型单元(HSE)模拟。为了建立这种有效的损伤区域新单元，首先，利用一阶剪切变形理论明确地确定弯曲波数和剪切波数。然后，在基于位移的有限元背景下，这些位于两个相互垂直的二维弹性动力学方向之一的波模被用来丰富拉格朗日插值函数。然后通过频域中的弱形式推导出平衡方程。通过粗略的离散化，可以用这种方式精确地形成频率相关的刚度和质量矩阵。该方法利用了(I)一维波传播的强形式和(Ii)可离散复杂几何的弱形式的优点。通过数值验证，验证了该方法的有效性。最后，用该方法研究了含多个横向裂纹和横向裂纹的梁中波的传播行为。
In this paper, a novel numerical technique based on the global-local hybrid spectral element (HSE) method is proposed to study wave propagation in beams containing damages in the form of transverse and lateral cracks. The ordinary spectral element method is employed to model the exterior or far field regions, while a new type of element (HSE) is constructed to model the interior region containing damages. To develop this efficient new element for the damaged area, first, the flexural and the shear wave numbers are explicitly determined using the first-order shear deformation theory. These wave modes, in one of the two mutually orthogonal directions for two-dimensional transient elastodynamics, are then used to enrich the Lagrangian interpolation functions in context of displacement-based finite element. The equilibrium equation is then derived through the weak form in the frequency domain. Frequency-dependent stiffness and mass matrices can be accurately formed in this manner with a coarse discretization. The proposed method takes the advantage of using (i) a strong form for one-dimensional wave propagation and also (ii) a weak form by which a complex geometry can be discretized. Numerical verification is carried out to illustrate the effectiveness of the method. Finally, this method is employed to investigate the behaviors of wave propagation in beams containing various types of damages, such as multiple transverse cracks and lateral cracks.