A spring element, based on spectral finite element method, was proposed to model the axial-flexural motion due to transverse crack and model the Lamb wave propagation in a composite beam. According to fractural mechanics, the stiffness of the spring was obtained and used to establish the deteriorated spectral finite element model of the composite cracked beam. Comparing with results from the conventional finite element method, the proposed model was verified to be effective and efficient. Formulations for calculating Lamb wave energy were derived in frequency domain, and the energy conservation at the crack location validates the proposed model. It is indicated that the change of the energy of Lamb wave modes versus the crack depth is monotonous, which may supply some practical foundations for quantitative crack identification in composite beams.%基于谱元法提出了一种弹簧元来模拟复合材料梁由于横向裂纹导致的轴弯耦合效应,分析复合材料裂纹梁中Lamb波的传播特性.由断裂力学的相关知识求得弹簧元的刚度,建立复合材料裂纹梁的损伤谱元模型.通过模拟复合材料裂纹梁内Lamb波传播,并和传统的有限元结果进行比较,验证了所提出模型的可行性和有效性.推导了频域内Lamb波各模态的能量计算公式,裂纹处的能量守恒证明了所提出模型的正确性,同时计算表明复合材料梁中裂纹处反射与透射的Lamb波各模态能量随着裂纹深度的变化规律具有单调性,结论可以为定量识别复合材料梁裂纹提供实用依据.
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