LAMB WAVE PROPAGATION IN A CRACKED BEAM USING SPECTRAL FINITE ELEMENT METHOD

A massless spring, coupling the longitudinal and rotational vibration, is proposed to model the transverse crack and to analyze wave propagation in a cracked beam, based on a spectral finite element method. The stiffness of the spring is obtained from Castigliano’s theorem and laws of fracture mechanics. The spring is used to establish force equilibrium and displacement compatibility conditions, by which a cracked spectral finite element model is developed. Compared with the conventional finite element method, the proposed model is proved to obviously improve calculation efficiency and have high accuracy in modal analysis and Lamb wave propagation. Power reflection and transmission are demonstrated to meet with an energy conservation law. Energy of Lamb wave modes varying with the crack depth is also calculated and changes monotonously, which may provide some practical foundations for the quantitative crack identification in structural health monitoring.