Modeling of Lamb Wave Propagation in Beam-Like Structures via Wavelet Finite Element Method

Beam-like structure is known as one of crucial engineering structures in practical application of aerospace, vessel, civil and machinery. The damages have a great influence on machine performance and may cause a serious threat for security of mechanical structures and systems. Thus it is very significant to identify the damage of beam-like structures for security of mechanical structures and systems. This paper presents a novel application of wavelet finite element method (WFEM) in Lamb wave propagation of beam-like structures. The WFEM, adopting excellent B-spline wavelet on interval (BSWI) basis as approximating functions, has been verified to possess some superiorities for structural dynamic analysis and damage detection. The motion equations of Lamb wave propagation are derived according to Hamilton’s principle and two-dimensional wavelet-based element is constructed by adopting BSWI scaling functions. The damage, which is modeled as open crack with duplicate nodes, is considered in beam-like structures and corresponding damage model is also added in proposed wavelet finite element model. Then central difference method in time domain is employed for wave propagation simulation. Firstly, the validity and accuracy of proposed WFEM are demonstrated on a beam-like structure without crack by comparing with traditional finite element method (FEM) using 2D plane element. What’s more, the obtained velocities of fundamental S0 and A0 mode waves are also compared with Lamb theoretical results to verify the validity and accuracy of proposed model once more. Then the wave propagation in beam-like structures with crack are performed and the process and interaction between Lamb wave and damage are analyzed and discussed in detail. The reflected mode wave and converted mode wave for incident wave interacting with crack are also observed in wave motion snapshots. In summary, this paper presents an accurate but simple and effective numerical method for wave propagation of beam-like structures.