Accurate modeling of PZT-induced Lamb wave propagation in structures by using a novel spectral finite element method

This paper presents the results of a computational and experimental validation exercise performed towards damage identification of a sagged rod with known damage by using the coupled axial–flexural wave interaction mechanics. Towards simulating the damage scenario in a sagged conductor made of steel wire rope, a prismatic steel rod is taken up for study. An initial axial wave, tangential to the curve of the arc, manifests as both axial and flexural waves as it propagates alongside the length of the rod. This interaction effect between axial and flexure wave propagation is studied in this paper. Impedance mismatch is made in the rod by changing its cross-sectional area along its length. Numerical simulations are implemented using the spectral finite element method with a combined axial and flexure effect. The concept of obtaining the exact spectral element dynamic stiffness matrix for a wave propagation analysis sagged rod is discussed. Computation is implemented in the Fourier domain using Fast Fourier Transform (FFT). In the time domain, post processing of the response is done, which is applicable in structural diagnostics in addition to the wave propagation problem. The predominant single-frequency-based amplitude-modulated, narrow-banded, burst wave propagation is found to be better matched if the elemental rod theory is replaced with a modified rod theory called the Love theory. The differences in the propagating waves allow identification of the damage location in a very clear-cut way. The methodology of the moving correlation coefficient is also successfully employed to detect the damage precisely. This fact is very encouraging for future work on structural health monitoring.

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

Volume 9: Mechanics of Solids, Structures and Fluids; NDE, Diagnosis, and Prognosis ◽

10.1115/imece2016-65366 ◽

2016 ◽

Author(s):

Hao Zuo ◽

Xuefeng Chen ◽

Zhibo Yang ◽

Laihao Yang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Wave Propagation ◽

Lamb Wave ◽

Structural Dynamic ◽

Mode Wave ◽

Wavelet Finite Element Method ◽

Wavelet Finite Element ◽

Lamb Wave Propagation ◽

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.

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