Wave analysis in one dimensional structures with a wavelet finite element model and precise integration method

TL;DR

This paper introduces a combined wavelet finite element and precise integration method for efficient and accurate ultrasonic wave simulation and crack detection in one-dimensional structures.

Contribution

It presents a novel integration of B-Spline wavelet finite elements with precise time integration for improved ultrasonic wave simulation and crack identification in 1D structures.

Findings

Higher accuracy in spatial discretization with fewer elements.

Lower computational cost compared to traditional methods.

Successful crack detection in simulated structures.

Abstract

Numerical simulation of ultrasonic wave propagation provides an efficient tool for crack identification in structures, while it requires a high resolution and expensive time calculation cost in both time integration and spatial discretization. Wavelet finite element model provides a highorder finite element model and gives a higher accuracy on spatial discretization, B-Spline wavelet interval (BSWI) has been proved to be one of the most commonly used wavelet finite element model with the advantage of getting the same accuracy but with fewer element so that the calculation cost is much lower than traditional finite element method and other high-order element methods. Precise Integration Method provides a higher resolution in time integration and has been proved to be a stable time integration method with a much lower cut-off error for same and even smaller time step. In this paper, a wavelet finite element model combined with precise integration method is presented for the numerical simulation of ultrasonic wave propagation and crack identification in 1D structures. Firstly, the wavelet finite element based on BSWI is constructed for rod and beam structures. Then Precise Integrated Method is introduced with application for the wave propagation in 1D structures. Finally, numerical examples of ultrasonic wave propagation in rod and beam structures are conducted for verification. Moreover, crack identification in both rod and beam structures are studied based on the new model.