High-Order B-spline approximation for solving time-dependent Timoshenko vibrating equations

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion Pub Date : 2025-02-21 DOI:10.1016/j.wavemoti.2025.103518

A. Ben-Abdellah , S. Belkouz , M. Addam

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引用次数: 0

Abstract

The aim of this work is to study the time-dependent coupled Timoshenko partial differential equations (PDEs) with mixed boundary conditions. These wave equations govern the beam displacements in the fields of structural mechanics and civil engineering. The modeling algorithm is implemented in two steps: Firstly, we transform the time-dependent coupled equations into coupled transverse vibrating equations depending on the frequency parameter and space variable. A Galerkin approximation built on Normalized Uniform Polynomial Spline (NUPS) basis functions is employed to compute the pairs of solutions that are the focus of this work. Secondly, we compute the Inverse Fourier Transform (IFT) solution using some quadrature. We also exhibit comparison results for the various calculations of IFT-integral solutions. The theoretical estimates are verified by several tests of Timoshenko wave equations with known analytical solutions. Numerous numerical experiments are presented to validate the numerical convergence rates, and a few examples are also included to demonstrate the high precision, the efficiency, and the outstanding resolution capabilities for both smooth and discontinuous solutions, as well as plots of the 3D beam’s field displacements.

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来源期刊

Wave Motion 物理-力学

CiteScore

4.10

自引率

8.30%

发文量

118

审稿时长

3 months

期刊介绍： Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.