Distributional Green’s functions for the vibrations of multi-cracked Timoshenko beams

IF 3.4 2区物理与天体物理 Q1 ACOUSTICS

Applied Acoustics Pub Date : 2024-09-30 DOI:10.1016/j.apacoust.2024.110302

Ilaria Fiore, Francesco Cannizzaro, Salvatore Caddemi, Ivo Caliò

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Abstract

In this study the forced vibrations of cracked beams in presence of damping are analysed. The adopted beam model is in accordance with the Timoshenko beam model and the presence of multiple bending and shear concentrated flexibilities, commonly used to model cracks, is accounted for. The strong discontinuities derived by the localised flexibilities are dealt with by means of a distributional approach avoiding the need of enforcing continuity conditions at the discontinuous sections. First, the exact Green’s functions, that is the steady-state response in the case of concentrated harmonic loads, are obtained via the presented distributional approach. The presented exact solutions are a computationally advantageous evaluation of the steady state response alternative to the direct time integration, as well as to a beam span sub-division. In addition, the presented distributional Green’s functions are employed to evaluate the response of multi-cracked beams subjected to arbitrary loading conditions (i.e. generic spatial distribution and time dependency), via convolution integral equation combined with an appropriate frequency domain analysis.

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多裂缝季莫申科梁振动的分布格林函数

本研究分析了存在阻尼的裂缝梁的受迫振动。所采用的梁模型与季莫申科梁模型一致，并考虑了通常用于裂缝建模的多重弯曲和剪切集中挠性的存在。局部挠性产生的强不连续性通过分布式方法处理，避免了在不连续性部分强制执行连续性条件的需要。首先，通过提出的分布式方法获得精确的格林函数，即集中谐波载荷情况下的稳态响应。与直接时间积分和梁跨度细分相比，所提出的精确解法在稳态响应评估方面具有计算优势。此外，通过卷积积分方程结合适当的频域分析，所提出的分布式格林函数还可用于评估受到任意加载条件（即通用空间分布和时间相关性）影响的多裂缝梁的响应。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Acoustics 物理-声学

CiteScore

7.40

自引率

11.80%

发文量

618

审稿时长

7.5 months

期刊介绍： Since its launch in 1968, Applied Acoustics has been publishing high quality research papers providing state-of-the-art coverage of research findings for engineers and scientists involved in applications of acoustics in the widest sense. Applied Acoustics looks not only at recent developments in the understanding of acoustics but also at ways of exploiting that understanding. The Journal aims to encourage the exchange of practical experience through publication and in so doing creates a fund of technological information that can be used for solving related problems. The presentation of information in graphical or tabular form is especially encouraged. If a report of a mathematical development is a necessary part of a paper it is important to ensure that it is there only as an integral part of a practical solution to a problem and is supported by data. Applied Acoustics encourages the exchange of practical experience in the following ways: • Complete Papers • Short Technical Notes • Review Articles; and thereby provides a wealth of technological information that can be used to solve related problems. Manuscripts that address all fields of applications of acoustics ranging from medicine and NDT to the environment and buildings are welcome.