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Forced vibration analysis of multi-cracked Timoshenko beam with the inclusion of damping by virtue of Green's functions

机译：利用格林函数对含裂纹阻尼的多裂纹Timoshenko梁进行强迫振动分析

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摘要

This paper concentrates on obtaining the closed-formed analytical solutions of the steady-state forced vibration of the multi-cracked Timoshenko beams with damping effects. Varying from the Euler-Bernoulli beam, the mechanical properties of a cracked section of the Timoshenko beam are described as a rotational spring and a transversal spring models. Initially, the Green's function of a one-cracked simple supported Timoshenko beam is derived. With the assistant of the solution of the one-cracked situation and the transfer matrix method, the Green's functions of the multi-cracked Timoshenko beams for various boundary conditions are also obtained. The present Green's functions can be degenerate to the Rayleigh and Euler-Bernoulli cases, and the multiple cracked-models can be reduced to the single cracked cases when the depths of some cracks are specified to be zero. In the numerical section, the FEM results and the solutions in some references are used to validate the present solutions. Some numerical examples in this research are to reveal the influences of the shearing effect on the vibration performances of the one-cracked Timoshenko model as well as the multiple cracks cases. Additionally, the effects of some significant physical parameters, like the crack depth and crack locations, are also discussed in some numerical examples. (C) 2019 Elsevier Ltd. All rights reserved.
机译：本文着重于获得具有阻尼效应的多裂纹Timoshenko梁稳态强迫振动的闭式解析解。与Euler-Bernoulli梁不同，Timoshenko梁裂纹段的机械性能描述为旋转弹簧和横向弹簧模型。最初，推导了单裂纹单支撑Timoshenko梁的格林函数。借助单裂纹情况的求解和传递矩阵法，获得了多裂纹蒂莫申科光束在各种边界条件下的格林函数。当前格林函数可以退化为Rayleigh和Euler-Bernoulli情况，并且当某些裂缝的深度指定为零时，可以将多个裂缝模型简化为单个裂缝情况。在数值部分，FEM结果和一些参考文献中的解决方案用于验证当前解决方案。本研究中的一些数值示例旨在揭示剪切效应对单裂纹Timoshenko模型以及多裂纹案例的振动性能的影响。此外，在一些数值示例中还讨论了一些重要的物理参数（如裂纹深度和裂纹位置）的影响。 （C）2019 Elsevier Ltd.保留所有权利。

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  • 来源
    《Applied Acoustics》 |2019年第12期|477-491|共15页
  • 作者

    Chen B.; Zhao X.; Li Y. H.; Guo Y.;

  • 作者单位

    Southwest Jiaotong Univ, Sch Mech & Engn, Chengdu 610031, Sichuan, Peoples R China;

    Southwest Petr Univ, Sch Civil Engn & Architecture, Chengdu 610500, Sichuan, Peoples R China;

    Southwest Jiaotong Univ, Sch Mech & Engn, Chengdu 610031, Sichuan, Peoples R China;

    Southwest Jiaotong Univ, Sch Mech & Engn, Chengdu 610031, Sichuan, Peoples R China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Timoshenko beam; Forced vibrations; Green's functions; Multi-cracked beam; Transfer matrix method;

    机译：Timoshenko梁;强制振动;绿色的功能;多裂梁;转移矩阵法;

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