Free vibration of the double tapered cracked beam

IF 1.1 4区工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY

Inverse Problems in Science and Engineering Pub Date : 2021-01-13 DOI:10.1080/17415977.2020.1870971

M. Haskul, M. Kısa

引用次数: 5

Abstract

This study presents the free vibration analysis of a double tapered beam having linearly varying both thickness and width, by using finite element and component mode synthesis methods. To determine the natural frequency and mode shape of the double tapered cracked beam, the stiffness and mass matrices of the beam have been obtained. The crack in the beam is modeled as a massless spring, and the beam is divided into two subcomponents from the crack section. The stiffness of spring has been derived from the linear elastic fracture mechanics theory as the inverse of the compliance matrix calculated using stress intensity factors and strain energy release rate expressions. It has been observed that natural frequencies and mode shapes vary depending on the location of the crack, the depth of the crack and the aspect ratios of the beam. The results of the present study and those in the literature are compared and a great deal of consistency has been found.

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双锥裂纹梁的自由振动

本文采用有限元和模态综合方法，对厚度和宽度均线性变化的双锥梁进行了自由振动分析。为了确定双锥裂纹梁的固有频率和振型，得到了该梁的刚度矩阵和质量矩阵。将梁中的裂纹建模为无质量弹簧，并将梁从裂纹截面上划分为两个子构件。弹簧的刚度由线弹性断裂力学理论推导为柔度矩阵的逆，柔度矩阵由应力强度因子和应变能释放率表达式计算得到。已经观察到，固有频率和模态振型的变化取决于裂纹的位置，裂纹的深度和梁的纵横比。本文的研究结果与文献的结果进行了比较，发现有很大的一致性。

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

Inverse Problems in Science and Engineering 工程技术-工程：综合

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Inverse Problems in Science and Engineering provides an international forum for the discussion of conceptual ideas and methods for the practical solution of applied inverse problems. The Journal aims to address the needs of practising engineers, mathematicians and researchers and to serve as a focal point for the quick communication of ideas. Papers must provide several non-trivial examples of practical applications. Multidisciplinary applied papers are particularly welcome. Topics include: -Shape design: determination of shape, size and location of domains (shape identification or optimization in acoustics, aerodynamics, electromagnets, etc; detection of voids and cracks). -Material properties: determination of physical properties of media. -Boundary values/initial values: identification of the proper boundary conditions and/or initial conditions (tomographic problems involving X-rays, ultrasonics, optics, thermal sources etc; determination of thermal, stress/strain, electromagnetic, fluid flow etc. boundary conditions on inaccessible boundaries; determination of initial chemical composition, etc.). -Forces and sources: determination of the unknown external forces or inputs acting on a domain (structural dynamic modification and reconstruction) and internal concentrated and distributed sources/sinks (sources of heat, noise, electromagnetic radiation, etc.). -Governing equations: inference of analytic forms of partial and/or integral equations governing the variation of measured field quantities.