Effect of Bed and Crack on the Natural Frequency for the Timoshenko Beam Using Finite Element Method

Subject Areas : Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering

افشین منوچهری فر ¹ , فرید ابطحی ²

1 - استادیار، دانشکده مکانیک، دانشگاه آزاد اسلامی واحد خمینی‌شهر
2 - کارشناس ارشد مکانیک، دانشگاه آزاد اسلامی واحد خمینی‌شهر

Received: 2015-11-07 Accepted : 2015-11-07 Published : 2014-12-22

Keywords: FEM, Timoshenko beam, Crack, Bed of Beam,

Abstract :

In this study, the natural frequencies and mode shapes of beams without cracks and cracked Timoshenko beams is calculated with different boundary conditions using finite element method. The energy method is used to solve the equations. Hardness and softness matrices for Timoshenko beam without crack are obtained by solving the potential and kinetic energy equations. Then for investigation of cracked condition, the cracked element stiffness matrix is used and the beam natural frequencies are obtained by entering the boundary conditions of the beam. After that the effect of bed is investigated by addition of it to the equations.

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]16[ چهارمحالی­پور، ا.، نحوی، ح.، بررسی رفتار ارتعاشی تیرهای دارای ترک، دانشکده مکانیک، دانشگاه آزاد خمینی‌شهر، 1387.