Variational Iteration Method for Free Vibration Analysis of a Timoshenko Beam under Various Boundary Conditions
محل انتشار: ماهنامه بین المللی مهندسی، دوره: 30، شماره: 10
سال انتشار: 1396
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 396
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شناسه ملی سند علمی:
JR_IJE-30-10_017
تاریخ نمایه سازی: 1 اردیبهشت 1397
چکیده مقاله:
In this paper, a relatively new method, namely variational iteration method (VIM), is developed for free vibration analysis of a Timoshenko beam with different boundary conditions. In the VIM, an appropriate Lagrange multiplier is first chosen according to order of the governing differential equation of the boundary value problem, and then an iteration process is used till the desired accuracy is achieved. Solution of VIM for natural frequencies and mode shapes of a Timoshenko beam is compared to the available exact closed-form solution and numerical results of differential quadrature method (DQM). The accuracy of VIM is approximately the same as exact solution and much better than the DQM for solving the free vibration of a Timoshenko beam. Also, convergence speed and simplicity of this method is more than the other two methods because it works with polynomial at the first iteration. Thus, VIM can be used for solving the complicate engineering problems which do not have analytical solution.
کلیدواژه ها:
نویسندگان
k Torabi
Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, Isfahan, Iran
m Ghassabi
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
m Heidari-Rarani
Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, Isfahan, Iran
d Sharifi
Department of Mechanical Engineering, University of Kashan, Kashan, Iran