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Technical Briefs

A New Approach to Analytical Solution of Cantilever Beam Vibration With Nonlinear Boundary Condition

[+] Author and Article Information
Hamid M. Sedighi

Department of Mechanical Engineering,  Shahid Chamran University, Ahvaz, 61357-43337 Iranh-msedighi@phdstu.scu.ac.ir

Kourosh H. Shirazi

Department of Mechanical Engineering,  Shahid Chamran University, Ahvaz, 61357-43337 Irank.shirazi@scu.ac.ir

J. Comput. Nonlinear Dynam 7(3), 034502 (Mar 19, 2012) (4 pages) doi:10.1115/1.4005924 History: Received August 24, 2011; Revised December 24, 2011; Published March 13, 2012; Online March 19, 2012

This paper presents the application of novel and reliable exact equivalent function (EF) for deadzone nonlinearity in an analytical investigation of nonlinear differential equations. A highly nonlinear equation of cantilever beam vibration with a deadzone nonlinear boundary condition is used to indicate the effectiveness of this EF. To obtain the analytical solution of dynamic behavior of the mentioned system, a powerful method, called He’s parameter expanding method (HPEM) is used. Comparison of the obtained solutions using a numerical method reveals the accuracy of this analytical EF.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Cantilever beam with deadzone nonlinear boundary condition

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Figure 2

Plot of EF deadzone nonlinearity

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Figure 3

The impact of nonlinear boundary condition on the response: first order periodic solution (continuous line) with the numerical solution (symbols)

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Figure 4

(a) Comparison of the approximate first order periodic solution (continuous line) with the numerical solution (circles) with A/δ=1.5. (b) Comparison of the approximate first order periodic solution (continuous line) with the numerical solution (circles) with A/δ=2.

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