Techno Press
You logged in as

Structural Engineering and Mechanics   Volume 27, Number 3, October20 2007, pages 333-345
DOI: https://doi.org/10.12989/sem.2007.27.3.333
 
Non linear vibrations of stepped beam system under different boundary conditions
E. Ozkaya and A. Tekin

 
Abstract     [Buy Article]
    In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained using Hamilton?s principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Forcing and damping terms were also included in the equations. The dimensionless equations were solved for six different set of boundary conditions. A perturbation method was applied to the equations of motions. The first terms of the perturbation series lead to the linear problem. Natural frequencies for the linear problem were calculated exactly for different boundary conditions. Second order non-linear terms of the perturbation series behave as corrections to the linear problem. Amplitude and phase modulation equations were obtained. Non-linear free and forced vibrations were investigated in detail. The effects of the position and magnitude of the step, as well as effects of different boundary conditions on the vibrations, were determined.
 
Key Words
    stepped beam; nonlinear vibration; perturbation method.
 
Address
E. Ozkaya: Dept. of Mechanical Engineering, Celal Bayar University, 45140, Muradiye, Manisa, Turkey
A. Tekin: Celal Bayar University, 45100, Soma, Manisa, Turkey
 

Techno-Press: Publishers of international journals and conference proceedings.       Copyright © 2019 Techno Press
P.O. Box 33, Yuseong, Daejeon 305-600 Korea, Tel: +82-42-828-7996, Fax : +82-42-828-7997, Email: technop@chol.com