Techno Press


Steel and Composite Structures   Volume 15, Number 4, October 2013, pages 439-449
DOI: http://dx.doi.org/10.12989/scs.2013.15.4.439
 
Nonlinear vibration of Euler-Bernoulli beams resting on linear elastic foundation
Mehran Javanmard, Mahdi Bayat and Alireza Ardakani

 
Abstract     [Full Text]
    In this study simply supported nonlinear Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads is investigated. A new kind of analytical technique for a non-linear problem called He\'s Energy Balance Method (EBM) is used to obtain the analytical solution for non-linear vibration behavior of the problem. Analytical expressions for geometrically non-linear vibration of Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads are provided. The effect of vibration amplitude on the non-linear frequency and buckling load is discussed. The variation of different parameter to the nonlinear frequency is considered completely in this study. The nonlinear vibration equation is analyzed numerically using Runge-Kutta 4th technique. Comparison of Energy Balance Method (EBM) with Runge-Kutta 4th leads to highly accurate solutions.
 
Key Words
    elastic foundation; nonlinear vibration; analytical method; Runge-Kutta 4th
 
Address
1) Mehran Javanmard: Department of Civil Engineering, University of Zanjan, Zanjan, Iran;
2) Mahdi Bayat: Department of Civil Engineering, Zanjan Branch, Islamic Azad University, Zanjan, Iran;
3) Alireza Ardakani: Faculty of Engineering and Technology, Imam Khomeini International University, Qazvin, Iran.
 

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