An efficient analytical solution for nonlinear vibrations of a parametrically excited beam

Mahmoudkhani, Saeed

Document Type : Research Paper

Author

saeed mahmoudkhani

Aerospace Engineering Department, Faculty of New Technologies and Engineering, Shahid Beheshti University, GC

Abstract

An efficient and accurate analytical solution is provided using the homotopy-Pade technique for the nonlinear vibration of parametrically excited cantilever beams. The model is based on the Euler-Bernoulli assumption and includes third order nonlinear terms arisen from the inertial and curvature nonlinearities. The Galerkin’s method is used to convert the equation of motion to a nonlinear ordinary differential equation, which is then solved by the homotopy analysis method (HAM). An explicit expression is obtained for the nonlinear frequency amplitude relation. It is found that the proper value of the so-called auxiliary parameter for the HAM solution is dependent on the vibration amplitude, making it difficult to rapidly obtain accurate frequency-amplitude curves using a single value of the auxiliary parameter. The homotopy-Pade technique remedied this issue by leading to the approximation that is almost independent of the auxiliary parameter and is also more accurate than the conventional HAM. Highly accurate results are found with only third order approximation for a wide range of vibration amplitudes.

Graphical Abstract

Keywords

Main Subjects

Nonlinear Solution

References

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Journal of Computational & Applied Research in Mechanical Engineering (JCARME)

An efficient analytical solution for nonlinear vibrations of a parametrically excited beam

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References

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Volume 7, Issue 1 - Serial Number 13
August 2017
Pages 127-136

An efficient analytical solution for nonlinear vibrations of a parametrically excited beam

References

References

Send comment about this article

Volume 7, Issue 1 - Serial Number 13August 2017Pages 127-136

Volume 7, Issue 1 - Serial Number 13
August 2017
Pages 127-136