Masoud Minaei ¹

Affiliations
1 Department of Mechanical Engineering, University of Tabriz, Tabriz, IR

Abstract

Objectives: In this study, large amplitude e free vibration behavior of Euler-Bernoulli beam subjected to the nonlinear thermal loads and resting on a Pasternak foundation is investigated. Methods: The Hamilton’s principle is used to derive the beam governing partial differential equation of motion. By implementing the Galerkin’s method and applying the clamped-clamped boundary condition, the partial differential equation is converted to an ordinary nonlinear differential equation. Results: Because of the large coefficient of the nonlinear term, the Modified Homotopy Perturbation Method (MHPM) is used to solve the obtained equation. The effect of nonlinear thermal load on the system nonlinear vibration behavior is studied. Applications: The results show that although increasing the nonlinear thermal load coefficients decreases both linear and nonlinear frequency, but it increases the frequency ratio.

Keywords

Euler-Bernoulli Beam, Modified Homotopy Perturbation Method, Nonlinear Thermal Load, Pasternak Foundation, Strongly Nonlinear Vibration.

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Masoud Minaei ¹

Affiliations
1 Department of Mechanical Engineering, University of Tabriz, Tabriz, IR

Abstract

Objectives: In present paper, large amplitude vibration behavior of an Euler-Bernoulli beam with immovable clampedclamped boundary conditions subjected to an external harmonic excitation resting on Pasternak foundation is investigated. Methods: Assuming the mid-plane stretching in the beam and using the Newton’s second law and then implementing the Galerkin’s method, the ordinary nonlinear differential equation is derived. Because of the large coefficient of the nonlinear term, the traditional perturbation methods based on the small coefficient of the nonlinear term lead to an invalid solution. Results: To solve the obtained strongly nonlinear non-homogeneous equation, the Modified Homotopy Perturbation Method (MHPM) is generalized. In order to validate the results of MHPM, some experimental tests carried out. Conclusion: The results show a good agreement between analytical and experimental data. Moreover, the time response of the first and second order generalized MHPM follows accurately the time response obtained by numerical solution.

Keywords

Euler-Bernoulli Beam, Generalized MHPM, Harmonic Excitation, Large Amplitude Vibration of Beams, Pasternak Foundation.

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