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Strongly Nonlinear Free Vibration Analysis of Beams using Modified Homotopy Perturbation Method subjected to the Nonlinear Thermal Loads


  • Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran, Islamic Republic of


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.


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

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