Nonlinear vibration of beam on elastic foundation

The large amplitude free vibration behaviour of an Euler-Bernoulli beam with immovable ends subjected to the thermal loads is investigated. Applying the Hamilton’s principle, the beam governing equation of motion is derived. By implementing the Galerkin’s method, the ordinary nonlinear differential equation is derived and because of the large coefficient of the nonlinear term, the Homotopy Perturbation Method (HPM) is used to solve the governing nonlinear equation and the accuracy of the mentioned method is investigated. The results are validated by comparing them with those available in the literature. Moreover, the effects of the system parameters including foundation coefficients, thermal load and vibrational modes on the system nonlinear vibration behaviour are investigated.