An analytical approach for the nonlinear forced vibration of clamped-clamped buckled beam

Analytical solutions are attractive for parametric studies and consideration of the problems physics. In addition, analytical solutions can be employed as a reference framework for verification of numerical results. In this paper Homotopy analysis method and Homotopy Pade technique which are approximate analytical methods, are used to obtain nonlinear forced vibration response of Euler-Bernoulli clamped-clamped buckled beam subjected to an axial force and transverse harmonic load for the first time. Analytical solutions for nonlinear frequency are derived via Homotopy analysis method, Homotopy Pade technique and Runge Kutta method and the results are compared with experimental results of literature. Also the time response of the beam is obtained for free and forced vibration via analytical and numerical methods. In addition, the frequency response is drawn. Comparison of analytical results with numerical results and literature results reveals that Homotopy analysis method and Homotopy Pade technique have excellent accuracy for wide range of nonlinear parameters and predict system behavior precisely.