Free Vibration Analysis of a Nonlinear Beam Using Homotopy and Modified Lindstedt-Poincare Methods

in this paper, homotopy perturbation and modified lindstedt-poincare methods are employed fornonlinear free vibrational analysis of simply supported and double-clamped beams subjected toaxial loads. mid-plane stretching effect has also been accounted in the model. galerkin'sdecomposition technique is implemented to convert the dimensionless equation of the motion tononlinear ordinary differential equation. homotopy and modified lindstedt-poincare (hpm) areapplied to find analytic expressions for nonlinear natural frequencies of the beams. effects ofdesign parameters such as axial load and slenderness ratio are investigated. the analyticexpressions are valid for a wide range of vibration amplitudes. comparing the semi-analyticsolutions with numerical results, presented in the literature, indicates good agreement. the resultssignify the fact that hpm is a powerful tool for analyzing dynamic and vibrational behavior ofstructures analytically.