چكيده لاتين :
In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for
nonlinear free vibrational analysis of simply supported and double-clamped beams subjected to
axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkinיs
decomposition technique is implemented to convert the dimensionless equation of the motion to
nonlinear ordinary differential equation. Homotopy and modified Lindstedt-Poincare (HPM) are
applied to find analytic expressions for nonlinear natural frequencies of the beams. Effects of
design parameters such as axial load and slenderness ratio are investigated. The analytic
expressions are valid for a wide range of vibration amplitudes. Comparing the semi-analytic
solutions with numerical results, presented in the literature, indicates good agreement. The results
signify the fact that HPM is a powerful tool for analyzing dynamic and vibrational behavior of
structures analytically.
