in this paper, the nonlinear free vibrations of thin symmetric and non-symmetric cross-ply composite plates subjected to biaxial initial stresses are investigated. because of their excellent properties such as specific strength and specific stiffness, composite plates have wide applications in aerospace and mechanical structures. based on von-karman's strain-displacement relations and using gal...

In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...

In this paper, a comparison is made between direct and indirect perturbation approaches to solve the non-linear vibration equations of a piezoelectrically actuated cantilever microbeam. In this comparison, the equation of motion is considered according to Euler-Bernoulli theory with considering the non-linear geometric and inertia terms resulted from shortening effect. In the direct perturbatio...

We investigate the hard nonresonant excitation of the forced Duffing equation with a positive damping parameter E. Using the symbolic manipulation system MACSYMA, a computer algebra system. we derive the two term perturbation expansion by the method of multiple time scales. The resulting approximate solution is valid for small values of the coefficient e As the damping parameter e increases, th...

The present article investigates effects of the multi-frequency excitation on the output power of a piezomagnetoelastic energy harvester. The piezomagnetoelastic power generator is assumed to operate in the mono-stable mode. A perturbation technique based on the method of multiple scales is employed to develop an analytical solution to nonlinear differential equations governing the system dynam...

This paper considers the problem of a beam with a small bending stiffness, within the framework of a non-linear beam model that includes both the classical cable and the linear beam as limiting cases. This problem, treated as a perturbation of the catenary solution, is solved with the multiple scales method. The resulting expressions of the beam deflection and of the internal forces, as well as...