Nonlinear vibration of FG beams subjected to parametric and external excitations

In this paper, the principal resonance and parametric vibration of functionally graded (FG) beams are investigated. The theoretical formulations and governing partial deferential equations of motion are derived based on the Hamilton's principle, Euler-Bernoulli beam theory, and von Karman geometric nonlinearity. The Galerkin technique and the static condensation method are employed in order to convert the nonlinear partial differential equations...