Transient nonlinear vibration of porous FGM sandwich beams with elastically restrained ends under uniform temperature rise

Abstract

An analytical-numerical framework is developed to evaluate the transient nonlinear vibration of porous functionally graded material (FGM) sandwich beams operating in thermal environments. The model simultaneously accounts for porosity, elastic axial restraint at the beam ends, initial geometric imperfection, interaction with a Winkler-Pasternak foundation, and a suddenly imposed uniform transverse load. Two sandwich configurations are analyzed: one with FGM face sheets and a homogeneous core, and another with an FGM core and homogeneous face sheets. Both even and uneven pore distributions are introduced through an effective-property formulation based on a modified mixture rule. The governing equations are derived from the first-order shear deformation beam theory, including von Karman geometric nonlinearity, thermal stress effects, initial imperfection and foundation reaction. Closed-form admissible functions are combined with the Galerkin procedure to reduce the field equations to a nonlinear time-dependent ordinary differential equation, which is integrated by a fourth-order Runge-Kutta scheme. The parametric results show that porosity weakens the dynamic bending stiffness, whereas elastic foundation stiffness improves the resistance to transverse vibration. Uniform temperature rise and stronger axial end restraint generally amplify the dynamic deflection. Initial imperfection may reduce the response at room temperature but becomes unfavorable when thermal stress is present.