Non-linear dynamic instability of functionally graded plates in thermal environments

Abstract

Geometrically non-linear parametric instability of functionally graded rectangular plates in thermal environments is investigated via a multi-degree-of-freedom energy approach. Non-linear higher-order shear deformation theory is used and the non-linear response to in-plane static and harmonic excitation in the frequency neighborhood of twice the fundamental mode is investigated. The boundary conditions are assumed to be simply supported movable. Numerical analyses are conducted by means of pseudo arc-length continuation and collocation technique to obtain force–amplitude relations in the presence of temperature variation in the thickness direction. The effect of volume fraction exponent and temperature variation on the onset of instability for both static and periodic in-plane excitation are fully discussed and the post-critical non-linear responses are obtained. Moreover, direct time integration of equations of motion is carried out and bifurcation diagrams, phase-space plots, Poincaré maps and time histories are obtained showing complex non-linear dynamics through period-doubling and Neimark–Sacker bifurcations.