Bifurcation and chaos of thin circular functionally graded plate in thermal environment

Highlights: → We study bifurcations and chaotic dynamics of a FGM circular plate. → We consider the effect of temperature-dependent material properties. → Increasing volume fraction index will increase chaotic regions. → Increasing temperature will reduce chaotic regions. → The FGM plate exists chaotic motions, multiple periodic and periodic motions. - Abstract: A ceramic/metal functionally graded circular plate under one-term and two-term transversal excitations in the thermal environment is investigated, respectively. The effects of geometric nonlinearity and temperature-dependent material properties are both taken into account. The material properties of the functionally graded plate are assumed to vary continuously through the thickness, according to a power law distribution of the volume fraction of the constituents. Using the principle of virtual work, the nonlinear partial differential equations of FGM plate subjected to transverse harmonic forcing excitation and thermal load are derived. For the circular plate with clamped immovable edge, the Duffing nonlinear forced vibration equation is deduced using Galerkin method. The criteria for existence of chaos under one-term and two-term periodic perturbations are given with Melnikov method. Numerical simulations are carried out to plot the bifurcation curves for the homolinic orbits. Effects of the material volume fraction index and temperature on the criterions are discussed and the existences of chaos are validated by plotting phase portraits, Poincare maps. Also, the bifurcation diagrams and corresponding maximum Lyapunov exponents are plotted. It was found that periodic, multiple periodic solutions and chaotic motions exist for the FGM plate under certain conditions.