Nonlinear forced vibrations of thin circular functionally graded plates

Nonlinear forced vibrations of thin functionally graded circular plates under classical clamped boundary conditions are investigated based on the classical plate theory. The von Karman strain-displacement relations are employed to include the geometrical nonlinearity caused by large transverse displacements of the order of the plate thickness. Modal expansion in polar coordinate system along with the perturbation method of multiple scales is used to solve the governing equations. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. Transverse forcing is supposed to be harmonic with the angular frequency near to the natural frequency of one particular asymmetric mode. Nonlinear vibration phenomena such as jump phenomenon and internal resonance are studied and the effects of boundary conditions, power-law distribution, amplitude and frequency of external load on dynamical behavior of circular plate are examined. The validity of results is established by comparison with the existing results in the literature as well as FEM results.