Nonlinear vibrations of axisymmetric circular plates with variable thickness

The BEM is developed for nonlinear vibration analysis of axisymmetric circular plates with variable thickness undergoing large deflections. General boundary conditions are considered which may be also nonlinear. The problem is formulated in terms of displacements. The solution is based on the concept of the analog equation, according to which the two coupled nonlinear differential equations with variable coefficients, pertaining to the inplane radial and transverse deformation, are converted to two uncoupled linear ones of a substitute beam with unit axial and unit bending stiffness, respectively, under fictitious quasi-static load distributions. Numerical examples are presented, which illustrate the method and demonstrate its efficiency and accuracy.