A Perturbation Analysis for General Nonlinear Continuous Systems Using Fourier Series and Green's Function Method

In this paper, a procedure based on renormalization group method with the aid of Fourier series and Green's function method is proposed to deal with continuous systems with general linear and nonlinear operators. In contrast to previous works, nonlinear operator has a general form (not necessarily quadratic and cubic form) and can be function of displacement, velocity, acceleration and time. The nonlinear operator may be non-analytic function of spatial coordinates and may be in an integro-differential form. We present our results for a general continuous system with and without internal resonance and general systems with nonlinear and non-homogenous boundary conditions. To show the effectiveness of the procedure, some examples are presented.