A Semi-Analytical Approach for the Response of Nonlinear Conservative Systems

This work applies Parameter expanding method (PEM) as a powerful analytical technique in order to obtain the exact solution of nonlinear problems in the classical dynamics. Lagrange method is employed to derive the governing equations. The nonlinear governing equations are solved analytically by means of He’s Parameter expanding method. It is demonstrated that one term in series expansion is sufficient to generate a highly accurate solution, which is valid for the whole domain of the solution and system response. Comparison of the obtained solutions with the numerical ones indicates that this method is an effective and convenient tool for solving these types of problems.This work applies Parameter expanding method (PEM) as a powerful analytical technique in order to obtain the exact solution of nonlinear problems in the classical dynamics. Lagrange method is employed to derive the governing equations. The nonlinear governing equations are solved analytically by means of He’s Parameter expanding method. It is demonstrated that one term in series expansion is sufficient to generate a highly accurate solution, which is valid for the whole domain of the solution and system response. Comparison of the obtained solutions with the numerical ones indicates that this method is an effective and convenient tool for solving these types of problems