Vibration evaluation of nonlinear system under random parametric excitations by probabilistic method

Vibration of a non-linear system under random parametric excitations was evaluated by probabilistic methods. The nonlinear characteristic terms of a system were quasi-linearized and excitation terms were remained as they were. An analytical method where the square mean of error was minimized was used. An alternative method was an energy method where the damping energy and restoring energy of the linearized system were equalized to those of the original non-linear system. The numerical results were compared with those obtained by Monte Carlo simulation. The comparison showed the results obtained by Monte Carlo simulation located between those by the analytical method and those by the energy method.