Comparison Between Two Analytical Solutions for Random Vibration Responses of a Spring-Pendulum System with Internal Resonance

내부공진을 가진 탄성진자계의 불규칙진동응답을 위한 두 해석해의 비교

An investigation into the stochastic bifurcation and response statistits of an autoparameteric system under broad-band random excitation is made. The specific system examined is a spring-pendulum system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. The Fokker-Planck equations is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. In view of equilibrium solutions of this system and their stability we examine the stochastic bifurcation and response statistics. The analytical results are compared with results obtained by Monte Carlo simulation.