Narrowband Outside Excitations Of Multi-degree Of Freedom Nonlinear Dynamic System Response

In this dissertation, the response in two-degree-of-freedom nonlinear system under random external excitation is investigated by using analytical and numerical method. Some conclusions are obtained. The main contents of the dissertation are as follows:Chapter one summarizes the situation and application of response in nonlinear dynamical system under narrow-band random excitation and presents the main contents and arrangement of the dissertation.In chapter two and chapter three, the response of two-degree-of freedom nonlinear system (1.1) is studied.In chapter two, the case when v = 0 is discussed. The method of multiple scales is used to determine the equations of modulation of amplitude and phase .The steady state response can be obtained by solving a couple of algebraic equations, which have been achieved by careful deduction under some conditions. And because of the complexity of the equations, programs are necessary to solve the equations mentioned above, and certain graphs are presented. Based on chapter two, In chapter three, the method of multiple scales is introduced to the study of the multiple-dimensional nonlinear stochastic systems under random external excitation. Using method of multiple scales, we strictly deduce the equation of modulation of amplitude and phase. The effects of random excitations are analyzed; numerical simulations verify the results. Theoretical and numerical simulations show that when the intensity of the random excitation increases, the nontrivial steady state solution may be changed from a limit cycle to a diffused limit cycle.In chapter four we concludes the work and points out some aspects to be further studied.