Abstract: Dynamic response optimization of mechanical system design has good application prospects. Dynamic response must meet the time-dependent differential equations. In order to obtain the optimal solution and satisfy the time-related constraints, the responses over the entire time should be obtained. The system dynamic response design based on time spectral element method is studied. The discrete dynamic response in time domain is discussed in depth. Motion differential equations are converted into algebraic equations, so as to accurately solve out the transient response. GLL(Gauss-Lobatto-Legendre) point method and key point method are used to deal with time constraints. The most simple multi-degree of freedom dynamic design problem─two degrees of freedom spring shock absorber, is taken as an example, artificial design variables are introduced, the advantages and disadvantages of the two methods of dealing with constraints are analyzed in detail, and the correctness of this method is also shown. These contents lay a foundation for further study of the dynamic optimization design of mechanical parts as well as the optimization design of dynamic load elasticity distribution parameter system, such as the dynamic optimization design of rectangular variable cross-section beam which bears vibration input at the fixed end, and the dynamical optimization design of elastic beam which bears vertical plane uniform transient dynamic loads under different boundary conditions.

Key words: Dynamic response optimization, GLL point method, Key point method, Spectral element method, Alignment, Automation, Evaluation index, Large component, Matching