Suspension being the assembly of vehicle affects the ride safety and comfort. Because the passive suspension system universally adopted in traditional vehicle can only absorb and store energy and doesn't change with the status of vehicle running and dynamic excitation, the vehicles' capabilities are limited. So the active/semi-active suspension are researched and applied widely. The capabilities of different suspensions are researched in the thesis including chaos phenomena occurring in non-linear suspension and time-domain response analysis of control suspension with time delay.Precision integral method has been very successfully and widely used in recent years. By combining with Romberg integral and linear interpolation, precision integral method is lucubrated in classical dynamics equation, Ricatti equation and dynamics equation with time delay.At last, algorithm programs are programmed with MATLAB. The simulation analyses of numerical examples demonstrate that the methods are superior conventional numerical method, and have excellent precision, efficiency and stability. So the methods suggested in this paper have great promise in applications and the results in the project provide some reference value for civil researchers.
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