Research Of Structural Dynamic Equation And Active Vibration Control Under Precise Integration

The research of nonlinear dynamic question is a front-line topic in engineering science field, up to now the algorithm with high precision and good efficiency is still a difficult problem, the analytical algorithm is merely suit to special questions and the conventional numerical methods have some disadvantages, such as the precision is sensitivity to time-step or some components of high frequency can't be obtained etc. The precise integration method (PIM) provides a new approach to deal with dynamic system for its striking high precision.This paper suggests that the integral of the state equation is evaluated directly through the exponential matrix based on the PIM, thus several series solutions are obtained. Utilizing the symmetry of matrices and the idea of substructure, the computational precision and efficiency of the PIM are improved. The methods are convenient to programming, more over, are very efficient to parallel computing and large-scale problems. Based on the PIM, the closed-loop and closed-open-loop control algorithm under the instantaneous optimal control strategy are acquired, so it has practical significance in active control.At last, the simulation analysis of numerical examples demonstrate that the methods are superior to the conventional numerical methods, and has excellent precision, efficiency and stability. So the methods suggested in this paper have great promise in applications.