The Study Of Precise Integration Method And Its’Algorithm Of Pseudo-dynamic Testing

Precise integration method (PIM) has attracted a wide range of concerns, because of the high stability and precision. It has been successfully applied to structural dynamics, random vibration, pseudo-dynamic test, transient heat conduction and optimal control, et al. So it has the important practical significance to further study the PIM. The main research contents are as follows:Firstly, the existing PIM is summarized and analyzed. According to ways of solution to nonlinear part of the nonlinear dynamic equations, the PIM is divided into calculating the-inversion-of-the-state-matrix method and avoiding calculating the-inversion-of-the-state-matrix method (Taylor method, numerical integration method, precise integration method of nonlinear part). Numerical examples show that the calculating the inversion of the state matrix method and precise integration method of nonlinear part have the same computation accuracy. The Analysis and conclusions can provide reference for reasonable selection of nonlinear integral method.Secondly, the precise integral methods based on improved piecewise quadratic interpolation is proposed. The traditional piecewise quadratic interpolation is improved to be applied to construct approximate polynomials of nonlinear part of nonlinear dynamic systems. By applying the polynomial representation of the nonlinear parts, the general discrete forms based on improved piecewise quadratic interpolation are derived, the precise integral single-step methods and precise integral multi-step methods are constructed. The theoretical analysis and numerical examples show that:A.=1/2, the single-step method has the highest accuracy. And, X=15/246, the multi-step method has the highest accuracy. The stability and precision of the proposed methods is better than the PIM methods established.Thirdly, new PIM algorithms of pseudo-dynamic testing are proposed. On the basis of the existing PIM and the existing PIM algorithm of pseudo-dynamic testing,2new explicit algorithms of pseudo-dynamic testing are constructed. The theoretical analysis and numerical examples show that:The stability and precision of the Trapezoidal Rule-PIM algorithm of pseudo-dynamic testing proposed in the paper is better than the existing PIM algorithm of pseudo-dynamic testing, so the proposed algorithm can be used into the pseudo-dynamic testing.