The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise w...The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.展开更多
In the analysis and design for linear systems in the form of state space,it is undisputed that state responses play a fundamentally important role.For continuous-time linear time-invariant(CT-LTI)systems,the well-know...In the analysis and design for linear systems in the form of state space,it is undisputed that state responses play a fundamentally important role.For continuous-time linear time-invariant(CT-LTI)systems,the well-known result is that the state responses are given in terms of matrix exponential functions[1].For discrete-time linear time-invariant(DT-LTI)systems,the state responses are expressed in terms of matrix power functions[1].展开更多
文摘The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.
基金supported by the Preeminent Youth Team Project of Guangdong Provincial Natural Science Foundation(Grant No.2024B1515040008)the National Natural Science Foundation of China(Grant No.62173112)+3 种基金the Shenzhen Science and Technology Program(Grant No.RCJC20210609104400005)the Science Center Program of National Natural Science Foundation of China(Grant No.62188101)the Joint Funds of the National Natural Science Foundation of China(Grant No.U2013203)the Fundamental Research Funds for the Central Universities(Grant No.HIT.OCEF.2023051)。
文摘In the analysis and design for linear systems in the form of state space,it is undisputed that state responses play a fundamentally important role.For continuous-time linear time-invariant(CT-LTI)systems,the well-known result is that the state responses are given in terms of matrix exponential functions[1].For discrete-time linear time-invariant(DT-LTI)systems,the state responses are expressed in terms of matrix power functions[1].
