Evaluation of improved precise integration method in structural dynamics using single value decomposition technique

Numerical techniques for solving dynamic structural problems often encounter significant challenges, including conditional stability, period elongation errors, amplitude decay errors, and the emergence of spurious frequencies. To address these issues, several first-order precise integration methods have been developed; however, these approaches still suffer from errors associated with the inversion of the state matrix. This study employs the singular value decomposition technique to enhance the efficiency of the precise integration method algorithm and eliminate the singularity of the state matrix. The robustness of the proposed method is evaluated across various transient dynamic problems. The results demonstrate that traditional approaches, such as the Newmark method, exhibit substantially larger errors—exceeding ۱۵۰% in certain cases. Ultimately, the findings emphasize that accurately estimating the dynamic response of multi-degree-of-freedom systems under impact loading requires careful consideration. Conventional methods, including the Newmark average acceleration technique, should therefore not be applied indiscriminately.

کلیدواژه ها:

Precise integration method ، Single value decomposition ، Inversion of state matrix ، Spurious frequency ، Newmark average acceleration method