Numerical evaluation of dynamic response by using modified Newmark’s method

It is well known that the Newmark’s method is considered one of the most popular methods for structural dynamic analysis. In this study, starting from the basic Newmark’s method, a new accurate method is investigated and developed. The basic idea of the proposed method is to use Richardson’s extrapolation to improve the basic Newmark’s method. To observe the accuracy of the proposed method, several numerical tests are performed for a single degree-of-freedom (SDM) dynamic system and the results are compared with results from Newmark’s method and the exact solution. The results show that the proposed method improves the solution accuracy of the structural dynamic problems compared to the Newmark’s method. Moreover, the results of the free oscillating case show that the modified Newmark’s method has more computational efficiency compared to the Newmark’s method.