مهدی بابایی قلعه جوق

Two numerical methods are proposed for dynamic analysis of single-degree-of-freedom systems. Basics of dynamics and elementary tools from numerical calculus are employed to formulate the methods. The energy conservation principles triggered the basic idea of the first method, so-called energy-based method (EBM). It is devised for dynamic analysis of linear damped system whose damping ratio is greater than 1%. The second method uses function approximation theory and integration scheme, and called simplified integration method (SIM). Several numerical examples are investigated through SIM. A detailed comparison is made between the proposed methods and the conventional ones. The results show that the proposed methods can estimate the dynamic response of linear damped systems with high accuracy. In the first example, the peak displacement is obtained 6.8747 cm and 6.8290 cm which closely approximate the highly exact response of Duhamel integral. Results show that Newmark-β method is the fastest one whose run-time is 0.0019 sec. EBM and SIM computational times are 0.0722 sec and 0.0021sec, respectively. SIM gives more accurate estimate and convergence rate than Newmark-β method. The difference of peak displacement obtained from two methods is almost less than 1%. Thus, SIM reliably estimates the dynamic response of systems with less computational cost.