Numerical and analytical study of seismic response of structural systems with new formulation using energy and impact methods

This paper presents two simple and robust technique for response estimating of single-degree-of-freedom (SDOF) structural systems. The impulse method, because it is formulated based on the fundamentals of dynamics; especially, the linear impulse concept, and also the energy method, because the main idea of this method is inspired by energy conservation principles. These methods can strongly cope with linear damped systems for which damping ratio ζ is greater than 0.01. Assessment of SDOF dynamic systems under any arbitrary excitations is easily possible through the proposed methods. There is no error propagation through the solving process. The numerical example reveals the simplicity and robustness of the new technique compared to Duhamel’s integral and similar techniques. Finally, a numerical example is investigated to demonstrate the efficiency of the algorithms. The most famous record of El Centro ground motion is applied to the systems. The obtained results show that the new algorithm works exactly enough to compete with a conventional method such as the Duhamel integration method and the Newmark-β method. A comparison between the results of this method with the solution methods used by other researchers is shown to be a good match.