A Numerical Method for Estimating the Dynamic Response of Structures

A novel numerical method is proposed for computing the seismic response of linear and nonlinear systems. Single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems are covered. The method is called load impulse method (LIM) because it uses the load impulse concept in its formulation. LIM is first extended for analyzing linear damped systems whose damping ratios are almost greater than ۱% and nonlinear systems in general. To formulate LIM, the governing differential equation of motion (DEOM) is modified to have appropriate form for numerical integration. Then, it is integrated over time step using trapezoidal integration rule. Rearranging the obtained equation, the required relations are generated for computing seismic response of dynamic systems through simple iteration. The seismic response of several linear and nonlinear structural systems under dynamic loads is determined through the proposed LIM. A detailed comparison is then carried out between the results of LIM and those obtained from Duhamel integral, Newmark-β, and Wilson-θ methods. The results clearly show that the proposed LIM can robustly estimate the displacement, velocity, and acceleration time-histories of the dynamic systems within satisfactory computational cost.

کلیدواژه ها:

Load Impulse Method (LIM) ، Numerical method ، Dynamic Response ، Linear and nonlinear analyses ، structural vibration ، Newmark-β ، Duhamel integral