Comparison of pseudo-acceleration spectrum obtained from linear interpolation of excitation with pseudo-acceleration spectrum obtained from interpolation with cubic spline function

In this paper, the pseudo-acceleration spectra of the three accelerograms of El Centro, Naghan and Tabas, which were obtained by the linear interpolation method of stimulation (Jennings’s method) and also by using the cubic spline function, are compared with each other. Jennings' method is based on linear interpolation of excitation and is acceptable for short periods of time. In this research, three accelerograms of El Centro, Naghan and Tabas were considered, and their pseudo-acceleration response spectrum (base shear coefficient) was calculated for different damping values using linear interpolation method and interpolation with spline function. The considered damping were zero, two, five, ten and twenty percent. In order to determine the difference between the linear interpolation method and the spline function interpolation method, the time interval between the accelerometer points was divided into 2, 5, 10, 20, 50, 100, and 200 equal parts, respectively. Then, once with the linear interpolation method and again with the spline interpolation method, the internal points between the internal acceleration points were obtained and their pseudo-acceleration spectrum was calculated using the Jennings method and the interpolation method with the spline function. The calculation results showed that the pseudo-acceleration spectrum values calculated by the spline interpolation method in very short periods and low damping have a significant difference with the corresponding values of the pseudo-acceleration spectrum calculated by the linear interpolation method. It should be noted that the initial time interval between the accelerogram points of El Centro, Naghan and Tabas is 0.02 seconds.