Seismic Response Analysis of Buildings Using the Laplace Transform: Methodology and Insights

This article explores how the Laplace Transform can be applied to the analysis of building motion and behavior under earthquake action. The main steps of this analysis are presented, including the application of the Laplace Transform to the differential equations, obtaining the transfer function, and interpreting the building response in the Laplace domain. Special attention is given to identifying and analyzing the pole and zero points of the system, which provide critical insights into the stability and resonance characteristics of the structure. Key advantages and limitations of this approach are discussed, highlighting its utility in predicting and enhancing structural safety, as well as its potential for optimizing design parameters in earthquake engineering. Through practical examples, the effectiveness of using the Laplace Transform in seismic response analysis is demonstrated, providing valuable insights for engineers and researchers in the field of structural dynamics.