A random seismic response analysis method for large-scale proportional damped structures

Abstract

The pseudo excitation method (PEM) offers an effective framework for the analysis of structural behavior under uncertain dynamic loading. This work presents a new PEM-based approach to investigate the dynamic behavior of large-scale, proportional damped structures under random seismic excitation. The computational process begins with the application of the large mass method (LMM) to derive governing equations. Our approach for obtaining frequency-domain solutions via PEM involves separating solutions into two components, i.e., lower-order modes and truncated modes. The lower-order modes are developed using the mode superposition method, while the Sturm sequence is used to select the appropriate number of lower-order modes. To tackle issues related to rigid body modes in the LMM, we also introduce a shifted eigenproblem. The decomposition of the shifted stiffness matrix is preserved and applied in an iterative algorithm designed to generate approximate solutions for the truncated modes. This algorithm can adaptively compute structural responses within specified tolerance levels. To verify this approach, we study the influence of random loading conditions on frame and platform structures.