MODAL ANALYSIS OF 2D PERIODIC STRUCTURES USING DYNAMIC CONDENSATION WITH PRIMAL ASSEMBLY

Abstract

Periodic structures, composed of repeating and regularly connected unit cells, are widely used in various engineering fields due to their functionality, aesthetics, producibility, and unique property of passively reducing vibrations. However, analyzing these structures can be challenging due to their high degrees of freedom (DOFs), and dynamic analysis of periodic structures requires solving multiple linear systems that can quickly become computationally demanding. Hence, this study presents an efficient method to predict the modal response of two-dimensional periodic structures, utilizing the improved reduced system (IRS) technique and primal assembly. The proposed method involves conducting the reduction process on the unit cells and connecting them using connectivity matrices, eliminating the need for the entire structure to be present during the analysis, resulting in improved efficiency. The accuracy and efficiency of the proposed method are demonstrated using numerical examples with complex geometry and varying material properties.