Boundary Element Method in Structural Mechanics for Periodic Structure Vibration Protection

Abstract

This paper investigates the adaptation of the direct boundary element method (BEM) for analyzing stationary vibrations in load-bearing structural components, specifically beams and plates, under intense dynamic loads. The study addresses the challenge of designing high-efficiency mitigation systems for engineered facilities with regular configurations, including cross-bar systems, multi-span floors, and pile foundations. A novel numerical scheme is proposed and substantiated to model bending wave propagation with high precision in periodically fixed elements. Fundamental solutions for one-dimensional and two-dimensional systems are derived using the Fourier integral transform combined with contour integration techniques. The computational advantages of the developed approach over the conventional finite element method (FEM) are demonstrated, focusing on dimensionality reduction and modeling accuracy in infinite domains, which is essential for foundation-soil interaction problems. The proposed methodology effectively identifies stop-bands-frequency ranges where wave propagation is suppressed. The findings establish a theoretical framework for designing innovative structural components capable of blocking undesirable oscillations, thereby ensuring structural safety and vibration isolation in residential and industrial environments.