Wave propagation in Pre-stressed Structures with Geometric Non-linearities through Carrera Unified Formulation

This paper investigates the wave propagation characteristics in pre-stressed structures with different geometric non-linearities utilizing the Carrera Unified Formulation (CUF). The CUF provides a versatile framework for modeling various structural configurations and non-linearity types, enabling a comprehensive analysis of wave propagation phenomena. The study considers different representative geometric non-linearities for which the governing equations are derived, and numerical solutions are obtained using a unified approach. The effects of pre-stress and geometric non-linearity on wave propagation behavior are systematically investigated. The results demonstrate that pre-stress can significantly influence wave propagation characteristics, such as modal frequencies and dispersion properties. The study provides insights into the wave propagation behavior in pre-stressed structures with different geometric nonlinearities, contributing to understanding wave propagation in complex acoustic-structural systems. Specifically, a CUF-modeled metallic box beam is considered herein. Initially, the first four non-rigid modal shapes of the unstressed, linear, and full non-linear box beam with a pre-stress are investigated, among which torsional and flexural modes can be recognized. Afterward, the equilibrium curves of such a structure for various geometrical non-linear approximations are traced, highlighting that all types of non-linearity induce a hardening behavior in the system, which increases with the pre-load, directly leading to a variation in modal frequencies. The investigation is further enriched through the comparison of the dispersion relations of the examined full non-linear structure as functions of the applied pre-load by exploiting Wave Finite Element Method (WFEM) capabilities. This knowledge paves the way for designing and optimizing pre-stressed systems with enhanced acoustic performance, fostering advancements in sound absorption, noise insulation, and structural isolation.