Dynamic Bending Model Describing the Generation of Negative Stiffness by Buckled Beams: Qualitative Analysis and Experimental Verification

Abstract

This work addresses the dynamic modeling of a negative stiffness absorber consisting of an assembly of curved beams. Design rules are derived from the orders of magnitude of stiffness and elastic energy stored by the negative stiffness elements. Although static and dynamic performances are widely documented using equivalent spring–mass system equations of motion, this paper presents a modeling approach based on beam dynamics to predict the behavior by incorporating the generation of negative stiffness with prestressed Euler beams. The static behavior is first recalled to feed the dynamic beam model with realistic orders of magnitude. The latter is derived from the beam balance instead of the spring–mass system and aims at solving the beam problem, which encompasses more realistic phenomena compared to introducing the equivalent stiffness in the spring–mass equation of motion. The consistency of the beam modeling is confirmed by comparison with available models in the literature and finite element simulations. A mock-up is built in which beam-type components are 3D-printed. Axial loading is introduced on the curved beams to evaluate its influence on the response of the isolator, and the observed softening trend complies with the theoretical predictions.