How internal vibro-impact nonlinearities yield enhanced vibration mitigation

• Published in: Nonlinear dynamics 2024-10, Vol.112 (20), p.17683-17708
• Main Authors: Gzal, Majdi O., Gendelman, Oleg V., Bergman, Lawrence A., Vakakis, Alexander F.
• Format: Article
• Language: English
• Subjects: Automotive Engineering; Classical Mechanics; Clearances; Configurations; Control; Dissipation; Dynamical Systems; Elasticity; Energy; Energy transfer; Engineering; Excitation; Frame structures; Mechanical Engineering; Nonlinearity; Original Paper; Resonance; Stiffness; Structural response; Structural vibration; Transient response; Vibration; Vibration control
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-024-09902-3

We study a fully passive and robust mechanism to mitigate the transient response of resonantly base-excited single- and multi-DOF structures by drastically reducing the portion of input energy that enters into the structures from base excitations. Unlike traditional approaches which are essentially resonance-driven and rely on adding either linear or nonlinear, typically dissipative, secondary attachment(s) to a main (primary) structure, the presented approach is based on incorporating intentional strong non-smooth nonlinearities due to Hertzian interactions. We show that these nonlinear interactions effectively “stiffen” the system and drive the structural response out of resonance by breaking the monotonic increase of input energy for the resonantly excited structure. To elucidate this mechanism, first we consider a resonantly base-excited single-floor frame structure incorporating a single-sided clearance. Subsequently the study is extended to a three-floor frame structure with an internal flexible core, featuring double-sided asymmetrical clearances, subjected to resonant excitation by ground acceleration. Three distinct structural configurations are considered, namely, a linear model serving as a reference for the unprotected structure, and two nonlinear configurations incorporating purely elastic and inelastic Hertzian contacts. Moreover, the influence of the type of contact stiffness magnitude is explored across a wide range, spanning from soft to stiff Hertzian contacts. For both the single- and three-floor structures, the results reveal an unexpectedly favorable regime of contact stiffness, characterized by multiple beneficial attributes, wherein soft, and even purely elastic, contacts exhibit a significant reduction in both input energy and acceleration levels along with an enhancement in the dissipation rate compared to the linear case. It was observed that the occurrence of contacts facilitates energy transfer to and from the primary structure, acting as a mechanism to drive the system out of resonance, and disrupting the monotonic increase in input energy when the base excitation is applied. As the contact stiffness increases, the amount of input energy further decreases and the dissipation rate is enhanced; however, this mitigation performance is accompanied by a modest rise in floor acceleration levels attributed to the stiff impacts. Surprisingly, it was found that for a fixed contact stiffness, the amount of input energy increases when ine