Wave attenuation investigation in a metamaterial beam using a Quad-Action vibration absorber with cascaded resonators

In this article, a new Quad-Action (QA) vibration suppression design for acoustic metamaterial beams is explored with the goal of mitigating the propagation of elastic waves. This design aims to generate two configurable and broad frequency stopbands by optimally selecting the passive parameters of the locally resonant substructures. The metamaterial beam comprises a series of miniature and evenly spaced QA vibration absorbers attached to an isotropic beam. The QA vibration absorber consists of two separate spring-mass subsystems interconnected to each isotropic beam segment at four uniformly distributed locations. An analytical approach based on finite element modeling (FEM) and Bloch's theorem is developed to showcase the presence of stopbands, resulting in the formation of two broad and configurable frequency stopbands. The design and modeling of the proposed metabeam's QA vibration absorber are illustrated. It is analytically demonstrated that the vibration suppression, and hence wave attenuation, in the presented metamaterial beam is based on the fundamental principles of basic mechanical vibration absorption. The QA absorber effectively prevents elastic wave propagation through the metabeam by generating four internal forces to counteract any incoming wave with a frequency that falls within the stopband ranges. Moreover, these internal forces can be manipulated by tailoring the effective properties of the QA vibration absorber, yielding the creation of configurable and broad stopbands. A thorough parametric investigation is conducted to analyze how the parameters of the QA absorber's subsystems, such as mass densities and stiffness coefficients, impact the locations and sizes of the frequency stopbands. The FEM simulation results exhibit a strong correlation with the dispersion curves across various prescribed configurations, providing robust validation for the proposed metamaterial design featuring the QA vibration absorber.