Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Exploring the inertial amplification mechanism in mono-coupled periodic rod structures
Submission Author:
Gabriel Moimás , SP , Brazil
Co-Authors:
Gabriel Moimás, Paulo José Paupitz Gonçalves
Presenter: Gabriel Moimás
doi://10.26678/ABCM.COBEM2023.COB2023-1106
Abstract
Recent developments in structural vibration control have emerged from the field of metamaterials in photonics, using the concept of periodic structures. The key idea in metamaterials used for vibration control is to achieve frequency ranges where disturbances cannot propagate or are severely attenuated. These frequency ranges are called as bandgaps, stopbands or attenuation bands. There are two basic mechanisms which can be explored to create a bandgap in a structure. The first is obtained by the Bragg scattering phenomena, which tend to occur at higher frequencies ranges and depend on the geometry and size of the periodic cells. The second strategy is based on resonant attachment, that creates mechanical filter tunned at a particular narrow frequency range, associated with the internal resonance of the attachment. In this present work, longitudinal vibration on a rod structure is investigated in terms of a single cell using the displacement transmissibility, which is defined by the ratio of the displacement from one side of the cell to the displacement of the other side. The study is developed by the comparison of a simple rod-spring-rod periodic element with an alternative design consisting of a rod-spring-rod periodic elements with an inertial amplification mechanism, i. e. a rigid and massless lever, with a concentrated mass in its tip, which is directly attached to both periodic rods. Considering the oscillations of concentrated mass are small and using the energy method the equations of motion of the periodic elements are derived and an analytical solution is obtained in terms of transfer matrix and dynamic stiffness matrix. Results indicate that an introduction of the inertial amplification mechanisms provoke an anti-resonant peak, previously not seen in rod-spring-rod periodic elements, which depends significantly on the lever length and concentrated tip mass. For lower frequencies than the anti-resonant frequency, the transmissibility is decreased in relation of rod-spring-rod set up, nevertheless for higher frequencies it is found that the minimum transmissibility remain constant due the inertial force. For some relations of lever length and concentrated mass the anti-resonant peak overlaps the transmissibility peak causing a wider bandgap frequency region. This wider bandgap region can be changed and chosen by setting different lever length and concentrated mass.
Keywords
Structural Vibration, periodic structures, stop bands, inertial amplification mechanism
