Eventos Anais de eventos
CONEM 2022
XI Congresso Nacional de Engenharia Mecânica - CONEM 2022
ON THE COUPLING OF A ONE-DIMENSIONAL PERIODIC STRUCTURE TO A BEAM HOST STRUCTURE
Submission Author:
Vinícius Santos , MG
Co-Authors:
Vinícius Santos, Thiago de Paula Sales
Presenter: Vinícius Santos
doi://10.26678/ABCM.CONEM2022.CON22-0361
Abstract
Phononic crystals (PCs) and locally resonant periodic structures have been intensively studied lately, as they can provide a means for vibration attenuation. This is due to their underlying dynamic behavior, which is characterized by frequency ranges on which wave propagation is entirely evanescent, which are known as bandgaps. These can be used to achieve vibration isolation, as well as to enable localized modes, when one defect is introduced on the periodic lattice, for example. On the other hand, there remains the question if periodic structure behavior can be leveraged for structures which already exist, i.e., is it possible to couple a periodic structure appendage to an existing structure so the latter is able to benefit from bandgaps on the former? To investigate this matter, in this work one considers the coupling of a one-dimensional periodic structure (1D-PS), whose unit cell can be arbitrary, which is attached ``in parallel'' to a beam host structure (HS). The former can be either a ``conventional structure'', a PC, or even a metastructure (MS). To model the dynamic behavior of the 1D-PS, the wave-based finite element method (WFEM) is employed. A strategy is presented to duly account for non-periodicities which ensue due to coupling on particular unit cells of the waveguide. To model the dynamic behavior of the HS, one employs the spectral element method (SEM). The coupling between the 1D-PS and the HS is modeled by lumped, discrete spring elements. To account for their influence, the WFEM and SEM equations are suitably modified. Numerical simulations are performed in MATLAB\textsuperscript{\textregistered}, enabling us to obtain dispersion relations for ``coupled'' and ``uncoupled'' unit cells, and to assess the dynamics of the coupled system. Traditional finite element analysis (FEA) is also performed in order to validate in-house implemented codes, as well as the proposed modeling strategy. Longitudinal and bending behaviors are investigated separately for the considered system. In these settings, one also assesses the influence of the value of the coupling spring stiffness, which is taken to be soft or hard. It is seen that the proposed strategy for modeling the coupled system behavior is adequate. Additionally, due to the underlying characteristics of the WFEM, it has been observed that a large number of wave modes needs to be taken into account to properly represent responses.
Keywords
periodic structures, coupling, WFEM, SEM, FEA
