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DINAME2019
DINAME2019
Shape optimization and forced response of phononic crystals using a spatial state space formulation
Submission Author:
José Arruda , SP
Co-Authors:
Vinícius Dias de Lima, Juan Camino, Jose Maria Campos dos Santos, José Arruda
Presenter: José Arruda
doi://10.26678/ABCM.DINAME2019.DIN2019-0090
Abstract
Due to Bragg type interference, periodic structures exhibit frequency bands where waves cannot propagate, the so-called bandgaps. These bands can be investigated using dispersion diagrams (i.e., wavenumber versus frequency plots), which are usually obtained using the Plane Wave Expansion (PWE) method. The spatial periodicity can be of the geometrical type, material type, or both. In this work we investigate geometrically periodic acoustic ducts aiming at optimizing a low frequency band gap. The periodic cell shape is optimized using different parametric strategies. The possibility of optimizing the spatial Fourier coefficients of the PWE method is one of these strategies. Given that the optimized shape is arbitrary, a spatial state space formulation is used to obtain a spectral element representation of the periodic cell. This strategy consists of transforming the boundary value problem in an initial value problem and recasting the latter into an impedance formulation in the form of a Riccati equation. Imposing arbitrary boundary conditions, a set of linear equations allows the computation of a spectral dynamic stiffness matrix, which can be used to compute the forced response of a structure composed of a finite number of periodic cells. This spectral solution is validated using an axisymmetric acoustic Finite Element (FE) model of the whole structure. Experimental results are also shown to validate the proposed models and optimization strategy.
Keywords
Phononic Crystals, Acoustics, size and shape optimization, state space model
