Abstract
This paper presents very large complete band gaps at low audible frequency ranges tailored by gradient-based design optimizations of periodic two- and three-dimensional lattices. From the given various lattice topologies, we proceed to create and enlarge band gap properties through controlling neutral axis configuration and cross-section thickness of beam structures, while retaining the periodicity and size of the unit cell. Beam neutral axis configuration and cross-section thickness are parameterized by higher order B-spline basis functions within the isogeometric analysis framework, and controlled by an optimization algorithm using adjoint sensitivity. Our optimal curved designs show much more enhanced wave attenuation properties at audible low frequency region than previously reported straight or simple undulated geometries. Results of harmonic response analyses of beam structures consisting of a number of unit cells demonstrate the validity of the optimal designs. A plane wave propagation in infinite periodic lattice is analyzed within a unit cell using the Bloch periodic boundary condition.
Highlights
This paper presents very large complete band gaps at low audible frequency ranges tailored by gradientbased design optimizations of periodic two- and three-dimensional lattices
Since a wavelength in periodic lattices is scaled with unit cell size, the low frequency band gap requires a significant increase in overall structural dimension, which is impractical
This study showed that complete band gaps exist for a certain distribution of stiffness and mass, and demonstrated how band gaps can be created at low frequency ranges by introducing a local resonator into periodic structures
Summary
The goal of the optimization is to maximize the relative band gap size between the two adjacent modes (j) and (j + 1). In the case #5 of optimal undulated design, a large complete band gap is generated between 9th and 10th modes in the frequency region 182~1,878 Hz, and the wave transmission is much lower than that of the original undulated design. The first band gap between 15th and 16th modes apparently shows low wave transmissions From this undulated design, we perform design optimization to maximize the first band gap (Case #6), and obtain the optimal design shown, where the optimal design attained significantly larger band gap in the frequency range of 166~1,019 Hz with enhanced wave attenuation, compared with those of original undulated design. The histories of design optimization for the cases are found in Supplement F
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