Gradient-based topology optimization of soft dielectrics as tunable phononic crystals

Abstract

Dielectric elastomers are active materials that undergo large deformations and change their instantaneous moduli when they are actuated by electric fields. By virtue of these features, composites made of soft dielectrics can filter waves across frequency bands that are electrostatically tunable.To date, to improve the performance of these adaptive phononic crystals, such as the width of these bands at the actuated state, metaheuristics-based topology optimization was used. However, the design freedom offered by this approach is limited because the number of function evaluations increases exponentially with the number of design variables. Here, we go beyond the limitations of this approach, by developing an efficient gradient-based topology optimization method for maximizing the width of the band gaps in an exemplary case study. We employ a finite element formulation of the governing equations, and use the properties of each element as the design variables. In order to iteratively update the design variables, we employ gradient-based optimization, namely the Method of Moving Asymptotes. We carry out and implement fully analytical sensitivity analysis for computing the gradient of the objective function with respect to each one of the design variables. The numerical results of the method developed here demonstrate prohibited frequency bands that are indeed wider that those that were generated using metaheuristics-based topology optimization, while the computational cost to identify them is reduced by orders of magnitude.

A Ternary Seismic Metamaterial for Low Frequency Vibration Attenuation

“…Therefore, the band gap frequency range of the metamaterial structure can be calculated faster through the equivalent mass-spring model. It also can be found from Equations (19) and ( 20) that the starting frequency and the cut-off frequency is very close to the resonance frequencies of steel scatter and soil matrix, respectively. This phenomenon agrees with the vibration mode analysis conclusion in Section 3.2.…”

“…Seismic metamaterials, with their inherent ability to manipulate low frequency elastic wave propagation, provide a key route for overcoming this challenge [ 8 , 9 , 10 , 11 , 12 , 13 ]. Based on the concept of phononic crystal, seismic metamaterials can block the propagation of elastic waves in a certain frequency range, which is called band gap [ 14 , 15 , 16 , 17 , 18 , 19 , 20 ]. Therefore, seismic metamaterial shows broad development prospects for the low-frequency vibration attenuation induced by elastic wave [ 21 , 22 , 23 , 24 ].…”

Acoustic Metamaterials for Low-Frequency Noise Reduction Based on Parallel Connection of Multiple Spiral Chambers

“…The most effective strategy to broaden the sound absorption bandwidth is to combine the various resonant response units [ 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 ]. It is difficult to accurately modulate the resonance frequencies of multiple units in the membrane AM due to the difficulty in controlling the membrane tension, so it is seldom used in low-frequency broadband noise control.…”

“…Liu et al [ 26 ] proposed a multilevel Helmholtz metamaterial with deep subwavelength thickness, composed of eight Helmholtz resonators, which can achieve perfect continuous acoustic absorption in a range of 400 Hz to 2800 Hz. The topology optimization was treated as a tool by Sharma et al [ 27 , 28 ] to design the acoustic metamaterials with the wideband width, and the reported numerical framework and inferences could show their potential use in the optimal design of soft compressible composites utilized in acoustic applications. All the above studies realized broadband sound absorption in a certain frequency range, but the defect of Helmholtz metamaterial is that the resonance frequency is determined by the structural parameters.…”

Vibration Band Gap Characteristics of Two-Dimensional Periodic Double-Wall Grillages

“…Analysis shows that it is reasonable to calculate the vibration band gap characteristics of periodic grillages by the WFEM. On the basis of meeting the basic strength requirements of the structures, the optimization method of structural vibration band gap performance through reasonable structural parameter design will also become a research hotspot in the future, assisted by various band gap optimization methods, such as structural topology optimization [ 43 , 44 ] and the replacement of piezoelectric elastic or piezothermoelastic composites [ 45 , 46 ]. The premise to achieve the goal is to accurately calculate and analyze the vibration band gap characteristics of periodic grillage structures.…”