Inverse design of phononic crystals by topology optimization

Abstract

Band gaps, i.e frequency ranges for which waves cannot propagate, can be found in most elastic structures if the material or structure has a specific periodic modulation of material properties. In this paper, we maximize phononic band gaps for infinite periodic beams modelled by Timoshenko beam theory, for infinite periodic, thick and moderately thick plates, and for finite thick plates. Parallels are drawn between the different optimized crystals and structures and several new designs obtained using the topology optimization method.

Directional bending wave propagation in periodically perforated plates

“…These designs have illustrated the ability to tailor equivalent material properties, and to achieve interesting dynamic phenomena such as negative refraction [5,6,7,8], wave beaming [9], and bandgaps [10,11,12,13]. Among the configurations proposed, the use of plate structures as propagation media is an attractive solution due to the existence of several theories to support the formulation of numerical models, and the ease of experimentation provided by optical measurement systems such as scanning laser vibrometers and interferometers.…”

“…For these reasons, a number of recent studies have investigated elastic plates with periodic inclusions and voids, microstructures, and sources of impedance mismatch such as surface mounted stubs [14,15,16] to generate phononic plates and elastoacoustic metamaterials [17,18]. In particular, the work of [12,8,6,7] focuses on flexural (transverse) waves in periodically perforated plates.…”

Coupled Acoustic-Mechanical Bandgaps

“…Previous studies have shown the possibility of combining bandgaps for bending and longitudinal waves [20], and combining this with the acoustical bandgap, in order to achieve truly full bandgaps, is a natural next step.…”

A high-quality narrow passband filter for elastic SV waves via aligned parallel separated thin polymethylmethacrylate plates

“…The forbidden band gaps in PnCs tend to be relatively narrow and the waves within the forbidden band gaps are usually located in the high frequency region. This has led to the increased research in order to increase the width of forbidden band gaps [7][8][9][10] and reduce the working frequency [11][12][13] of PnCs.…”