The objective of this paper is to present a peer-review of the literature and trends surrounding the design of phononic crystals (PnCs) using topology optimization methods. After first providing a brief review of new developments, improvements, and applications of PnCs, this paper investigates the techniques and applications of topology optimization methods for phononic band gaps and functional structures. Both gradient-based and non-gradient-based topology optimization methods have been employed in the design of PnCs. The advantages and drawbacks of the methods used in this area are discussed in detail in this paper. Based on observations of the current state, we highlight suggestions and ideas for future research in the field of phononic crystal design optimization. The paper examines how applying topology optimization techniques into the design of PnCs yields promising performance and functions. This literature survey is designed to provide an overview of the recent advances and novel applications of popular topology optimization methods for the design of PnCs.

A comprehensive survey on topology optimization of phononic crystals

The paper analyses the wave propagation through a piezoelectric semiconductor slab sandwiched by two piezoelectric half-spaces. The two piezoelectric half-spaces (left and right) are both AlN materials, the middle piezoelectric semiconductor slab is ZnO material and is assumed to be transversely isotropic. The semiconductor effect is emphasized by considering the coupling mechanical displacement, electric potential and the carrier in the slab. The state transition differential equation is derived based on the reduction of order of the governing equations and the transfer matrix of state is obtained by solving the state transition equation. The present method can deal with not only the homogeneous slab but also the heterogeneous slab. Two cases (incident QP wave and incident QSV wave) are considered, and the energy reflection and transmission coefficients varying with the incident angle are calculated. The results show that the steady carrier density and the exterior biasing electric field have obvious influences on the reflection and transmission coefficients. This investigation provides a new thought for the adjustment and controlling of elastic wave propagation in the laminated structures.

Wave propagation through a piezoelectric semiconductor slab sandwiched by two piezoelectric half-spaces

Evanescent Bloch waves and complex band structure in magnetoelectroelastic phononic crystals

The propagation of longitudinal acoustic waves in a 1D phononic crystal (PnC) contains a piezomagnetic material (Terfenol-D) as a defect layer is analyzed and discussed theoretically. A resonant mode was generated inside the phononic band gap when the piezomagnetic material thickness becomes around its half wavelength. The present results revealed that the frequency of the generated resonant mode can be controlled by applying an external magnetic field. In addition, the resonant mode is shifted towards higher and lower frequencies by applying an external pressure on the PnC structure. The simulated results are very valuable in the application of sensors measuring magnetic fields and in the early detection of building cracks.

Acoustic Wave Sensor Based on Piezomagnetic Phononic Crystal

Bandgaps in functionally graded phononic crystals containing graphene origami-enabled metamaterials

The band gaps of a laminated piezoelectric/piezomagnetic phononic crystal with graded interlayer are studied in this paper. First, the transfer matrix method and the Bloch theorem are used to derive the dispersion equation. Next, the graded interlayer with different gradient profiles between the piezoelectric and the piezomagnetic materials is considered. The graded interlayer is modeled as a system of homogenous sublayers with both piezoelectric and piezomagnetic effects simultaneously. The effect of the graded interlayer on the band gap is introduced by inserting an additional interlayer transfer matrix in the calculation of the total transfer matrix. Finally, the dispersion equation is solved numerically, and the dispersive curves are shown in the Brillouin zone. The band gaps of the phononic crystal with graded interlayer are compared with that without graded interlayer. The influences of the graded interlayer with different gradient profiles on the band gap of a laminated piezoelectric/piezomagnetic phononic crystal are discussed based on the numerical results.

Band gap of piezoelectric/piezomagnetic phononic crystal with graded interlayer

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Band gap of piezoelectric/piezomagnetic phononic crystal with graded interlayer