Chuanzeng Zhang

Bandgap calculation of two-dimensional mixed solid?fluid phononic crystals by Dirichlet-to-Neumann maps

A numerical method based on the Dirichlet-to-Neumann (DtN) map is presented to compute the bandgaps of two-dimensional phononic crystals, which are composed of square or triangular lattices of circular solid cylinders in a fluid matrix. The DtN map is constructed using the cylindrical wave expansion in a unit cell. A linear eigenvalue problem, which depends on the Bloch wave vector and involves relatively small matrices, is formulated. Numerical calculations are performed for typical systems with various acoustic impedance ratios of the solid inclusions and the fluid matrix. The results indicate that the DtN-map based method can provide accurate results for various systems efficiently. In particular it takes into account the fluid–solid interface conditions and the transverse wave mode in the solid component, which has been proven to be significant when the acoustic impedance of the solid inclusions is close to or smaller than that of the fluid matrix. For systems with an acoustic impedance of the inclusion much less than that of the matrix, physical flat bands appear in the band structures, which will be missed if the transverse wave mode in the solid inclusions is neglected.

Reducing symmetry in topology optimization of two-dimensional porous phononic crystals

In this paper we present a comprehensive study on the multi-objective optimization of two-dimensional porous phononic crystals (PnCs) in both square and triangular lattices with the reduced topology symmetry of the unit-cell. The fast non-dominated sorting-based genetic algorithm II is used to perform the optimization, and the Pareto-optimal solutions are obtained. The results demonstrate that the symmetry reduction significantly influences the optimized structures. The physical mechanism of the optimized structures is analyzed. Topology optimization combined with the symmetry reduction can discover new structures and offer new degrees of freedom to design PnC-based devices. Especially, the rotationally symmetrical structures presented here can be utilized to explore and design new chiral metamaterials.

Acousto-optical interaction of surface acoustic and optical waves in a two-dimensional phoxonic crystal hetero-structure cavity.

Phoxonic crystal is a promising material for manipulating sound and light simultaneously. In this paper, we theoretically demonstrate the propagation of acoustic and optical waves along the truncated surface of a two-dimensional square-latticed phoxonic crystal. Further, a phoxonic crystal hetero-structure cavity is proposed, which can simultaneously confine surface acoustic and optical waves. The interface motion and photoelastic effects are taken into account in the acousto-optical coupling. The results show obvious shifts in eigenfrequencies of the photonic cavity modes induced by different phononic cavity modes. The symmetry of the phononic cavity modes plays a more important role in the single-phonon exchange process than in the case of the multi-phonon exchange. Under the same deformation, the frequency shift of the photonic transverse electric mode is larger than that of the transverse magnetic mode.

Bandgaps and directional properties of two-dimensional square beam-like zigzag lattices

In this paper we propose four kinds of two-dimensional square beam-like zigzag lattice structures and study their bandgaps and directional propagation of elastic waves. The band structures are calculated by using the finite element method. Both the in-plane and out-of-plane waves are investigated simultaneously via the three-dimensional Euler beam elements. The mechanism of the bandgap generation is analyzed by studying the vibration modes at the bandgap edges. The effects of the geometry parameters of the xy- and z-zigzag lattices on the bandgaps are investigated and discussed. Multiple complete bandgaps are found owing to the separation of the degeneracy by introducing bending arms. The bandgaps are sensitive to the geometry parameters of the periodic systems. The deformed displacement fields of the harmonic responses of a finite lattice structure subjected to harmonic loads at different positions are illustrated to show the directional wave propagation. An extension of the proposed concept to the hexagonal lattices is also presented. The research work in this paper is relevant to the practical design of cellular structures with enhanced vibro-acoustics performance.

Simultaneous guiding of slow elastic and light waves in three-dimensional topology-type phoxonic crystals with a line defect

Phoxonic crystals (PXCs) which exhibit simultaneous phononic and photonic bandgaps are promising artificial materials for optomechanical and acousto-optical devices. In this paper, we theoretically investigate the phononic and photonic guided modes in the three-dimensional topology-type PXCs with a line defect. By varying the geometrical parameters, simultaneous guidance of the slow elastic and light (electromagnetic) waves can be realized. Both elastic and optical energies can be highly confined in and near the defect region. Small elastic and optical group velocities with small group velocity dispersions can be achieved. The group velocities are about 10 and 20 times smaller than the transverse velocity of the elastic waves in silicon and the speed of light in vacuum, respectively.

Topology Optimization of Chiral Phoxonic Crystals With Simultaneously Large Phononic and Photonic Bandgaps

We study theoretically the simultaneous existence of large phononic and photonic bandgaps in chiral phoxonic crystals by topology optimization. By analyzing the effect of the chiral symmetry with different material orientations in both the square and triangular lattices, we discuss the most suitable structural properties for opening large phononic and photonic bandgap widths simultaneously and demonstrate the key role of the chiral topological feature. We also present the sensitivity analysis on the optimized phoxonic crystals and suggest the relatively robust structures. It will be shown that topology optimization can discover novel types of simple structures, offering new degrees of freedom to the beneficial design of phoxonic crystals for manipulating photons with phonons.

Effective thermal conductivity of ultra-high temperature ceramics with thermal contact resistance

A model of effective thermal conductivity is established by combining the previous model of effective thermal conductivity of gas–solid composite materials and approximately effective medium theory. Based on the previous model of single idealized contact, the thermal contact resistance between the particles is considered. The study shows that the effective thermal conductivity predicted by the new model, which considers the thermal contact resistance, agrees well with the experimental data. However, the deviation of original predictions from the experimental data is rather large for the case of high porosity. The new model is applied to the effective thermal conductivity of ultra-high temperature ceramics. The predictions agree well with the experimental data.

Transmission of elastic and acoustic waves propagating in phononic crystals analyzed by a boundary element method

The transmission properties of elastic and acoustic waves propagating in a two-dimensional mixed solid-fluid phononic crystal are studied by using the boundary element method (BEM). The phononic system is composed of a series of periodically spaced infinite solids embedded in a fluid matrix, in which the solid has finite periodic layers in one direction and are periodically spaced in another direction. Taking into account the periodicity of the scattered wave field, we adopt the periodic Greens functions as the fundamental solutions, which satisfy the elastic wave/acoustic equations and the Blochs periodicity condition. Based on the periodic Greens functions, the boundary integral equations (BIEs) are constructed. For convenience, we use the constant boundary elements to discretize these BIEs. By using the boundary and continuity conditions, the discretized BIEs are solved numerically to obtain the transmitted wave field. The relations between the transmission coefficient and the frequency are determined, from which the band gaps of the phonic system can be clearly recognized. To show the efficiency and the accuracy of the present BEM, numerical examples for a mixed solid-fluid phononic system composed of steel cylinders in the water are presented. The results calculated by the present BEM are compared with those obtained by other methods. The results obtained by these methods agree well. It is shown that the present BEM is an efficient numerical method to compute the transmission properties of elastic and acoustic waves in phononic crystals with mixed solid-fluid components.

SH wave propagation along a periodic grating surface with grooves in a magneto-electro-elastic substrate

This paper investigates the shear horizontal wave (SH wave) propagation along the periodic grating surface with grooves in a magneto-electro-elastic (MEE) substrate. The theoretical derivation is given for an arbitrary surface profile. Based on the Bloch-Floquet theorem and by using the Taylor-Mclaurins series as well as the orthogonality condition of the wave modes, the mechanical, electric and magnetic boundary conditions at the profile surface are first transformed into the equivalent boundary conditions at the reference surface, and then further converted into an infinite set of linear homogeneous equations, whose determinant determines the dispersion relation. In the numerical examples, rectangular grooves are considered and the coupled-mode approximation is applied for truncating the infinite series. Numerical examples are presented for a magneto-electro-elastic (80% PZT4 and 20% CoFe2O4) composite. The results show that a band-gap occurs at the resonance frequency. With the increase of the wave-number, both the frequency and the wave velocity are reduced.

Bem based evaluation of piezoelectric crack-tip fracture parameters using interaction integral and modified crack closure integral

In this paper, the crack-tip field intensity factors of a piezoelectric crack are respectively evaluated by an interaction integral (M-integral) and a modified crack closure integral method (MCCI). By applying the dual BEM to piezoelectric crack models, the crack-tip fracture parameters using M-integral and MCCI are verified by the existing analytical solutions and compared with the results by the classical displacement extrapolation and J-integral methods. Some examples are presented to show the high accuracy of M-integral and the improvement of MCCI for the piezoelectric crack problems.