Evanescent waves in multi-resonator metamaterials: Mechanisms and characteristic parameters of wave attenuation

Cellular materials not only show interesting static properties, but can also be used to manipulate dynamic mechanical waves. In this contribution, the existence of phononic band gaps in periodic cellular structures is experimentally shown via sonic transmission experiment. Cellular structures with varying numbers of cells are excited by piezoceramic actuators and the transmitted waves are measured by piezoceramic sensors. The minimum number of cells necessary to form a clear band gap is determined. A rotation of the cells does not have an influence on the formation of the gap, indicating a complete phononic band gap. The experimental results are in good agreement with the numerically obtained dispersion relation.

Based on the principle of phononic band gap materials, the control of acoustic frequency gaps by altering the geometry of the system is analyzed in the particular case of a set of parallel solid square-section columns distributed in air on a square lattice. This system is shown to be sensitive enough to the rotation of the columns to be considered for a practical sonic band gap width engineering. For different geometric configurations, experimental and theoretical results are presented and a discussion about the application of such structures as sound insulators is discussed. We acknowledge the use of the Namur Scientific Computing Facility (Namur-SCF), a common project between FNRS, IBM Belgium, and the Facultés Universitaires Notre-Dame de la Paix (FUNDP). [C. Goffaux acknowledges the financial support of the FIRST program of the Walloon Region Government and the Research and Development Centre of Cockerill-Sambre (ARCELOR Group).]

In this work, we numerically investigate the existence of phononic band gaps in the layer-by-layer rods structure. For the numerical calculations the finite difference time domain method was used and the transmission, as well as the band structure (using periodic boundary conditions and the Bloch theorem), was calculated. Several different materials (considered as the rods materials) were examined and the effects of all the geometric parameters of the structure were also numerically investigated. The results show that this structure seems to have very promising features as a phononic crystal giving, under certain conditions, a full 3D band gap. Taking into account that it is already known for its use as a photonic crystal, a certain belief for its use simultaneously as a photonic and phononic crystal rises.

The coupling of sound to buried targets can be associated with acoustic evanescent waves when the sea bottom is smooth. To understand the excitation of flexural waves on buried shells by acoustic evanescent waves, the partial wave series for the scattering is found for cylindrical shells at normal incidence in an unbounded medium. The formulation uses the simplifications of thin-shell dynamics. In the case of ordinary waves incident on a shell, a ray formulation is available to describe the coupling to subsonic flexural waves [P. L. Marston and N. H. Sun, J. Acoust. Soc. Am. 97, 777–783 (1995)]. When the incident wave is evanescent, the distance between propagating plane wavefronts is smaller than the ordinary acoustical wavelength at the same frequency and the coupling condition for the excitation of flexural waves on shells or plates is modified. Instead of matching the flexural wave number with the propagating part of the acoustic wave number only at the coincidence frequency, a second low-frequency wave number matching condition is found for highly evanescent waves. Numerical evaluation of the modified partial-wave-series appropriate for an evanescent wave is used to investigate the low-frequency coupling of evanescent waves with flexural wave resonances of shells.

Plane wave propagation and frequency band gaps in periodic plates and cylindrical shells with and without heavy fluid loading

Evanescent acoustic-gravity waves in a rotating stratified atmosphere

This research problem is an investigation of wave propagation in a rotating initially stressed monoclinic piezoelectric thermo-elastic medium under with the effect of a magnetic field. A two-temperature generalized theory of thermo-elasticity in the context of Lord-Shulman’s theory is applied to study the waves under the magnetic field. The governing equations of a rotating initially stressed monoclinic piezoelectric thermo-elastic medium with a magnetic field are formulated. This research problem is solved analytically, for a two-dimensional model of the piezo-electric monoclinic solid, and concluded that there must be four piezo-thermoelastic waves, three coupled quasi waves (qP (quasi-P), qT (quasi-thermal), and qSV (quasi-SV)) and one piezoelectric potential (PE) wave propagating at different speeds. It is found that at least one of these waves is evanescent (an evanescent wave is a non-propagating wave that exists) and that there are therefore no more than three bulk waves. The speeds of different waves are calculated and the influence of the piezoelectric effect, two-temperature parameter, frequency, rotation, and magnetic field on phase velocity, attenuation coefficient, and specific loss is shown graphically. This model may be used in various fields, e.g. wireless communications, signal processing, and military defense equipment are all pertinent to this study.

We present an optical theorem for evanescent (near field) electromagnetic wave scattering by a dielectric structure. The derivation is based on the formalism of angular spectrum wave amplitudes and block scattering matrix. The optical theorem shows that an energy flux is emitted in the direction of the evanescent wave decay upon scattering. The energy emission effect from an evanescent wave is illustrated in two examples of evanescent wave scattering, first, by the electrical dipole and, second, one-dimensional grating with line-like rulings. Within the latter example, we show that an emitted energy flux upon evanescent wave scattering can travel through a dielectric structure even if the structure has a forbidden gap in the transmission spectrum of incident propagating waves.

Noise reduction is an interesting and important subject in the piping systems of many applications, in order to suppress noise in the pipe, many significative researches have been done. In recent years, the acoustic wave propagation in the phononic crystal pipe has received increasing attention. The characteristic band gaps in phononic crystal pipe can forbid wave to propagate within the band-gap frequency range, which provides a new way to control the noise in piping system. In this paper, the acoustic properties of phononic crystal pipe consisting of expansion chambers with the extended inlet/outlet are investigated theoretically and numerically. By combining the two-dimensional mode matching method and the transfer matrix method, the band structure and transmission loss, especially the band-gap properties of the phononic crystal structure are presented. The obtained results exhibit excellent agreement with the results from the finite element method. Then, this theoretical method is compared with the one-dimensional plane wave method, and it is found that the results from the proposed method are more accurate within the studied frequency range. Further, the effect of modal order in the band-gap frequency range is analyzed, which shows that the mode matching method has a good convergence.The wave scattering and resonance of the chamber will induce the Bragg and locally-resonant band gaps in the periodic pipe, respectively. Further analysis on the transmission coefficient in a band gap is conducted. It shows that the transmission coefficient decays exponentially with the periodic number increasing, which demonstrates that the suppression of the wave propagation in phononic crystal pipe is caused by the band-gap rather than the impedance mismatch. Then the effects of variable parameters including the lattice constant and the length of the insertion on the location and width of the band gaps are investigated. The results show that the lattice constant mainly controls the Bragg band gaps and the length of the insertion exerts a significant influence on the locally-resonant band gaps. Finally, the coupling behaviors of band gaps are studied to expand their widths. It is found that the Bragg band gaps can be coupled with the locally-resonant band gaps via changing the lattice constant and the length of the insertion, which can give rise to wider band gaps. Furthermore, the coupling between two locally-resonant band gaps is proposed by changing the length of the insertion, which also produces wider band gaps.This study can provide new ideas for designing the phononic crystal pipe to suppress the noise in piping system.

A quasi-stationary approach to particle concentration and distribution in gear oil for wear mode estimation

Evanescent waves must be considered in propagation problems whenever scattering, diffusion, or diffraction by a finite object are investigated. In the context of phononic crystals, they appear very naturally within frequency band gaps. Since no waves can propagate within a band gap, only evanescent waves are left to explain the exponentially-decreasing transmission of acoustic waves. We have extended the classical plane wave expansion (PWE) method so that it includes complex wave vectors in the direction of propagation. To do so, it is necessary to consider a fixed frequency and to solve for the wave vector, in contrast to the traditional way of obtaining band structures by considering any Bloch wave vector within the first Brillouin zone and solving for the frequency of allowed modes. The new complex PWE method has been used to generate band structures for two-dimensional silicon - void phononic crystals. Both propagative and evanescent solutions are found at once. The decay constants within band gaps are thus found and shown to depend on the wave polarization. The consideration of complex wave vectors also allows us to identify clearly the different branch systems in the band structure and to connect bands below and above band gaps. Furthermore, the distribution of the acoustic fields of evanescent modes can be computed. Their transformation from below to above a band gap as well as within the band gap itself is shown.

Over recent decades, many revolutionary research advances have proven that a deep understanding of the properties of materials can help us make innovations in mechanical, electronic, and optical fields. To modulate a tremendous range of properties, scientists have invented many artificial materials, which will be the basis of future technologies and devices. Analogously, a low-loss dielectric medium, called a photonic crystal (PtC), enables complete control over light propagation. Due to the existence of periodic potential, the electron movements in the crystal will be influenced by the Bragg scattering. Therefore, gaps may occur in the energy band structure of crystals, meaning that photonics are forbidden with certain energies in certain directions. If the material constants in the crystals are sufficiently different, we can obtain the complete band gaps, preventing light form propagating in any possible direction from any source. Since light can be prohibited in the band gap, it is possible to freely modulate the behavior of light in PtCs, e.g., designing the photonic metamaterials4–6 and low-loss optical devices. Following PtCs, the analogous concept of phononic crystals (PnCs) is proposed based on the concept that a structure with periodic elastic moduli and mass densities, resulting in elastic wave (acoustic wave) propagation, can be affected quite strongly. Many efforts have focused on designing wave dispersion through Bragg scattering or local resonances to explore important properties, such as the band gap, band edge states, and slow wave effects. Due to these fundamental properties, PnCs can be designed by selecting physical and geometrical parameters for different and surprising potential applications, e.g., damping, isolation, and rectification of acoustic or elastic waves. In addition, based on the design of equal-frequency contours, negative refraction, focusing, beam splitting, self-collimation, and acoustic diodes can be obtained. Furthermore, the introduction of defect modes (cavities and waveguides) leads to selective frequency filters, waveguides, wavelength demultiplexing devices, delayers, effective acoustic circuits, and so on. Moreover, designing structures with a deep subwavelength scale can dramatically change acoustic wave propagation, rendering it possible to achieve a superlens, high-resolution imaging, superabsorption, and a cloak via transformation acoustics. To achieve tunable and reversible PnCs, external physical stimuli such as electric or magnetic fields, tensile deformation, and variation of temperature or phase transformation play a fundamental role and provide more chances to better control the bulk waves, plate waves, and surface waves in the artificial periodic structures. Furthermore, PnCs represent an entirely novel aspect to develop new materials for manipulating heat transport by managing heat flow in the same manner as sound waves, rendering PnCs useful for future thermoelectric devices. In recent years, much effort has been aimed at simultaneous control of the acoustic and optical properties in the same system based on phoxonic crystals (PxCs). Such periodic materials, also known as phononic–photonic or optomechanical structures, have dual band gaps for both photons and phonons simultaneously, leading to quite promising applications, i.e., enhancing the acoustical–optical or optomechanical interactions, effectively manipulating photons with phonons,and colocalizing photonic and phononic resonances. Obviously, PxCs provide the interesting purpose of designing new compact acousto-optic and sensing devices, while retaining high-frequency phonons. Obviously, how to better control, localize, and guide the sound (acoustic waves) and light (electromagnetic waves) simultaneously is an appealing and challenging research topic. Throughout the developments of PtCs, PnCs, and PxCs, a great deal of interest has been devoted to material and structural parameter studies for modulating photons and phonons, based on different targets and physical properties. With the in-depth research for applications, however, we should answer the following two problems from the perspective of structural design. What structures have interesting photonic and phononic properties? How can we design a device with certain outstanding properties prepared from PtCs, PnCs, and PxCs?

A Gradient-Based Optimization Method for the Design of Layered Phononic Band-Gap Materials

Effect of soil texture on the propagation and attenuation of acoustic wave at unsaturated conditions

Capacitive micromachined ultrasonic transducer (CMUT) arrays are made up of microscale (10–100µm wide) membranes with embedded electrodes for electrostatic excitation and detection of acoustic waves. The main application of CMUTs has been in medical imaging where advantages of miniaturization and electronics integration are significant. In addition to generating bulk waves in the far-field imaging medium, CMUT arrays also support dispersive evanescent surface waves. These surface waves derive their dispersive properties not only from the periodic structure of the array, but also from the membrane resonance. The CMUTs can tune the surface wave by changing the applied bias voltage to the membranes, which in effect changes the membrane stiffness. This tunability allows the possibility of CMUTs to exploit these slowly propagating evanescent waves as a means for creating subwavelength resolution fields for high-resolution ultrasound imaging and sensing in the near field. The dispersive behavior of these evanescent surface waves propagating along a CMUT array is quantified using a computationally efficient, boundary element method based model capable of adding parameter variation enabling more realistic modeling. The model is validated with experimental data obtained from a 1×16 CMUT array with a membrane resonance tunable between 5 and 6.5MHz. The effect of random variation of the CMUT properties on the surface wave characteristics is investigated. Analysis was done on transient signals from simulations and experiments in addition to using a time-frequency method to track the group velocity that varied from 1500m/s to 400m/s.