Bloch–Floquet waves and controlled stop bands in periodic thermo-elastic structures

An algorithm for controlling the stop bands for elastic Bloch–Floquet waves within a periodic structure is proposed. Explicit asymptotic estimates of frequencies of translational and rotational standing waves, together with the numerical estimates of the stop band frequencies, are given. Thermal pre-stress is introduced and used to control the position of the stop bands on the dispersion diagram.     

Shear Bloch waves and coupled phonon–polariton in periodic piezoelectric waveguides

Coupled electro-elastic SH waves propagating in a periodic piezoelectric finite-width waveguide are considered in the framework of the full system of Maxwell’s electrodynamic equations. We investigate Bloch–Floquet waves under homogeneous or alternating boundary conditions for the elastic and electromagnetic fields along the guide walls. Zero frequency stop bands, trapped modes as well as some anomalous features due to piezoelectricity are identified. For mixed boundary conditions, by modulating the ratio of the length of the unit cell to the width of the waveguide, the minimum widths of the stop bands can be moved to the middle of the Brillouin zone. The dispersion equation has been investigated also for phonon–polariton band gaps. It is shown that for waveguides at acoustic frequencies, acousto-optic coupling gives rise to polariton behavior at wavelengths much larger than the length of the unit cell but at optical frequencies polariton resonance occurs at wavelengths comparable with the period of the waveguide.     

Propagation of elastic waves through two-dimensional lattices of cylindrical empty or water-filled inclusions in an aluminum matrix

The layer-multiple-scattering method is developed to study wave propagation through two-dimensional lattices of cylindrical inclusions in an elastic medium. The lattices are a series of periodically spaced infinite one-dimensional periodic gratings (or rows) of inclusions. The layer-multiple-scattering method allows the analysis of the reflection and transmission properties of the two-dimensional lattice, provided those of each row are known. These are later determined by means of an exact multiple scattering formalism based on modal series developments. A new characteristic equation is obtained that describes the Bloch wave propagation into the infinite lattice. Lattices with empty and fluid-filled inclusions are compared. The comparison shows the existence of pass and stop bands due to the resonances of the fluid-filled inclusions. Resonant inclusions allow the opening of narrow pass bands inside phononic stop band, which is an interesting phenomenon for demultiplexing problems. It is worth noting that inclusion resonances have nothing to do with resonances due to defects, as they involve the whole lattice. In addition, it is shown that stop bands, at an oblique incidence, due to a strong coupling between longitudinal and transverse waves, are related to dispersive guided waves that propagate in the direction of the reticular planes of the lattices.     

Li-impurity effect in optical spectra of KTaO<Subscript>3</Subscript>:Er<Superscript>3+</Superscript> crystals

The optical properties of one-dimensional photonic crystals based on porous anodic aluminum oxide films have been studied by measuring transmittance and specular reflectance spectra in the visible and UV spectral regions. Angular dependences of the spectral positions of optical stop bands are obtained. It is shown that the reflectance within the first stop band varies from point to point on the sample surface, reaching a level of 98–99% at some points. The dispersion relation for electromagnetic waves in the model of infinite periodic structure is calculated for the samples under study. The possibility of using models with an infinite or finite number of layers to calculate reflectance spectra near the first optical stop band is discussed.     

Waves in an active medium guided by a reactive surface with reactance of gain modulation

The characteristics of surface waves (i) in a passive medium supported by a passive surface with reactance modulation and an active surface with the modulation of either the reactance or the negative resistance, and (ii) in an active medium supported by a passive surface with a reactance modulation are investigated with emphasis on the band regions. The periodic variation is sinusoidal and is in the propagation direction. For a passive medium terminated by a passive surface with a reactance modulation, there are stop bands in frequency for the surface waves and the structure of the first two stop bands is analyzed. For a passive medium terminated by an active surface and for an active medium terminated by a reactance-modulated passive surface, the characteristics of the absolute instabilities occurring in the first-order band are examined. The nature of the convective instability taking place in the second-order band for an active medium terminated by a reactance-modulated surface is discussed. Analytical expressions for the frequency shift of the second-order band are deduced. The Floquet theory is used to obtain the exact dispersion relation in the form of a continued fraction which is analyzed by singular expansions.     

Sound wave motion in pipes having time-variant ambient temperature

The classical time-invariant acoustic waveguide theory is extended by allowing for temporal variations of the speed of sound. Essentially, what distinguishes the present theory from the classical waveguide theory is that, while the latter predicts stable waves for all frequencies, the present theory predicts that stable waves may occur only in certain frequency bands. Implication of the theory for engine exhaust pipes is discussed.     

Propagation of guided elastic waves in 2D phononic crystals

The phononic band structure of two-dimensional phononic guides is numerically studied. A plane wave expansion method is used to calculate the dispersion relations of guided elastic waves in these periodic media, including 2D phononic plates and thin layered periodic arrangements. We show that, for any guided elastic wave, Lamb or generalised Lamb modes, stop bands appear in the dispersion curves, displaying a phononic band structure in both cases.     

Wave transmission through structural inserts

The transmission of waves through two discontinuities in a one-dimensional waveguide system is considered. Attention is focused on transmission through a structural insert, which is defined here to be a waveguide segment which is inserted into an otherwise continuous structural member with different properties. A general expression for the net transmission through the insert is found. It has bandpass/stop characteristics and its frequency average is somewhat greater than that normally assumed due to the coherent interaction of the waves in the insert. The particular case is then considered where the insert comprises a three-layer composite beam inserted in a thin beam which vibrates in bending. The composite beam comprises two elastic faceplates and a core filled with a tunable electro- or magneto-rheological fluid. The net transmission and the stop bands depend on the properties of the insert. Since these properties are tunable by adjusting the field to which the tunable fluid is exposed, then so too are the transmission characteristics of the insert.     

A microstrip resonator filter using sandwich structure

We present results for a compact, multiple gap and multiple pass band microstrip resonator filter. The microstrip resonator filter, consisting of a sandwich substrate with a metallic fractal pattern, shows multiple gaps from 40 MHz to 10 GHz. The transmission characteristics of the microstrip resonator filter show multiple pass bands and stop bands for electromagnetic waves over the microwave frequency range. Experimental observations are in good agreement with the results of finite difference time domain (FDTD) simulations. These properties can be useful in the application in compact microwave circuits, microwave filters, and microwave switches. PACS 84.30.Vn; 84.40.Az; 95.85.Bh     

Effect of particle adhesion and interactions on motion by traveling waves on an electric curtain

A discrete-element/boundary-element method is developed for simulation of adhesive particle transport by traveling waves on an electric curtain. The study shows that both wall adhesion and particle–particle collisions have an important influence on particle transport on electric curtains at different wave frequencies. The most significant effect of particle collisions occurs for cases with medium frequencies in which particles with large negative-charge collect in high-concentration bands and move in a synchronous surfing mode, pushing forward particles with lower charge. Cases with higher and lower frequencies exhibited hopping motion, for which adhesion determines the range of non-transported particles.     

An experimental study of the characteristics of the acoustic field of zero normal plate modes

The sources of systematic errors in measuring the amplitude and propagation velocity of normal waves are analyzed. Criteria are proposed for estimating the distances beyond which a wave can be considered a normal wave. The measurement method and corresponding experimental setup are described. Experimental estimates are obtained for the distances necessary for the formation of symmetric zero modes of horizontally polarized normal waves and Lamb waves in thin strips at frequencies of 1.8 and 2.5 MHz.     

Formulation and validation of a Ritz-based analytical model of high-frequency periodically layered isolators in compression

Periodically layered isolators exhibit transmissibility “stop bands” or frequency ranges in which there is very low transmissibility. A two-dimensional axisymmetric model was developed to accurately predict the location of these stop bands for isolators in compression. A Ritz approximation method was used to model the axisymmetric elastic behavior of layered cylindrical isolators. A modal analysis was performed for a single elastomer and metal layer combination or cell. A modal synthesis approach was then used to obtain a model of an n-celled isolator, from which overall isolator modal properties are determined. This model of the dynamic behavior of layered isolators was validated with experiments. Analytical and experimental transmissibilities are compared for test specimens having identical elastomer components, but different geometries and different numbers of cells. In all cases, experimental and analytical transmissibilities are in close agreement at frequencies ranging from zero to those associated with the initial roll-off of the stop bands. For three and four cell cases, minimum stop band analytical transmissibilities lie below the minimum experimental measurements, although an experimental noise floor imposed a minimum transmissibility measurement of approximately 1.4×10⁻⁴. Experiment suggests a practical isolator design could limit the minimum number of cells to three or four to ensure a pronounced stop band attenuation effect. In addition, analytical and experimental transmissibilities are compared for geometrically similar test specimens with differing elastomeric damping properties. The analytical and experimental results show that stop band effectiveness is not appreciably affected by the addition of modest damping.     

Modelling and simulation of acoustic wave propagation in locally resonant sonic materials

Sonic crystals are artificial structures consisting of a periodic array of acoustic scatterers embedded in a homogeneous matrix material, with a usually large impedance mismatch between the two materials. They exhibit strong sound attenuation at selective frequency bands due to the interference of multiply reflected waves. However, sound attenuation bands in the audible range are only achieved by unfunctionally large sonic crystals. If local resonators are used instead of simple scatterers, the frequencies of the attenuation bands can be reduced by about two orders of magnitude. In the present paper we perform numerical simulations of acoustic wave propagation through sonic crystals consisting of local resonators using the local interaction simulation approach (LISA). Three strong attenuation bands are found at frequencies between 0.3 and 6.0 kHz, which do not depend on the periodicity of the crystal. The results are in good qualitative agreement with experimental data. We analyze the dependence of the resonance frequencies on the structural parameters of the local resonators in order to create a tool for design and optimization of any kind of sonic crystal.     

Free vibration of a thin cylindrical shell with periodic circumferential stiffeners

The theory is developed for obtaining the propagation constants of a thin uniform cylindrical shell, periodically stiffened by uniform circular frames of general cross-section. The free wave motion is analyzed and the stop and pass bands of free wave motion in the structure are located. Hysteretic damping is included. The natural frequencies of two stiffened finite cylindrical shells are deduced. The relative effects of the frame cross section and pitch on the free vibration characteristics of the whole structure are discussed.     

Ultrasonic wave interaction with multidirectional composites: modeling and experiment

Phenomena of wave transmission through a multidirectional composite laminate immersed in a fluid have been investigated. Based on a recently-developed recursive stiffness matrix method time-domain beam models have been developed to simulate the problem. Experimental and theoretical results at frequency 2.25 MHz show that the transmission amplitude is highly dependent on lamina orientation and angle of incidence. Large transmission amplitude appears at small (<10 degrees) and large incident angles (45 degrees-60 degrees). At intermediate incident angles (16 degrees-40 degrees) the transmission amplitude is almost zero. At high frequency, the residue epoxy layers between each lamina become important and corresponding resonances may be observed. These transmission phenomena have been interpreted in terms of Floquet waves. It shows that the pass and stop bands of the three Floquet waves obtained from the unit cell stiffness matrix determine the transmission amplitude distribution in frequency, incident angle and rotation angle domains. The effect of random deviation of the laminated structure periodicity has also been assessed. At normal incidence, the variation of the thickness of the epoxy residual layer between composite lamina has little effect on the overall stop and pass band structures but introduces random reverberation and scattering in the pass bands. It is shown that for oblique incidence the transmittivity spectrum of a composite with random lamina lay-up converges with increase of randomness to that of a [0/-45/90/45]2s quasi-isotropic composite. Randomization of lamina lay-up produces a small effect in the transmittivity spectrum for a quasi-isotropic composite.     

Light exiting from real photonic band gap crystals is diffuse and strongly directional

Any photonic crystal is in practice periodic with some inevitable fabricational imperfections. We have measured angle-resolved transmission of photons that are multiply scattered by this disorder in strongly photonic crystals. Peculiar non-Lambertian distributions occur as a function of frequency: due to internal diffraction, wide angular ranges of strongly reduced diffuse transmission coincide with photonic stop bands, while enhancements occur for directions outside stop gaps. We quantitatively explain the experiment with a model incorporating diffusion and band structure on equal footing. We predict that in the event of a photonic band gap, diffuse light at frequencies near band gap edges can exit only along isolated directions. Angle-resolved diffuse transmission appears to be the photonic equivalent of angle-resolved photoelectron spectroscopy.     

Spiral-wave dynamics in excitable medium with excitability modulated by rectangle wave

We numerically study the dynamics of spiral waves in the excitable system with the excitability modulated by a rectangle wave. The tip trajectories and their variations with the modulation period T are explained by the corresponding spectrum analysis. For a large T ,the external modulation leads to the occurrence of more frequency peaks and these frequencies change with the modulation period according to their specific rules,respectively. Some of the frequencies and a primary frequency f 1 determine the corresponding curvature periods,which are locked into rational multiplies of the modulation period. These frequency-locking behaviours and the limited life-span of the frequencies in their variations with the modulation period constitute many resonant entrainment bands in the T axis. In the main bands,which follow the relation T/T 12 = m/n,the size variable R x of the tip trajectory is a monotonic increasing function of T . The rest of the frequencies are linear combinations of the two ones. Due to the complex dynamics,many unique tip trajectories appear at some certain T . We find also that spiral waves are eliminated when T is chosen from the end of the main resonant bands. This offers a useful method of controling the spiral wave.     

一种减小尺寸的声彩虹捕获效应结构*

该文提出了一种减小尺寸的彩虹捕获效应结构,在铁板上刻上深度相同的空气凹槽阵列并加入周期性缝板单元,通过调节缝宽得到不同的等效折射率。该文对1000 Hz～2000 Hz的声波进行仿真实验,仿真结果表明不同频率的声波被局域在不同的位置,即实现了彩虹捕获效应。由于局域处声波群速度很小,局域处声场能量得到很大的提升。相对于传统的深度渐变的空气凹槽结构,我们的结构尺寸更小,可调性更强,更容易实现对低频声波的捕获效应。该结构具有能量加强和声波空间分离的效应,相信在声吸收、声波识别等领域有着潜在的应用前景。     

Imaging ripples on phononic crystals reveals acoustic band structure and Bloch harmonics

Broadband surface phonon wave packets on a phononic crystal made up of a microstructured line pattern are tracked in two dimensions and in real time with an ultrafast optical technique. The eigenmode distribution and the 2D acoustic band structure are obtained from spatiotemporal Fourier transforms of the data up to 1 GHz. We find stop bands at the zone boundaries for both leaky-longitudinal and Rayleigh waves, and show how the structure of individual acoustic eigenmodes in k space depends on Bloch harmonics and on mode coupling.     

Quantum photonic crystals—Quantytes

Optical properties and structural characteristics of quantum photonic crystals??quantytes??are investigated. Quantytes are crystalline structures with periodically arranged quantum dots of dielectrics, ferroelectrics, magnets, or metals. They feature so-called stop bands in which anomalous reflection of electromagnetic radiation from the photonic crystal surface is observed. It is found that quantytes are characterized by a negative refractive index and anomalous deceleration of electromagnetic waves in some spectral ranges. Possible uses of quantytes as devices for recording and reading of optical information, optical elements with negative refraction, selective mirrors, and narrow-band light filters are discussed.