Resonance frequencies of piezoelectric plates surrounded by solid and fluid half-spaces

The design of ultrasound transducers, resonators and other piezoelectric devices usually requires the calculation of the resonance frequencies of piezoelectric plates. Recent studies have shown that the resonance frequencies for plates in vacuum correspond to frequencies where the waveguide group velocity vanishes (zero-group-velocity points). However, those studies are limited to vacuum boundary conditions. The objective of the present study is to analyze the resonance frequencies of layered piezoelectric plates in contact with solid and fluid half-spaces and their relation to the dispersion behavior of the elastic guided wave propagation. Theoretical analysis using partial-wave approach of leaky Lamb waves is performed to study wave propagation in, and resonance behavior of, multilayered plates in contact with solid and fluid half-spaces. A novel observation resulted from this analysis is that, for plates in contact with solid and fluid half-spaces, the resonance frequencies occur at points where the magnitude of the wavenumber reaches a minimum. This frequency is named as a ‘transition frequency’. Such observations are important because they allow an easy identification of resonance frequencies with high amplitude response directly from the dispersion curves. This study will be helpful for the design of piezoelectric components used for resonators and sensors.     

Approximations to wave propagation through doubly-periodic arrays of scatterers

The propagation of waves through a doubly-periodic array of identical rigid scatterers is considered in the case that the field equation is the two-dimensional Helmholtz equation. The method of matched asymptotic expansions is used to obtain the dispersion relation corresponding to wave propagation through an array of scatterers of arbitrary shape that are each small relative to both the wavelength and the array periodicity. The results obtained differ from those obtained from homogenization in that there is no requirement that the wavelength be much smaller than the array periodicity, and hence it is possible to examine phenomena, such as band gaps, that are associated with the array periodicity.     

气泡线性振动时近海面气泡群的声散射

海洋中的不同成因的气泡群是常见的水下声学目标及声呐混响源,因此对水下气泡群进行声学建模意义重大。利用有效媒质理论描述气泡群内部的相速度及声衰减变化,并考虑到海洋中气泡群往往产生于不同界面附近,进一步利用球面波叠加原理描述海面对气泡群散射声波的再辐射,导出了平海面作用下气泡群声散射截面的一般表达式,建立了其声散射模型,研究了单一尺寸及混合尺寸气泡群的声学特性。数值分析表明,气泡群的谐振频率会随其半径或孔隙率增加而降低;由于海面的存在,气泡群声散射截面会随频率进行周期性变化,且随气泡群远离海面,这一变化逐渐加剧。此外,若气泡的黏滞阻尼项在全部阻尼项中占比较高,气泡群声散射强度会在谐振频率附近存在起伏振荡。该模型可为近海面鱼群、气泡羽流及海底泄漏的甲烷气体的声学建模提供一定的理论基础。     

Effective response and scattering cross section of spherical inclusions in a medium

The Maxwell-Garnett theory for a right-handed homogeneous system is extended in order to investigate the effective response of a medium consisting of low density distributed 3-dimensional inclusions. The polarisability factor is modified to account for inclusions with binary layered volumes and it is shown that such a configuration can yield doubly negative effective permittivity and permeability. Terms representing second-order scattering interactions between binary inclusions in the medium are derived and are used to reformulate conventional effective medium theory. In the appropriate limit, the one-body theory of Maxwell-Garnett is recovered. The scattering cross section of the spherical inclusions is determined and comparison is made to homogeneous dielectric scatterers in the Rayleigh limit. It is found that the scattering resonances can be manipulated using the inclusion parameters. Furthermore, the effect that two-interacting spherical inclusions in a medium have on the scattering cross section is investigated via higher order dipole moments while the issue of reducing the scattering cross section to zero is also examined.     

Propagation of guided waves through weak penetrable scatterers

The scattering of a scalar wave propagating in a waveguide containing weak penetrable scatterers is inspected in the Born approximation. The scatterers are of arbitrary shape and present a contrast both in density and in wavespeed (or bulk modulus), a situation that can be translated in the context of SH waves, water waves, or transverse electric/transverse magnetic polarized electromagnetic waves. For small size inclusions compared to the waveguide height, analytical expressions of the transmission and reflection coefficients are derived, and compared to results of direct numerical simulations. The cases of periodically and randomly distributed inclusions are considered in more detail, and compared with unbounded propagation through inclusions. Comparisons with previous results valid in the low frequency regime are proposed.     

Special features of calculation for processes of scattering by contrast and strongly absorbing two- and three-dimensional inhomogeneities

A direct problem of scattering for refractive-absorbing scatterers of different shapes and strengths is considered. A rigorous solution for two- and three-dimensional problems and its numerical implementation are obtained on the basis of equations of the Lippmann-Schwinger type in the coordinate space and in the space of special frequencies that is Fourier-conjugate to it. Attention is given to selection of parameters for problem sampling that are fundamentally important for providing adequacy of numerical simulation. Techniques for restricting the Green’s function support and introducing a reserve band are used. The results of numerical calculation for wave fields and secondary sources are given for different scatterers. The major laws connected with the effects of sound wave rescattering are illustrated and discussed.     

EXACT SOLUTIONS OF CLASSICAL SCALAR FIELD EQUATIONS

We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wave-like behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term renormalized in the dispersion relation through a term depending on the coupling and an integration constant. When spontaneous breaking of symmetry is considered, such wave-like solutions show how a mass term with the wrong sign and the nonlinearity give rise to a proper dispersion relation. These latter solutions do not change the sign maintaining the property of the selected value of the equilibrium state. Then, we use these solutions to obtain a quantum field theory for the case of a quartic massless field. We get the propagator from a first-order correction showing that is consistent in the limit of a very large coupling. The spectrum of a massless quartic scalar field theory is then provided. From this we can conclude that, for an infinite countable number of exact classical solutions, there exist an infinite number of equivalent quantum field theories that are trivial in the limit of the coupling going to infinity.     

Gravitational Wave in Lorentz Violating Gravity

By making use of the weak gravitational field approximation, we obtain a linearized solution of the gravitational vacuum field equation in an anisotropic spacetime. The plane-wave solution and dispersion relation of gravitationaJ wave is presented explicitly. There is possibility that the speed of gravitational wave is larger than the speed of light and the easuality still holds. We show that the energy-momentum of gravitational wave in the ansiotropic spacetime is still well defined and conserved.     

Gravitational Wave in Lorentz Violating Gravity

By making use of the weak gravitational field approximation, we obtain a linearized solution of the gravitational vacuum field equation in an anisotropic spacetime. The plane-wave solution and dispersion relation of gravitational wave is presented explicitly. There is possibility that the speed of gravitational wave is larger than the speed of light and the casuality still holds. We show that the energy-momentum of gravitational wave in the ansiotropic spacetime is still well defined and conserved.     

Electromagnetic radiation from filamentary sources in the presence of axially magnetized cylindrical plasma scatterers

Electromagnetic radiation from filamentary electric-dipole and magnetic-current sources of infinite length in the presence of gyrotropic cylindrical scatterers in the surrounding free space is studied. The scatterers are assumed to be infinitely long, axially magnetized circular plasma columns parallel to the axis of the filamentary source. The field and the radiation pattern of each source are calculated in the case where the source frequency is equal to one of the surface plasmon resonance frequencies of the cylindrical scatterers. It is shown that the presence of even a single resonant magnetized plasma scatterer of small electrical radius or a few such scatterers significantly affects the total fields of the filamentary sources, so that their radiation patterns become essentially different from those in the absence of scatterers or the presence of isotropic scatterers of the same shape and size. It is concluded that the radiation characteristics of the considered sources can efficiently be controlled using their resonance interaction with the neighboring gyrotropic scatterers.     

Normal modes of a continuous system with quadratic and cubic non-linearities

A power series solution is presented for the free vibrations of simply supported beams resting on elastic foundation having quadratic and cubic non-linearities. The time-dependence is assumed harmonic and the problem is posed as a non-linear eigenvalue problem. The spatial variable is transformed into an independent variable that satisfies the boundary conditions. This permits a power series expansion of the beam motion in terms of the new variable. A recurrence relation is obtained from the governing equation and used in conjunction with the Rayleigh energy principle to compute the natural frequencies. The results show that, for a first order approximation, only the lower frequencies and first mode shape are significantly affected by the cubic non-linearity.     

Localization of nonlinear waves in elastic bodies with inclusions

By the example of the problem of the motion of a semi-infinite string lying on an elastic base, a method for describing wave localization near inclusions is proposed for the case of a cubic nonlinearity of the base. The method applies the perturbation technique to the amplitude of a localized mode. The nature of the divergences is revealed, and the secular terms are found to belong to one of two types: inphase or antiphase with the localized wave. It is shown that a combination of the renormalization method and multiscale method provides a convergence of the solutions, which are sought for in the form of power series in the amplitude of the localized mode. It is found that the localization process is determined by the type of the discrete spectrum, type of the nonlinearity, and type of dispersion. The nonlinearity of the elastic base produces two characteristic effects. First, the frequency of the localized wave becomes dependent on the wave amplitude. Second, the system can generate traveling waves at multiple frequencies, which withdraw energy from the localized wave and cause it to decay. The decay behavior is determined by the minimum frequency of these traveling waves (because it must be higher than the cutoff frequency). The lifetime of the localized wave as a function of the mass of a dynamic inclusion exhibits a number of maxima. In particular, the first maximum corresponds to the minimum amplitude of the traveling wave at the triple frequency.     

Dimensional optical resonances in atomic nanostructures

A nanostructural object consisting of two atoms is proven to contain two or four dimensional resonances depending on whether these atoms are identical or different. Each of the atoms is characterized by linear isotropic polarizability and contains one isolated resonance. The frequency of the dimensional resonances considerably differs from the resonance frequencies of the isolated atoms, and the effective resonance polarizabilities of the atoms in the nanostructure approximately coincide with the resonance values of polarizabilities of the isolated atoms. It is shown that, in the nanostructure consisting of two different atoms, two of four resonances have a negative dispersion. It is also shown that the nanostructural object has an induced anisotropy in the case of a fixed position of the object axis relative to the direction of incidence of the external wave.     

托卡马克等离子体的快波模转换和吸收

本文对托卡马克位形,用动力理论研究了非均匀热等离子体的ICRF快波模转换及有关的阻尼机制。结果表明,对于多种离子成分的等离子体,在离子-离子混杂共振层和二次谐波回旋共振层附近,存在快波和离子伯恩斯坦波(IBW)之间的模转换;模转换层附近的色散关系与k_(?),离子种类浓度以及等离子体密度有明显的相关性。适当选择这些参数可大大改善快波能量的吸收和吸收的局域性。而在一种离子成分的等离子体中、无模转换过程发生。     

Complete low-frequency bandgap in a two-dimensional phononic crystal with spindle-shaped inclusions

A two-dimensional phononic crystal(PC) structure possessing a relatively low frequency range of complete bandgap is presented. The structure is composed of periodic spindle-shaped plumbum inclusions in a rubber matrix which forms a square lattice. The dispersion relation, transmission spectrum and displacement field are studied using the finite element method in conjunction with the Bloch theorem. Numerical results show that the present PC structure can achieve a large complete bandgap in a relatively low frequency range compared with two inclusions of different materials, which is useful in low-frequency noise and vibration control and can be designed as a low frequency acoustic filter and waveguides. Moreover,the transmission spectrum and effective mass are evaluated to validate the obtained band structure. It is interesting to see that within the band gap the effective mass becomes negative, resulting in an imaginary wave speed and wave exponential attenuation. Finally, sensitivity analysis of the effect of geometrical parameters of the presented PC structure on the lowest bandgap is performed to investigate the variations of the bandgap width and frequency.     

Resonance blocking and passing effects in two-dimensional elastic waveguides with obstacles

Resonance localization of wave energy in two-dimensional (2D) waveguides with obstacles, known as a trapped mode effect, results in blocking of wave propagation. This effect is closely connected with the allocation of natural resonance poles in the complex frequency plane, which are in fact the spectral points of the related boundary value problem. With several obstacles the number of poles increases in parallel with the number of defects. The location of the poles in the complex frequency plane depends on the defect's relative position, but the gaps of transmission coefficient plots generally remain in the same frequency ranges as for every single obstacle separately. This property gives a possibility to extend gap bands by a properly selected combination of various scatterers. On the other hand, a resonance wave passing in narrow bands associated with the poles is also observed. Thus, while a resonance response of a single obstacle works as a blocker, the waveguide with several obstacles becomes opened in narrow vicinities of nearly real spectral poles, just as it is known for one-dimensional (1D) waveguides with a finite number of periodic scatterers. In the present paper the blocking and passing effects are analyzed based on a semi-analytical model for wave propagation in a 2D elastic layer with cracks or rigid inclusions.     

A Comparative Study of Dispersion Characteristics Determination of a Trapezoidally Corrugated Slow Wave Structure Using Different Techniques

The linear dispersion relation of a trapezoidally corrugated slow wave structure(TCSWS) is analyzed and presented.The size parameters of the TCSWS are chosen in such a way that they operate in the x-band frequency range.The dispersion relation is solved by utilizing the Rayleigh-Fourier method by expressing the radial function in terms of the Fourier series.A highly accurate synthetic technique is also applied to determine the complete dispersion characteristics from experimentally measured resonances(cold test).Periodic structures resonate at specific frequencies when the terminals are shorted appropriately.The dispersion characteristics obtained from numerical calculation,synthetic technique and cold test are compared,and an excellent agreement is achieved.     

Cubic dispersion relation for a relativistic backward-waveoscillator

The cubic approximation to the dispersion relation for a relativistic backward-wave oscillator is obtained, and the utility and limits of the approximation are presented. The approximation is obtained by Taylor series expansion of the wave admittance in the dispersion relation for the transverse-magnetic and free-streaming modes of a relativistic, thin, hollow, cylindrical electron beam moving along the axis of a disc-loaded waveguide in a strong axial magnetic field. The resulting cubic dispersion relation yields instability growth rates and frequencies which fall off beyond their maximum more sharply with increasing wavenumber than for the complete dispersion relation. The approximation is found to be quite good near the operating points of contemporary high-power relativistic backward-wave oscillators, namely, for relatively long wavelength and small ratio of Budker's parameter to the relativistic gamma factor of the beam     

Dispersion relation of LT mixed mode polaritons

Simple equations are presented for polariton dispersion relations in anisotropic medium for an arbitrary direction of wave vector, where LT (longitudinal-transverse) mixed modes occur in general. The use of the polarizability tensor defined for pure external (not for the total) field is essentially important to obtain the simple result. The relation between all the tensor components of the polarizability and dielectric function is also explicitly given. The result can be used for any elementary excitations relevant to dielectric function. In the case of multi-component excitons of LT mixed mode character, the dispersion equation is rewritten in a matrix form, which is useful to obtain the allowed values of polariton wave vector for a given frequency.     

Nanocomposite-based ultrathin polarization beamsplitter

In terms of the effective medium approximation, the optical properties of heterogeneous composite materials with disordered nanosized metal inclusions of spheroidal shape with plasmon resonances lying in the visible spectral range are studied. The conditions are analyzed under which the optical characteristics of the composite with axial symmetry of the inclusion orientation distribution with respect to a certain preferential direction significantly depends on the electric field direction in the electromagnetic wave. It is shown that, in the vicinity of the plasmon resonance of inclusions, the composite layer of subwavelength thickness may exhibit a high polarization selectivity in both reflection and transmission with moderate absorption. The effect of the orientational disorder of inclusions on the optical characteristics of a polarization splitter of this kind is discussed. The predictions based on equations of quasi-electrostatic effective-medium model agree well with the results of exact numerical solution of the Maxwell equations.