Piezoelectromagnetic waves guided by the surface of a ceramic cylinder

Summary The propagation of shear horizontal (SH) waves over the surface of a circular cylinder of polarized ceramics is studied from the three-dimensional equations of linear piezoelectromagnetism with full electromagnetic coupling. An exact solution is obtained.     

Propagation of thickness-twist waves in a piezoelectric ceramic plate in contact with viscous fluids

We study theoretically the propagation of thickness-twist waves in an unbounded piezoelectric ceramic plate with unattached electrodes and viscous fluids between the plate surfaces and the electrodes. Based on the theories of piezoelectricity and viscous fluids, an equation that determines the dispersion relations of the waves is obtained, showing the dependence of the phase velocity on material and geometric parameters. Due to the viscosity of the fluid, the dispersion relations are complex in general, representing damped waves with attenuation. The dispersion relations obtained can reduce to the results of a few special cases with known results. The results of the present paper are useful for developing and designing fluid sensors for measuring fluid viscosity or density.     

Thermoelastic waves in a thin plate

Summary In the present work we deal with the propagation of thermoelastic waves in a thin plate occupying the Cartesian space (x ₁[–, +],x ₂[–, +],x ₃[–, +]). The analysis is based on the generalized theory of thermoelasticity proposed by Lord and Shulman modified for plane stress problems. A mathematical analysis is presented to study the wave motion characteristics of the plate and the proposed analysis is applied for the special cases of very short and very long waves.     

Edge waves in a thermoelastic plate

Temperature-rate-dependent thermoelasticity theory is employed to study waves propagating along the edges of a thin flat plate of infinite length, which is in a state of plane stress. Governing equations of the plane stress problem are derived and it is found that the speed of heat waves in this problem is, in general, less than that in the plane strain and the general three-dimensional problems. The waves of the desired type are analysed for isothermal and insulated edge conditions, and the paths of particles as well as the cut-off frequencies are determined. Waves in a thin bar and in a semi-infinite plate are discussed as limiting cases. The effects of the finiteness of the neat propagation speed are analysed in some detail.     

Temperature stresses in a heat-sensitive ceramic plate

The quasistatic thermoelastic state of a rectangular ceramic plate freely supported around the perimeter is discussed. The problem is reduced to the solution of a system of nonlinear inhomogeneous integrodifferential equations consisting of a nonlinear differential heat-conduction equation with allowance for the temperature dependence of the thermophysical characteristics of the material and an integrobiharmonic equation characterizing the plate's deflection. The expression for the components of the temperature stresses caused by a nonlinear temperature field are derived in the form of ternary series. The thermoelastic state is calculated for a rectangular backing-type plate produced from the commercial ceramic VK 94-1.Translated from Problemy Pochnosti, No. 10, pp. 88–93, October, 1990.     

Thermal coupling of waves in a plate

Summary It is shown within the framework of the linear theory of thermoelasticity that, for thermal radiation conditions at the boundary, pure compressional and flexural modes of motion cannot exist in a traction-free plate. Rigorously, the modes become uncoupled only for the special cases of isothermal and adiabatic boundary conditions: approximately, however, they are uncoupled even in the general case if the analysis is confined to the lowest-order terms in the small dimensionless frequency associated with such problems. Then the motions represent generalizations of the classical Rayleigh-Lamb waves. The effect of thermal conductivity is to reduce the phase velocity and introduce disipation, and is noticeable primarily for long waves.

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Thermische Kopplung von Wellen in einer Platte

Zusammenfassung Im Rahmen der linearen Thermoelastizitätstheorie wird gezeigt, daß in einer Platte mit Wärmestrahlung und Spannungsfreiheit an den Oberflächen reine Kompressions- und Biegeformen der Bewegung nicht auftreten können. Streng genommen entkoppeln sich die beiden Formen nur für isotherme oder adiabatische Bedingungen an den Oberflächen; näherungsweise, sofern die Untersuchung sich auf die Werte niedrigster Ordnung in der solchen Problemen zugeordneten dimensionslosen Frequenz beschränkt, entkoppeln sie sich auch im allgemeinen Fall. Die Bewegungen sind dann Verallgemeinerungen der klassischen Rayleigh-Lamb-Wellen. Durch die thermische Leitfähigkeit wird die Phasengeschwindigkeit vermindert und die Bewegungen gedämpft, insbesondere für lange Wellen.

     

Steady microwave heating of a ceramic plate

A model is developed of interaction between microwave radiation and a flat ceramic plate made of alumina. A calculation is performed of the thermal and electromagnetic characteristics of the plate in the air depending on the power and frequency of electromagnetic field.     

Shear waves in a fluid saturated elastic plate

In the present context, we consider the propagation of shear waves in the transverse isotropic fluid saturated porous plate. The frequency spectrum for SH-modes in the plate has been studied. It is observed that the frequency of the propagation is damped due to the two-phase character of the porous medium. The dimensionless phase velocities of the shear waves have also been calculated and presented graphically. It is interesting to note that the frequency and phase velocity of shear waves in porous media differ significantly in comparison to that in isotropic elastic media.     

Phononic plate waves

In the past two decades, phononic crystals (PCs) which consist of periodically arranged media have attracted considerable interest because of the existence of complete frequency band gaps and maneuverable band structures. Recently, Lamb waves in thin plates with PC structures have started to receive increasing attention for their potential applications in filters, resonators, and waveguides. This paper presents a review of recent works related to phononic plate waves which have recently been published by the authors and coworkers. Theoretical and experimental studies of Lamb waves in 2-D PC plate structures are covered. On the theoretical side, analyses of Lamb waves in 2-D PC plates using the plane wave expansion (PWE) method, finite-difference time-domain (FDTD) method, and finite-element (FE) method are addressed. These methods were applied to study the complete band gaps of Lamb waves, characteristics of the propagating and localized wave modes, and behavior of anomalous refraction, called negative refraction, in the PC plates. The theoretical analyses demonstrated the effects of PC-based negative refraction, lens, waveguides, and resonant cavities. We also discuss the influences of geometrical parameters on the guiding and resonance efficiency and on the frequencies of waveguide and cavity modes. On the experimental side, the design and fabrication of a silicon-based Lamb wave resonator which utilizes PC plates as reflective gratings to form the resonant cavity are discussed. The measured results showed significant improvement of the insertion losses and quality factors of the resonators when the PCs were applied.     

磁电弹功能梯度材料板中的波动特性

假设材料常数和电、 磁常数沿板厚方向呈梯度变化, 将电磁功能梯度材料板沿厚度方向划分为层单元, 建立单元的控制方程, 然后根据单元之间的连续条件将单元控制方程装配成系统的控制方程, 求解控制方程, 得到不同模态波的弥散曲线, 分析了电磁参数对波的弥散特性的影响, 同时研究了材料梯度对弹性位移、 静电势和静磁势分布的影响, 并对磁电功能梯度材料中波的六个特征波面进行了分析。计算结果表明材料梯度引起弹性位移、 静电势、 静磁势的分布集中于材料参数梯度减少的方向, 材料为正交各向异性弹性材料。      

Theoretical analysis of a ceramic plate thickness-shear mode piezoelectric transformer

We perform a theoretical analysis on a ceramic plate piezoelectric transformer operating with thickness-shear modes. Mindlin's first-order theory of piezoelectric plates is employed, and a forced vibration solution is obtained. Transforming ratio, resonant frequencies, and vibration mode shapes are calculated, and the effects of plate thickness and electrode dimension are examined.     

Rayleigh-Lamb waves in magneto-thermoelastic homogeneous isotropic plate

The propagation of magnetic-thermoelastic plane wave in an initially unstressed, homogeneous isotropic, conducting plate under uniform static magnetic field has been investigated. The generalized theory of thermoelasticity is employed, by assuming electrical behaviour as quasi-static and the mechanical behaviour as dynamic, to study the problem. The secular equations for both symmetric and skew-symmetric waves have been obtained. The magneto-elastic shear horizontal (SH) mode of wave propagation gets decoupled from rest of the motion and it is not influenced by thermal variations and thermal relaxation times. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to Rayleigh surface wave frequency equation, because a finite thickness plate in such a situation behaves like a semi-infinite medium. Thin plate results are also deduced at the end. Dispersion curves are represented graphically for various modes of wave propagation in different theories of thermoelasticity. The amplitudes of displacement, perturbed magnetic field and temperature change are also obtained analytically and computed numerically. The result in case of elastokinetics, magneto-elasticity and coupled magneto-elasticity has also been deduced as special cases at appropriate stages of this work.     

斜面型厚度变化板中导波的研究

针对单一模式导波入射的情况，利用混和边界元模型计算了斜面型散射区域的反射系数和透射系数与各种入射模式、入射频率以及斜面倾角变化的关系，研究了在单一模式导波入射时导波与散射体的相互作用。文章的结果可以用来提高大量实际的无损检测工程中的检测灵敏度与能量的穿透能力，尤其是在那些发生了斜面状厚度变化波导中的情形。     

The interaction of shock waves with a boundary layer on a sharp plate and a blunted plate

The interaction of shock waves with a turbulent boundary layer on a sharp plate and a blunted plate is numerically investigated. The shock waves in the flow are generated by wedges installed on the flat plate. The flow is simulated by the dynamic equations of a viscous perfect gas. The effect of the blunting radius of the plate’s leading edge and the wedge angle on the flow field and the local aerodynamic coefficients is shown. The calculated results are in agreement with the experimental data.     

Oblique diffraction of surface waves by a submerged vertical plate

A train of small-amplitude surface waves is obliquely incident on a fixed, thin, vertical plate submerged in deep water. The plate is infinitely long in the horizontal direction. An appropriate one-term Galerkin approximation is employed to calculate very accurate upper and lower bounds for the reflection and transmission coefficients for any angle of incidence and any wave number thereby producing very accurate numerical results.     

Propagation of thickness-twist waves in a quartz plate with asymmetric mass layers

An exact solution is obtained for thickness-twist waves in a quartz plate with asymmetric mass layers. A simple, approximate expression for cutoff frequencies is given.     

Dispersive waves in composites, a comparison between various laminated plate theories

The exact Rayleigh-Lamb wave dispersion spectrum of laminated plates is obtained by applying a recursive algorithm developed for the analysis of stress waves in anisotropic layered media. Results from this benchmark problem are used in comparisons between the classical laminated plate, first-order shear deformation, and two higher-order shear deformation theories. Attention is paid to the effects of the number of layers, direction of propagation, and lay-up (symmetric or asymmetric), on the range of frequencies where these theories apply.     

板状功能梯度材料中的超声波频散特性的计算

1引言功能梯度材料(FGM)是一种新型的复合材料。在材料的制备过程中,根据其使用要求,连续地改变材料的各组分含量和微观结构,使材料常数在空间位置上呈现出梯度变化,从而使材料的性质和功能     

Hydroelastic behaviour of compound floating plate in waves

The paper deals with the plane problem of the hydroelastic behaviour of floating plates under the influence of periodic surface water waves. Analysis of this problem is based on hydroelasticity, in which the coupled hydrodynamics and structural dynamics problems are solved simultaneously. The plate is modeled by an Euler beam. The method of numerical solution of the floating-beam problem is based on expansions of the hydrodynamic pressure and the beam deflection with respect to different basic functions. This makes it possible to simplify the treatment of the hydrodynamic part of the problem and at the same time to satisfy accurately the beam boundary conditions. Two approaches aimed to reduce the beam vibrations are described. In the first approach, an auxiliary floating plate is added to the main structure. The size of the auxiliary plate and its elastic characteristics can be chosen in such a way that deflections of the main structure for a given frequency of incident wave are reduced. Within the second approach the floating beam is connected to the sea bottom with a spring, the rigidity of which can be selected in such a way that deflections in the main part of the floating beam are very small. The effect of the vibration reduction is quite pronounced and can be utilized at the design stage.     

Heat transfer between a ceramic plate and the flame of a moving plasmotron

The procedure and results for determining the amount of heat entering a plate with the motion of a plasmotron with different velocities are presented.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 46, No. 3, pp. 466–469, March, 1984.