Showing papers on "Lamb waves published in 1969"

Elastic Surface Waves in Crystals

Abstract: Elastic surface waves in a general semi-infinite, anisotropic medium are discussed in terms of a six-dimensional vector formalism. The six-dimensional state vectors have the physical significance that their first three components constitute the displacement of and their last three components the force on the surface of the medium. For a semi-infinite medium with no sources of energy in its interior, a definite relation exists between force and particle velocity at the surface. This relation defines an impedance matrix for the semiinfinite medium which is a function of frequency, wave vector, and material parameters. The impedance matrix exhibits interesting symmetry properties and provides us with some generally valid relations for surface waves. In particular, formulas for energy and power relations attain attractive forms especially suitable for numerical computation. Finally, some characteristic properties of surface waves along free surfaces are discussed, including undamped and damped ("leaky") surface waves.

Reflection of Plane Waves from the Flat Boundary of a Micropolar Elastic Half‐Space

Abstract: Reflection of plane waves from stress free flat surface of micropolar elastic half space, presenting reflection laws and amplitude ratios

Some Simple Modes of Wave Propagation in an Infinite Piezoelectric Plate

Abstract: Exact solutions of the equations of the fully coupled linear theory of piezoelectricity are obtained for some simple types of two‐dimensional waves in an infinite plate. It is shown that the coupling of the mechanical and the electrical fields can give rise to dispersion curves with complex branches and to waves that are largely confined to the region near the major surfaces of the plate.

Lamb waves in a nearly isothermal atmosphere

Abstract: If the variations in sound speed c (z) and wind u (z) with height z are not too great, there is a mode of propagation of acoustic waves in the atmosphere in which the wave energy E (z) decreases exponentially with z with a scale c02/(2 – y) g (about 16 km), and the phase speed cm is given approximately by (about 300 m s−1).

Microwave Network Methods for Guided Elastic Waves

Abstract: The possibility of obtaining true microminiaturization by the use of elastic wave circuitry on solids is hampered by the lack of knowledge regarding the behavior of the constituents of those circuits Since boundary value problems involving elastic waves in solids are generally very intricate and difficult to solve, a direct frontal attack on those problems will in many cases lead to frustration In this paper, a series of steps is outlined which avoids the frontal attack and lends itself to a systematic procedure for achieving the understanding sought It involves the application of concepts and techniques of proven value in electromagnetic microwaves to corresponding categories of problems in elastic guided waves To demonstrate the value of this approach, it is used to derive the properties of several well-known types of elastic wave on layered media, such as Rayleigh surface waves, leaky Rayleigh waves, Lamb waves, and Love waves In the building-block approach employed, the results derived separately include transmission-line models for body waves in fluids and isotropic solids, with expressions for the characteristic impedances and the velocity and stress vector mode functions, and equivalent networks for several types of interface which are constituents of the layered media mentioned above The propagation properties of the guided waves are then obtained by the use of the transverse resonance procedure in a systematic, simple, and direct fashion

On the Transmission of Plane Waves through Layered Linear Viscoelastic Media

Abstract: The propagation of two‐dimensional time harmonic waves through a plane layered viscoelastic medium is considered in terms of the equivalent elastic plane strain problem with modified Lame constants that are complex and frequency dependent. The problem is formulated directly in terms of stresses and displacements rather than potentials and is solved by matrix methods. If the incident wave is not attenuated in the direction parallel to the layering, as would occur if the incident wave were to travel through a semi‐infinite elastic half‐space before striking the viscoelastic layers, interface waves could be generated only if one of the layers is “pseudoelastic,” i.e., has at least one real wave speed. In this case, interface waves may be generated in the same manner as in the purely elastic case. If the incident wave is attenuated in this direction, however, interface waves could be generated for specific angles of incidence and material properties.

Rayleigh Waves on Curved Surfaces

Abstract: Rayleigh waves, which are elastic surface waves occurring at the interface between a solid elastic body and vacuum, are investigated. The exact solution of some canonical elastodynamic problems in a circular cylindrical geometry is given, from which the Rayleigh wave contribution is isolated. The dispersion—i.e., the dependence of the velocity of propagation of these waves on the local radius of curvature (of the interface)—is investigated. The propagation velocity diminishes as the ratio between wavelength and radius of curvature diminishes, reaching an asymptotic value at “zero wavelength.” A comparison is made with the small‐wavelength asymptotic approach of Keller and Karal, which does not take dispersion into account. It is found that the effects of dispersion should not be ignored down to rather small wavelengths. Moreover, it is found that there occurs a “critical” or “cutoff” wavelength, above which no proper Rayleigh wave can exist. Thus, a Rayleigh wave that propagates on an interface of variabl...

Rayleigh and Lamb Waves on Cylinders

Abstract: Acoustic waves propagating on the surface of solid and hollow elastic cylinders immersed in water were observed and their characteristics shown to be consistent with theory These waves were excited by an 11‐μsec pulse, projected onto the cylindrical surface at an excitation angle given by sin 1(co/cs), where co is the velocity of sound in water and cs is the velocity of the surface wave The waves may be observed, since they continually radiate energy back into the water at the excitation angle Surface waves were observed to exist on pure (98%) aluminum, 304 stainless steel, and various aluminum‐alloy cylinders Circumference‐to‐wavelength ratios were varied from 10 to 400 to discern the dispersive effects owing to the curvature of the target It was also found that inhomogeneities correlate with pure propagation characteristics in some of the targets The waves observed on air‐ and water‐filled cylinders immersed in water are shown to correspond to the symmetric and antisymmetric vibrations in the shell

Propagators of atmospheric motions 1. Excitation by point impulses

Abstract: Linear equations for the motions of inviscid ideal gas atmospheres are considered, a brief description of the climatology of the relevant propagation parameters being given An operational formalism is developed for obtaining elementary solutions for point impulse sources The propagation of a pulse according to the Boussinesq gravity wave model is analyzed in terms of convergent series solutions for small time and in terms of asymptotic series solutions for large time Elementary propagators for the gravity wave mode and buoyancy oscillation mode are defined by contour integrals about the singularities of the propagator operator The theory is extended to the propagation of a pulse in a stratified compressible atmosphere All motion is then confined within an acoustic front expanding radially with the speed of sound Series solution in powers of the distance behind the front is described Sufficiently far behind the front, the motion is given by an acoustic oscillation, buoyancy oscillation, and gravity wave mode Consideration of the analogous problem, except for a hydrostatic atmosphere on a rotating plane, indicates when and where the assumptions of hydrostatic balance and absence of rotation are tenable With rotation, a potential vorticity mode describing time-independent motion also occurs, or, if the variation of the earth's vorticity is included in the model, Rossby waves occur Addition of a lower boundary is discussed with emphasis on the horizontal propagation of the Lamb wave mode Impulsive addition of heat excites a Lamb pressure wave pulse strongly modulated by buoyancy oscillations

Pulsed Circumferential Waves on Aluminum Cylinders in Water

Abstract: Three types of waves that contribute to the total acoustic diffracted field of an aluminum cylinder in water are isolated by generating each wave to the exclusion of the other two. The “Franz‐type” or “creeping” wave is generated separately on the outside of aluminum cylinders with ka values ranging from 54 to 1008. The circumferential‐wave speed is found to be 1% less than that of the free waterborne wave, in agreement with the theory for a rigid cylinder. The attenuation of these waves on aluminum cylinders is significantly less than that predicted by the theory for the rigid cylinder. Another circumferential wave, with approximately a 30° incidence and emergence angle, is found to propagate on the inside of the curved boundary. This wave has an attenuation ranging between 0.10 and 0.18 Np/rad and has a speed of 2.5 times that of the free waterborne wave. This is classified as a “Rayleigh type” wave. A third wave is observed that is similar to the wave generated at 30° incidence but has a 15° incidence and emergence angle. The attenuation is between 0.08 and 0.14 Np/rad and has a speed of 6.5 times that of the free waterborne wave. Experimental measurements of differential‐scattering cross section are compared with those calculated by means of the creeping‐wave formulation.

Velocity logger for logging intervals

Abstract: Method and apparatus for acoustically logging of a borehole wherein a beam of ultrasonic energy is transmitted from the borehole to the formation to produce substantially only shear waves in the formation. The shear waves are received at a position spaced from the point at which the acoustical waves were generated. The system includes means to measure the time required for the shear waves to travel from the transmitting point to the receiving point and/or the reduction in amplitude of the received shear waves.

Seismic pulse in a layered sphere: Normal modes and surface waves

Abstract: An exact solution is obtained for the displacement of the surface of a layered sphere caused by an explosive point source located within the sphere. The solid elastic mantle and the fluid core have densities and elastic constants taken as averages for Bullen's model B. For all modes of periods 4 sec and longer seismograms were computed at several distances from deep and shallow sources. They show Rayleigh waves, higher-mode surface waves, and reflected and diffracted waves. Stoneley waves are found to be due to a source located on the interface. Rayleigh waves are more highly dispersed in the layered sphere than in the homogeneous sphere. Second-mode surface waves have a larger angular component than radial component, and in most cases under consideration they have a larger angular component than any other arrival. The third higher-mode surface waves have a larger radial component. The correspondence between reflected pulses and several modes of surface waves is discussed.

Wave propagation in inhomogeneous elastic media, solution in terms of Bessel functions

Abstract: Wave propagation in an inhomogeneous elastic solid, when the elastic parameters of the solid depend on one space co-ordinate only, is considered. The stress and displacement components are assumed to depend on this same space co-ordinate and time alone. For the situations considered here the motion is governed by the wave equation with variable wave speed. The values of the elastic parameters which correspond to the solution of this equation in terms ofBessel functions are determined and some particular problems are considered.

Dynamics of Fixed Towers in Deep-Water Random Waves

Abstract: This paper is concerned with the design of offshore, bottom-supported structures which are subject to deflections and stresses due to deep water wave forces. Both periodic and random waves are considered. It is shown that the wave force on the structure can be adequately expressed by the inertia force component and that this linearization of the wave force expression leads to a criterion for the optimum spacing of structural supports which is a function of the random wave spectrum. Equations for the dynamic response of the platform are developed. The theoretical considerations were verified experimentally and the results indicated that for structures designed with optimum support spacing, the magnitude of structural response is relatively insensitive to wave direction.

Multiple scattering of plane harmonic elastic waves in an infinite solid by an arbitrary configuration of obstacles

Abstract: The multiple scattering of plane harmonic P and S waves in an infinite elastic solid by arbitrary configurations of obstacles is considered. Integral equations relating the far-field multiple scattering amplitudes to the corresponding single scattering functions are obtained and asymptotic solutions are found by an iterative procedure. The scattering of a plane harmonic P wave by two identical rigid spheres is investigated.

Modulated simple waves: an approach to attenuated finite amplitude waves

Abstract: : The paper describes some of the techniques which are currently being used to investigate finite amplitude waves in elastic and viscoelastic materials In particular we show how the simple wave solutions, which describe finite amplitude plane progressing waves in elastic materials, may be modified to describe the effects of reflection from boundaries, deformations behind curved wave fronts, and the effects of locally small damping mechanisms

On the propagation of acoustic gravity waves over a spherical earth

Abstract: Acoustic gravity waves, propagating over a spherical earth with an isothermal and windless atmosphere, are considered. The perturbed pressure is expressed as a sum of discrete modes which are shown to be orthogonal. It is found that the excitation for the modes is determined by the specified normal particle velocity over a conical surface enclosing the source. One of the modes excited is shown to have characteristics closely akin to a Lamb wave on a flat earth for an isothermal atmosphere.