Showing papers on "Lamb waves published in 1972"

Analysis of the resistance increase in waves of a fast cargo ship

Abstract: A new method to calculate the added resistance of a ship in longitudinal waves is discussed. For the particular case of a fast cargo-ship the calculated values are compared with experimental results, and a satisfactory agreement is shown. In addition the experiments with the considered shipform confirm that added resistance varies as the squared wave height for constant speed and wave length.

Lamb waves in the presence of realistic distributions of temperature and dissipation

Abstract: Lamb waves are the fundamental free oscillations of a dissipationless, compressible, isothermal atmosphere. They can exist at all periods (less than a pendulum day) and though their energy is confined to within a few scale heights of the surface, their amplitudes increase exponentially with height. When realistic temperature distributions or dissipation or both are included then for periods in excess of about 15 min truly free oscillations no longer exist. However, there do exist oscillations analogous to Lamb waves that yield a highly magnified response to forcing and that should therefore dominate the atmospheric response to various lower atmosphere excitations. The lifetime (or equivalently the magnification) is shown to depend primarily on surface friction. The amplitudes of such waves grow with altitude until limited by a combination of molecular diffusion and ion drag. The detailed vertical structure of such waves is described.

The propagation of a weak nonlinear wave

Abstract: We consider the propagation of a weak nonlinear wave whose energy is concentrated in a narrow band of wavenumbers in a fluid which is both dispersive and dissipative. We use the small amplitude equations of Whitham's theory of slowly varying wave trains, modified slightly to include dissipation, to show that the modulation of the wave may be described by a nonlinear Schrodinger equation. For long waves which are purely dispersive we obtain the Kortewegde Vries equation, and for long waves which are dissipative we obtain Burgers’ equation by suitable transformations of the nonlinear Schrodinger equation. We mention the problem of Stokes waves in deep water and comment briefly upon invariant far-field theory.

Wave propagation in a micropolar elastic half-space

Abstract: Wave propagation in an infinite micropolar elastic half space and the reflection of plane longitudinal displacement waves from a fixed flat surface of a micropolar elastic half space are investigated. Reflection laws and amplitude ratios are presented for specific cases. New propagating and reflected waves are found in addition to the classical ones.

Elastic surface waves

Abstract: Devices that exploit the properties of elastic surface waves can perform very complex signal‐processing functions, identical to those carried out by conventional electromagnetic devices. The great advantage to using surface waves instead of electromagnetic waves is the tremendous reduction in size of surface‐wave devices compared to their electromagnetic counterparts. This great reduction in size is the result of the great difference between the elastic and electromagnetic velocities. Surface waves propagate at velocities approximately 105 times slower than electromagnetic velocities; thus, at the same frequency, the elastic wavelength is 105 times shorter than the electromagnetic wavelength. A further advantage is that the energy in the elastic surface wave can readily be sensed anywhere along its path.

Phase and signal velocities of waves in dissipative media. Special relativistic theory

Abstract: The signal and phase velocities (and their frequency dependence) for all possible plane waves in a relativistic gas (of molecules or photons) with dissipation have been determined from the linearized relativistic 13-moment theory For each direction in 3-space, and for each frequency, one transverse and two longitudinal waves were found (In addition, some waves are associated with the mass flow and have the mass flow speed) Of the longitudinal waves, the fast one is a pressure (sound) wave It is accompanied by a slow longitudinal thermal dissipation wave and a transverse viscous dissipation wave The pressure wave has a velocity larger than the Laplace adiabatic speed of sound, while the two dissipation waves have a velocity less than the Laplace speed All the speeds have been expressed explicitly in terms of quantities associated with the state of equilibrium which existed before passage of the wave It has also been shown that in the ultrarelativistic limit (extremely high temperatures) all signal speeds remain less than the speed of light in vacuo

Analysis of Floating Plate under Ocean Waves

Abstract: The interactions between a large elastic floating plate and ocean waves are investigated. The plate is moored to the ocean bottom and the type of waves considered are either wind-induced random waves or Tsunami-runup-like tidal waves. The analysis is based on a boundary-value problem formulation; i.e., the plate and ocean together are considered as an integral system and related through the continuity conditions at the fluid-solid interface. The wind-induced random waves are simulated through a digital computer according to the spectrum of ocean surface elevation and the response analyses are performed in the time domain using a technique consisting of modal expansion and numerical integration. The results show that a large floating plate with or without anchors can be excited by waves with wave length comparable to the width of the plate producing very large bending moments.

Wave-propagation in uniaxially-stressed elastic media

Abstract: The propagation of waves of small amplitude in an elastic medium, with a particular form of strain-energy function, and subjected to a large homogeneous uniaxial stress, is considered in detail. The main characteristics, including speed and polarisation, of these waves in an unbounded medium are calculated numerically, and the existence and general properties of Rayleigh waves on the surface of a semi-infinite medium are investigated.

Wave propagation in elastic membranes

Abstract: The problem of wave propagation in linear elastic membranes is treated using the method of Hadamard. Speeds of propagation, wave shape and decay, as well as coupling effects, are obtained for longitudinal and transverse waves. Examples are considered which illustrate the features of the theory.

Probing of acoustic shear wave radiation in surface wave devices

Abstract: Simultaneous Rayleigh and shear wave generation has been achieved using interdigital transducers on a yz LiNbO3 sample at a frequency of 104 MHz. A large‐diameter laser beam of 5145‐A wavelength and 1‐W cw power was transmitted through the sample and was modulated by two acoustic waves. The double‐modulated laser beam causes fringes at the recording plane, which were used for an accurate determination of the shear wave velocity vs and of the shear wave acoustic radiation angle α into the crystal. It was found that vs = 3.547 ×103 m/sec for α = 14.3°. The shear wave conversion loss of the transducer was approximately 6 dB.

Reflection and transmission of elastic waves by a moving slab

Abstract: Scattering of elastic waves by a moving slab is considered. Two cases corresponding to strong contact and good lubrication are treated. It is shown that the motion introduces new effective compressional and shear wave velocities in the moving slab. The amplitude of the reflection and transmission coefficients are given for various angles of incidence, frequencies and velocities of motion.

Wave propagation in elastic shells

Abstract: The problem of wave propagation in shells within the framework of a simplified linear shell theory is treated using the method of Hadamard. Speeds of propagation, wave shape and decay, as well as coupling effects, are obtained for longitudinal, transverse and bending waves. The theory is applied to wave propagation on a spherical shell.

Wave-front singularities for two-dimensional anisotropic elastic waves.

Abstract: Wavefront singularities for the displacement functions, associated with the radiation of linear elastic waves from a point source embedded in a finitely strained two-dimensional elastic solid, are examined in detail. It is found that generally the singularities are of order d to the -1/2 power, where d measures distance away from the front. However, in certain exceptional cases singularities of order d to the -n power, where n = 1/4, 2/3, 3/4, may be encountered.

Waves in Solid Media and Loads on Structures

Abstract: : The book considers the propagation of shock and continuous waves in solid plastic media, wave refraction on media interfaces, and also interaction with the elements of structures. The problem of considering viscous properties of media when solving certain wave problems is considered. The results are applied also to waves in rods. Specific attention is given to the presentation of laboratory findings on the dynamic properties of soils and on the regularities of the propagation of pressure waves in soils. Information from the general theory of shock waves, which is necessary for understanding the basic material, is presented. (Author)

Fracture by Shear Waves

Abstract: The equation of motion and the stability conditions for cracks interacting with transversal waves and surface waves are given. Threshold conditions for crack propagation relate the crack to a critical duration of the pulse and a second condition gives a relation between initial pulse amplitude and crack length. For surface waves the influence of the length is overshadowed by the penetration depth of the wave. For longitudinal, as well as for transversal pulses, the pulse must have a least‐action density in order to propagate a crack. This law loses its meaning for surface waves. Some applications of the derived results to fracture by earthquakes are indicated.

Analysis of Wave Propagation in Elastic Cylindrical Shells by the Perturbation Method

Abstract: Description of the perturbation method for solving propagation problems of transient, axisymmetric stress waves in elastic cylindrical shells. It is shown that the method provides remarkably accurate solutions for these problems and that it can be applied to a variety of related problems, such as the propagation of compressional waves in elastic rods.

Asymptotic Solution of the Wave Equation with Variable Velocity and Boundary Conditions

Abstract: The wave equation is considered in media with variable velocity of propagation and a plane interface. The singular part of the Green’s function is constructed as a sum in which the $( {N + 1} )$st term is a degree less singular than the Nth with certain restrictions when a ray is tangent to the boundary. This expansion provides a uniformly valid approximation in a neighborhood of the arrival time at the observation point of the main reflected or transmitted wave surface, lateral waves, or surface waves. For first arrivals the result is asymptotic, whereas for subsequent wave fronts there is an error due to residual waves. One of the main results is that this method provides an estimate of the surface waves (if any). Also the method is directly applicable to more complicated hyperbolic equations or systems.