Showing papers on "Lamb waves published in 1968"

Longitudinal capillary waves. Part 1.—Theory

Abstract: The existence of hitherto unobserved surface waves with a longitudinal character is deduced theoretically and the properties of these waves are predicted. In contrast to capillary waves, the longitudinal waves are governed by the surface elastic modulus rather than by surface tension; they are accompanied by a horizontal rather than by a vertical surface movement and they are connected with a liquid flow of a highly dissipative character causing a rapid damping. Under normal experimental conditions capillary waves and longitudinal waves are superimposed, but the longitudinal wave is usually damped out much more rapidly, except at high elastic modulus.

Frequency response of an interdigital transducer for excitation of surface elastic waves

Abstract: Excitation of elastic waves in a piezoelectric solid by an interdigital transducer, in terms of a simplified model, has been analyzed using Lamb's integral solution. The transducer generates three types of disturbances propagating at the velocities of irrotational, equivoluminal, and Rayleigh waves. While the amplitudes of the former two waves diminish as the three-half power of the distance from the transducer, that of the latter does not decay with distance on the surface. Dependence of particle displacement of the waves on electric fields, number of electrodes, electrode width, and wave numbers has been derived. It has been shown that a conventional interdigital transducer, in which all the electrode widths and all the spacings are respectively equal among themselves, can respond to fundamental and odd harmonic excitations, but not to the even harmonics. Means to improve the insertion loss and the bandwidth of the transducer are discussed. A flat overall frequency response can be synthesized by parallel operation of two or more transducers, the fundamental frequencies of which are properly staggered.

The effect of wave energy spectra on wave run-up

Abstract: Previous investigations carried out "by the Delft Hydraulics laboratory have shown the necessity of applying irregular waves m studies on wave run-up. The installation of a wave generator driven "by hydraulic actuators has created the possibility of producing irregular waves with arbitrary wave spectra. Investigations performed with this type of wave generator show the influence of the shape of the energy spectrum on the wave run-up on smooth straight slopes of 1:4 and 1:6. The results are compared with run-up figures derived from experiments with wind generated waves and with monochromatic waves.

Higher Modes of Longitudinal Wave Propagation in Thin Rods

Abstract: The propagation of the higher modes of longitudinal wave propagation in a dispersive elastic rod was investigated, both analytically and experimentally. The Pochhammer‐Chree equation was solved for the mode shapes and group velocities as a function of wavenumber for the axisymmetric modes of longitudinal wave propagation. By integration of the axial displacement across a cross section, an indication of the planeness of the waves was obtained. In the experimental investigation, elastic waves generated in a colored‐glass pressure bar by absorption of luminous energy from a Q‐switched laser were measured using a thin piezoelectric crystal sandwiched in the pressure bar. The gross experimental results showed good agreement with the response as predicted by Love's modified wave equation. Higher modes of wave propagation not predicted by the one‐dimensional theory were evident in the experimental record. These effects were related to the results obtained from the Pochhammer‐Chree equation.

Growth of Acceleration Waves in Isotropic Elastic Materials

Abstract: The growth of acceleration waves propagating in an isotropic elastic material is examined. The underlying assumption made is that the material is at rest in its reference configuration. First, we establish that only longitudinal or transverse acceleration waves may propagate, and the wave speeds are determined. Then, we derive the differential equation governing the growth of the amplitude of longitudinal acceleration waves and obtain explicit solutions for plane, cylindrically or spherically expanding waves. These results indicate that the amplitude of acceleration waves may either decay to zero in infinite time or become infinite (shock formation) in finite time; the radius effect on the amplitudes of cylindrical or spherical acceleration waves are not of the form 1/r12 or 1/r, as predicted by lineary theory. On the other hand, the behavior of transverse waves is similar to that obtained by linear theory.

Diffraction of elastic waves by a rigid circular disc

Abstract: The problem of the diffraction of axisymmetric harmonic elastic waves by a rigid circular disc is reduced to finding the solution of a pair of integral equations of the second kind suitable for iteration at low frequencies. Using the principle of contraction mapping, the rate of convergence of the iteration procedure is discussed and the error caused by stopping at any particular stage estimated. Detailed calculations are given for plane compressional waves at normal incidence.

Ultrasonic non-destructive testing apparatus and method

Abstract: A CONTINUOUS FREQUENCY-MODULATED ELECTRICAL WAVE HAVING A CONTINUOUS FREQUENCY-MODULATION OF REPETITIVE WAVE SHAPE IS GENERATED AND IS CONVERTED INTO AN ULTRASONIC TRANSMITTED WAVE WHICH IS CONTINUOUS AND FREQUENCYMODULATED OF THE REPETITIVE WAVE SHAPE. THE ULTRASONIC WAVE IS IMPINGED ON AN OBJECT SUCH THAT A SERIES OF ULTRASONIC PULSES EACH CORRESPONDING TO A LAMB WAVE MODE IS INDUCED THEREIN. THE ULTRASONIC PULSES ARE CONVERTED TO ELECTRICAL TEST PULSES WHICH ARE THEN CORRELATED WITH THE MODULATING FREQUENCIES.

The elastic-plastic boundary in one dimensional wave propagation.

Abstract: : The problem of moving boundaries separating elastic regions from plastic regions in one dimensional plastic wave propagation was considered by several investigators. These boundaries are called unloading waves if the material at a section changes from a plastic state to an elastic state as the wave passes the section. If the material changes from an elastic state to a plastic state, the moving boundary is called a loading wave. It was shown by other authors that the speed of an unloading wave or a loading wave must satisfy certain conditions if the time derivatives of the stress sigma sub t, on both sides of the elastic-plastic boundary are not zero. The purpose of the note is to clarify the situation in which sigma sub t and its higher derivatives are zero on both sides of the elastic-plastic boundary. (Author)

An orthonormality relation for elastic body waves

Abstract: Herrera9s orthonormality relation for elastic surface waves is generalized for elastic body waves. As an example, the normalization of a P -wave incident on the surface of a half space is considered. The Green9s function for body waves and surface waves is obtained.

Diffraction of elastic waves by a rigid 90° wedge Part I

Abstract: Integrals representing the reflected and diffracted elastic waves generated by the incidence of a plane compressional wave on a rigid quarter-plane are evaluated by an application of the Cagniard-De Hoop technique. It is shown that diffracted spherical waves radiate away from the tip of the quarter-plane at the shear and compressional wave speeds. The spherically spreading compressional wave excites secondary shear waves on the surfaces and edges of the quarter-plane. These secondary spherical wavelets envelope a ruled surface which is conical in shape at the edges of the scatterer. The envelope propagates away from the quarter-plane at the critical angle and forms a Mach wave or bow wave. The usual reflected shear and compressional plane waves are also present and combine with the diffracted waves to form the geometric shadow of the quarter-plane.

Finite amplitude waves in fluid-filled elastic tubes - Wave distortion, shock waves, and Korotkoff sounds

Abstract: Theory of finite amplitude waves in fluid-filled elastic tubes, including wave distortion, shock wave propagation, and Korotkoff sounds

Wave forces on piles in relation to wave energy spectra

Abstract: The determination of wave forces on piles is for an important part based upon data obtained with regular laboratory waves. Nonlmearities m the mechanism that underlies these forces may lead to deviations when applying the data to predict forces exerted by irregular waves. Experiments have been performed with irregular waves to investigate wave forces, more particularly to study the influence of the energy density spectrum of the waves. Within the range of conditions m the experiments, the wave motion is sufficiently characterized by its energy and the frequency (or wave period) at which the energy density is maximum to determine the probability distribution of wave forces.

Critical Angles Associated with the Reflection‐Refraction of Elastic Waves at an Interface

Abstract: Goodier and Bishop established that there is a “critical” incident angle that a train of Sv waves makes with the traction‐free surface of an elastic half‐space and that as the incident angle passes through this critical value from above, the reflected P wave passes through grazing incidence and emerges as a surface wave. In this paper, study is made of the fate of a train of Sv waves on striking the plane interface between two elastic materials. It is found that there are five critical angles associated with such a wave and the emerging wave which passes through grazing incidence corresponding to each angle is transformed into a surface wave. The wave is like a Rayleigh wave in that the magnitude of motions accompanying it decay exponentially away from the interface, particle motions have an elliptical orbit, and the wave travels with a constant phase velocity. The wave is unlike a Rayleigh wave in that its velocity is not the velocity of Rayleigh waves and, in fact, depends on the incident angle. The met...