Stress-wave propagation in truncated cones against a “rigid” wall

The reflection of stress waves from the conical end of a rod which is placed against a “rigid” wall is investigated. The reflection takes place at the lateral surface of the cone and at the cone-“rigid” wall boundary at low stress amplitudes. When the sum of the amplitudes of the amplified incident and reflected pulses reach the elastic limit near the cone-“rigid” wall boundary, a part of the pulse is reflected at the resulting elasto-plastic boundary.     

Elastic waves in a fiber-reinforced composite

The propagation of time-harmonic elastic waves in a fiber-reinforced composite is studied. The circular fibers are assumed to be parallel to each other and randomly distributed with a statistically uniform distribution. The direction of propagation and the associated particle motion are considered to be normal to the fibers. It is shown that the average waves in the composite separate into compressional and shear types. General formulae for the complex wave number giving the phase velocity and the damping are obtained. It is shown that these formulae lead to the Hashin-Rosen expressions for the transverse bulk modulus and the lower bound for the transverse rigidity, if the correlation in the positions of the fibers can be ignored. The correlation terms, for exponential correlation, are shown to have a significant effect on the damping property of the composite, especially at high frequencies and concentrations.     

Elastic waves in an electro-microelastic solid

The present study is concerned with the wave propagation in an electro-microelastic solid. The reflection phenomenon of plane elastic waves from a stress free plane boundary of an electro-microelastic solid half-space is studied. The condition and the range of frequency for the existence of elastic waves in an infinite electro-microelastic body are investigated. The constitutive relations and the field equations for an electro-microelastic solid are stemmed from the Eringen’s theory of microstretch elasticity with electromagnetic interactions. Amplitude ratios and energy ratios of various reflected waves are presented when an elastic wave is made incident obliquely at the stress free plane boundary of an electro-microelastic solid half-space. It has been verified that there is no dissipation of energy at the boundary surface during reflection. Numerical computations are performed for a specific model to calculate the phase speeds, amplitude ratios and energy ratios, and the results obtained are depicted graphically. The effect of elastic parameter corresponding to micro-stretch is noticed on reflection coefficients, in particular. Results of Parfitt and Eringen [Parfitt, V.R., Eringen, A.C., 1969. Reflection of plane waves from a flat boundary of a micropolar elastic half-space. J. Acoust. Soc. Am. 45, 1258–1272] have also been reduced as a special case from the present formulation.     

Elastic waves in a turbulent fluid

It is shown that a turbulent flow can support elastic waves for which the fluctuating stress is essentially proportional to the strain field. These fluctuations are described by a hyperbolic system and hence they do not decay away from a solid boundary. Their behaviour is also consistent with Taylor's frozen field hypothesis that turbulent fluctuations are advected with the local mean flow speed.     

Elastic waves in crystals and anisotropic media

The results of investigation of propagation of elastic waves in anisotropic media are discussed taking into account the two-dimensional problem of a source in an infinite medium and the Lamb problem for a half-plane. The media considered in the investigation are those for which the equations of motion under plane deformation conditions are characterized by four constants.     

Elastic interface acoustic waves in twinned crystals

A new type of interface acoustic waves (IAW) is presented, for single-crystal orthotropic twins bonded symmetrically along a plane containing only one common crystallographic axis. The effective boundary conditions show that the waves are linearly polarized at the interface, either transversally or longitudinally. Then the secular equation is obtained in full analytical form using new relationships for the displacement–traction quadrivector at the interface. For gallium arsenide and for silicon, it is found that the IAWs with transverse (resp. longitudinal) polarization at the interface are of the Stoneley (resp. leaky) type.     

Elastic waves in bodies with initial stresses

Conclusions An analysis of research available on the problem under consideration shows that at this time: a) Wave propagation in unbounded, bounded, and composite laminar bodies with homogeneous initial states has been studied sufficiently extensively; b) methods to determine the third-order elastic constants have been developed on the basis of existing theories; c) an ultrasonic nondestructive method to determine the stress in solids has been developed, where the stresses averaged over the bulk of the body are determined.In light of the above, in the authors' opinion, the following should be considered the most urgent questions for further investigations on the problem: a) the investigation of wave propagation regularities in bodies with inhomogeneous initial states (it is hence important to execute quantitative and qualitative analyses of the phenomenon); b) development of an ultrasonic nondestructive method of determining the stress in the near surface layers of a solid, which will afford a possibility of determining not only the membrane stresses but also the bending stresses; c) an investigation of the wave propagation regularities in fibrous composites with initial stresses.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 15, No. 4, pp. 3–23, April, 1979.     

Supersonic aerodynamic performance of truncated cones with repetitive laser pulse energy depositions

We investigate the drag characteristics of truncated cones in Mach 1.94 flow with repetitive laser pulse energy depositions with a frequency of up to 80 kHz. The drag decrement is almost in proportion to the laser pulse repetition frequency, and scales with a greater-than-square power of the truncation diameter. The performance of the latter is associated with the effective area of pressure modulation and the effective residence time of vortices which are baroclinically generated after the interaction between laser-heated gas bubbles and the bow shock wave. With employing a concave head, the drag decrement is enhanced. With increasing the truncation diameter, the efficiency of energy deposition becomes higher; yet, within the operation range of this study the drag coefficient still remains high.     

Elastic waves against a corrugated boundary

A train of plane waves travels in an elastic semi-infinite medium bounded by a corrugated line having a sinusoidal shape. When the primary waves impinge against the surface, a new train of reflected waves is generated, and the question arises of determining the effect of roughnesses of the boundary on the shape and amplitude of the reflected waves.The case of perpendicular incidence may be treated without difficulty by extending a solution found by Rayleigh [2, Art. 272] for reflection of sound waves from a corrugated surface.

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Sommario Un treno d'onde piane viaggia in un mezzo elastico semi-indefinito limitato da una linea corrugata di forma sinusoidale. Quando l'onda primaria urta contro la frontiera, si genera un nuovo treno d'onde, e si pone la questione di determinare l'effetto della rugosità del contorno sulla forma e l'ampiezza delle onde rillesse.Il caso di incidenza perpendicolare si può trattare senza difficoltà estendendo una soluzione trovata da Rayleigh [2, Art. 272] sulla riflessione delle onde sonore da parte di una superficie corrugata.

     

Elastic waves in piezoceramic cylinders of sector cross-section

The propagation of elastic waves in piezoceramic cylindrical waveguides of circular cross-sections with sector cut is investigated on the basis of the linear theory of electroelasticity. Dispersion functions are obtained from boundary conditions in an analytical form of functional determinants for each value of the generalized wave number. A selected set of numerical results including real, imaginary and complex branches of full dispersion spectrums with various symmetry of wave movements is presented to describe the essential characteristics of the waves. Leading effects of spectrums transformation by change of waveguide’s angular measure are enlightened, and wave asymptotic behavior is analyzed. The variation of the cross-section is considered as a mechanism to control the dispersion characteristics of waveguides.     

Elastic waves from localized sources in composite laminates

This paper is concerned with the analysis of elastic waves generated by localized dynamic sources in structural composites. The source can be external, involving acoustic wave loading as in the so called leaky Lamb wave experiment, and low-velocity foreign object impact on the surface of the structure, or internal, as in sudden crack initiation and its rapid growth from existing internal flaws. All three problems are of critical importance in the safe operation of composite structures, due to their vulnerability to hidden delaminations that can occur in composite materials when they are subjected to this type of loads. It is well known that both the dynamic surface loading associated with impact, and the sudden “opening” of an internal crack associated with the extension of a preexisting flaw act as sources of elastic waves in the material of the structure. The research reported here consists of model-based analysis of the guided waves generated by surface loading and microcrack initiation in graphite epoxy composite laminates commonly used in aircraft and aerospace structures. The objective of this study is to develop a mechanics based understanding of the causal relationship between the properties of the source and the characteristics of the waves generated by its initiation and propagation. The results of this research are expected to be useful in developing effective health monitoring systems for new as well as aging aircraft and aerospace structures.     

Second-order interaction of irregular waves with a truncated column

A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column. The fluid domain is divided into interior and exterior regions. In the exterior region, the second-order velocity potential is expressed in terms of ‘locked-wave’ and ‘free-wave’ components, both are solved using Fourier and eigenfunction expansions. The resulting ‘locked wave’ potential is expressed by one-dimensional Green's integrals with oscillating integrands. In order to increase computational efficiency, the far-field part of the integrals are carried out analytically. Solutions in both regions are matched on the interface by the potential and its normal derivative continuity conditions. Based on the present approach, the sum-and difference-frequency potentials are efficiently evaluated and are used to generate the quadratic transfer functions which correlates sum-frequency QTFs for a TLP column are present, which are compared for some frequency pairs with those from a fully numerical procedure. Satisfactory agreement has been obtained. QTF spectra for a case study TLP column, generated using the semi-analytical solution are presented. Also given are the results for nonlinear wave field around the column.     

Elastic waves guided by a material interface

The propagation of interfacial small-amplitude waves along a rectilinear thin film separating two pre-stressed, incompressible, elastic media is addressed. The film is modelled as a material surface possessing its own mass density and normal and flexural stiffnesses. It is shown that these features induce dispersion as the obtained secular equations are polynomials of the second degree in the wavenumber when bending stiffness is absent (membrane-like interface), and of the fourth degree otherwise (plate-like interface). In both case, beyond the modified Stoneley mode, a bending mode for the interface, an additional propagating wave can exist, with amplitude polarized along the interface (extensional mode). The associated bifurcation problem is analyzed with focus on the effects of compressive residual forces at the interface. The buckling strain of a compressed metal layer embedded in an elastomeric medium is computed also with an exact approach, to provide the range of validity of the proposed simplified model of material interface.     

Elastic waves in a solid subjected to shear deformation

All-Union Scientific Research Institute of Nondestructive Testing, Kishinev. Odessa Polytechnical Institute. Translated from Prikladnaya Mekhanika, Vol. 26, No. 1, pp. 77–82, January, 1990.     

Elastic waves in a Timoshenko beam with boundary damping

In this paper we consider a Timoshenko beam with a damping moment applied to one of the endpoints. The elastic waves that develop from two sets of localised initial disturbances in the beam, are simulated and it is shown that properties of the spectrum adequately explain the features of the waves. We also show, using energy calculations, that the boundary moment is significantly more effective in reducing vibrations in the beam in one of the cases under consideration. The so-called second spectrum of the Timoshenko beam plays a prominent part in explaining this phenomenon.     

Elastic responses of a flotation ring in water waves

The gravity-type fish cage is extensively applied in open-sea fishery aquaculture. Its practicality is closely related to the reliability of the flotation ring which is its main load-bearing component. Therefore, it is necessary to study the elastic responses of the flotation ring in ocean waves. Here, an analytical method is proposed to analyze the elastic deformations of a circular ring subjected to water waves. The governing equations of six degree-of-freedom motions and elastic deformations are obtained according to Euler's laws and curved beam theory. In order to examine the method, a series of physical model tests were carried out. The surge and heave displacements of the ring between the predicted results and experimental measurements are compared, and good correlation is represented. The effects of the propagation directions of the incident wave on elastic responses of the ring are then analyzed. It is concluded that small deformations of the ring occur when the configuration of the mooring cables is symmetrically arranged along the propagation direction of the incident waves. Additionally, the out-of-plane stiffness is suggested to be strengthened in order to diminish the corresponding deformations.