Narrow Results

This is a duplicate pubication and the authors submitted and published the same article in APL.

In the present paper, we have studied the propagation of axial symmetric cylindrical surface waves through rotating cylindrical bore in a micropolar porous medium of infinite extent possessing cubic symmetry. The frequency equation for surface wave propagation in the micropolar porous medium has been derived and liquid filled bore are derived. The effect of the rotation on phase velocity of surface wave has been studied in detail. Radius of bore and other material parameters for empty and liquid filled bore are derived. A particular case of interest has been deduced. Numerical results have been obtained and illustrated graphically to understand the behavior of phase velocity versus wave number of a wave. The results have indicated that the effect of rotation on phase velocity is highly pronounced. Comparisons are made in the absence of rotation.

In order to understand the role of superconductivity in superconducting transmission line resonator, we derive the mode equations using the macroscopic wavefunction of the Cooper pairs. We make an appropriate scaling to obtain the dimensionless form of equations and establish the validity of good conductor approximation under most circumstances. Quantization of superconducting transmission line resonator is realized by the black-box principle. We also briefly discuss that the deviation from good conductor behavior would result in the observable effects, such as the considerable decrease of phase velocity and the soliton.

Primary shear horizontal (SH) mode propagation and its second harmonic are generated and detected using wedge transducers on the surface of an elastic plate. In the far field region, the clear second-harmonic response can be observed at the frequency where the phase velocity of the primary SH mode equals that of the symmetric double-frequency Lamb mode. Based on the measured results, the ratio of the second-harmonic amplitude to the square of the primary SH mode amplitude is numerically evaluated for different propagation distances. It is experimentally verified that under some conditions the second harmonic of the primary SH mode propagation grows in amplitude with propagation distance.

This paper deals with the axisymmetric acoustic wave propagating along the perfect gas in the presence of a uniform flow confined by a rigid-walled pipeline. Under the linear acoustic assumption, mathematical formulation of wave propagation is deduced from the conservations of mass, momentum and energy. Meanwhile a method based on the Fourier–Bessel theory is introduced to solve the problem. Comprehensive comparisons of the phase velocity and wave attenuation between the non-isentropic and isentropic acoustic waves are provided. Meanwhile the effects of flow profile, acoustic frequency, and pipeline radius are analyzed.

The properties of ultrasonic Lamb waves, such as relatively small attenuation and high sensitivity to structural changes of the object being investigated, allow performing of non-destructive testing of various elongated structures like pipes, cables, etc. Due to the dispersion effect of Lamb waves, a waveform of the received informative signal is usually distorted, elongated and overlapping in the time domain. Therefore, in order to investigate objects using the ultrasonic Lamb waves and to reconstruct the dispersion curves, it is necessary to know the relationship between frequency, phase and group velocities and thickness of the plate. The zero-crossing technique for measurement of phase velocity of Lamb waves (the A₀ and S₀ modes) has been investigated using modelled dispersed signals and experimental signals obtained for an aluminium plate having thickness of 2 mm. A comparison between two reconstruction methods of Lamb wave phase velocity dispersion curves, namely, the two-dimensional fast Fourier transform (2D-FFT) and zero-crossing technique, along with the theoretical (analytical) dispersion curves is presented. The results indicate that the proposed zero-crossing method is suitable for use in reconstruction of dispersion curves in the regions affected by strong dispersion, especially for the A₀ mode.

Starting from experimental data, this work exploit the similarity of pressure and axial wave’s propagation of both pressure and axial waves in large vessel (e.g., aorta) with the solution of a mathematical model developed to describe the motion of acoustic waves in solid. In particular, we show how the motion parameters derived by fitting the experimental data measured in living dog arteries are related to mechanical properties of the vessel tissue using the same theoretical model. Furthermore, we briefly discuss the consequence on the predicted forced wave motion of inferring from experimental data a phase velocity depending from frequency.

The present paper is devoted to study the Love wave propagation in a fiber-reinforced medium laying over a nonhomogeneous half-space. The upper layer is assumed as reinforced medium and we have taken exponential variation in both rigidity and density of lower half-space. As Mathematical tools the techniques of separation of variables and Whittaker function are applied to obtain the dispersion equation of Love wave in the assumed media. The dispersion equation has been investigated for three different cases. In a special case when both the media are homogeneous our computed equation coincides with the classical equation of Love wave. For graphical representation, we used MATLAB software to study the effects of reinforced parameters and inhomogeneity parameters. It has been observed that the phase velocity increases with the decreases of nondimensional wave number. We have also seen that the phase velocity decreases with the increase of reinforced parameters and inhomogeneity parameters. The results may be useful to understand the nature of seismic wave propagation in fiber reinforced medium.

In this paper, the effect of initial stress on the propagation of Love waves in a layered structure with a thin piezoelectric film bonded perfectly to an elastic substrate has been investigated. General dispersion equations, describing the properties of Love waves in both cases, electrically open case and electrically shorted case of the piezoelectric layer, have been obtained. The effects of inhomogeneity parameters in the substrate and the initial stress in both, the layer and the substrate on the phase velocity of Love waves, are analyzed and presented graphically. The analytical method and obtained results may find applications for designing the resonators and sensors.

The rotary inertia defined by Timoshenko to account for the angular velocity effect in flexural vibration of beams has been questioned by some researchers in recent years, and it caused some confusions. This paper discusses the appropriate rotary inertia in Timoshenko beam theory (TBT) and evaluates the influence of the two forms of the rotary inertia on the prediction of the higher-mode frequencies of transversely vibrating beams. Based on the theory of elasticity and variational principle, this work shows that the rotary inertia in the original TBT, defined in terms of the rotation of beam cross-section induced by bending deformation, is variational consistent and is capable of yielding good results of the phase velocities of transversely vibrating beams even in the case where the wavelength of vibrating beams approaches the beam height. On the other hand, the so-called corrected TBT, in which the rotary inertia is defined in terms of the slope of beam deflection, is neither variational consistent nor accurate when the wavelength of vibrating beams approaches the beam height. Therefore, the rotary inertia in TBT defined by Timoshenko is correct and should be used in the dynamic analysis of beams.

This paper investigates the elastic wave propagation through soft materials that are being subjected to finite deformations. The nonlinear elastic and linearized incremental theories have been exploited to formulate governing wave equations and elastic moduli in Lagrangian space. Semi-analytical finite element (SAFE) method, a numerical approach has been formulated for computing dispersive relations of guided waves in compressible hyper-elastic plates. This framework requires finite element discretization of the cross section of the waveguide and harmonic exponential function assumes the motion along the wave propagation direction. Here, explicit phase velocity results have been shown for soft materials with a prominent stiffening effect by employing the Gent model, and these results are analyzed for elastic wave propagation through compressible materials. It has been noticed that Lamb waves have a strong dependence on the frequency-thickness product, prestretch, and direction of wave propagation. Moreover, with the strain stiffening effect, the dependence becomes stronger, especially for fundamental symmetric and anti-symmetric modes. The numerical results display that at certain prestretch the Gent material encounter snap-through instability resulting from geometrical and material nonlinearities. The influence of material properties like Gent constant and direction of wave propagation on snap-through instability has been discussed. The proposed SAFE framework reveals that finite deformations can affect elastic wave propagation through stiffness and compressibility.

Investigations are carried out to predict the characteristic behavior of Love-wave fields propagating in a non-local elastic model under the effects of irregular boundary surfaces, reinforcement, and porosity distributions. The model includes an anisotropic fiber-reinforced medium lying over an anisotropic porous half-space. Two different porosity distributions are investigated within the porous half-space, namely uniform porosity and asymmetrical porosity. Analytical solutions to the displacement fields for both the upper layer and the lower porous half-space are calculated. Solutions to the latter porosity distribution are obtained by using the asymptotic expansions of the Kummer hypergeometric functions of the second kind. Both the interface and the upper surface of the two-layered media are subjected to irregular boundary conditions, which leads to a complex form of the dispersion relation. We analyze the phase velocity and damped velocity behavior of the traveling Love-wave fields separately by using the real and imaginary components of the velocity dispersion relation. The calculated phase velocity curves obtained at the same parameters have been compared to demonstrate the accuracy of the established model. The effects of corrugation parameters, porosity distributions, non-local elasticity, and reinforcement on the phase velocity and the damped velocity curves are analyzed in detail using MATLAB software.

Bone filled with marrow is modeled as poroelastic bore filled with a fluid in the frame work of Biot's theory in wave propagation phenomena. Axially symmetric unattentuated waves are considered. Frequency equations are derived in the cases of permeable boundary and impermeable boundary, and are found to be dispersive. The existing data of bony materials has been exploited. Phase velocity versus ratio of wavelength to bone diameter curves are plotted. From this model and analytical results, some conclusions are drawn.

This paper delves into the analysis of shear wave propagation with a sandwiched structure comprising a piezoelectric layer and an elastic layer, with a transversely isotropic layer in between. The frequency equation has been derived following Biot’s theory. The dimensionless phase velocities numerical values are computed and visually depicted to demonstrate their dependencies on anisotropy, piezoelectricity, initial stress and porosity in a comparative manner. The explicit demonstration of the relationship between each parameter and the geometry has been presented. The observation shows that as porosity in the medium increases, the phase velocity also increases. Furthermore, the existence of medium anisotropy results in a decrease in the phase velocity of shear waves. Moreover, a correlation is observed where higher tensile initial stress within the medium leads to a corresponding reduction in the phase velocity of shear waves. We conclude that considered parameters (viz. piezoelectricity, anisotropy, porosity, initial stress and thickness of layers) affect the velocity profile of the shear waves significantly. This study holds practical significance in the development of innovative-layered composites, surface acoustic wave (SAW) devices and sensors utilizing intelligent piezoelectric devices for engineering purposes.

A possible medium is considered with a large number of diverse but possibly similar relaxation processes. The equations for single spatially located relaxation processes of general type are developed and extended to a large spatially extended system. Each process is characterized by a relaxation time and a relaxation strength and is excited by the local pressure in an incident acoustic wave. A constant frequency model is initially assumed with complex amplitudes associated with acoustic pressure and relaxation responses. A smearing process results in the collective relaxation responses being regarded as a continuous function of relaxation times. An expression for entropy perturbation is developed in terms of the relaxation responses. The equations of fluid mechanics then lead to an expression for the pressure perturbation in terms of the dilatation and the relaxation processes. The extended result yields a time-domain wave equation for propagation through an inhomogeneous medium with distributed relaxation processes. Expressions for frequency-dependent attenuation and phase velocity are derived in which relaxation is characterized by a single function giving strength as a continuous function of relaxation time. Possible choices for this function are discussed, and it is shown that some choices lead to an attenuation varying nearly as a power of the frequency over any fixed and possibly large range of frequencies. A model set of parameters leads to good agreement with attenuation and phase velocity measurements for a suspension of human red blood cells in saline solution, as communicated to the authors by Treeby and analogous to those reported by Treeby, Zhang, Thomas, and Cox.

The following sections are included:

• Introduction
• Light (Plane Wave)
• Realization of Pulse: Result of Interference
• Representation of a Pulse under SVEA
• Brief Summary
• Definition of Intensity
• Intensity of Ultrafast Pulse
• The Gaussian Pulse: Field Envelope vs. Intensity Envelope
• Time-Bandwidth Product (TBP)
• Characteristics of Ultrafast Pulses: Experimental Aspects
• Further Reading