Dimensionless Phase Velocity Research Articles

A modified experimental approach for generating internal solitary waves using the dual paddle technique

A modification to the dual paddle wave generation method for internal solitary waves (ISWs) has been achieved through the implementation of the adjusted high-order unidirectional (aHOU) model and the Miyata–Choi–Camassa (MCC) model. This modified method utilizes layer-averaged horizontal velocities from ISWs in both the upper and lower fluid layers to control the operational velocities of the corresponding paddles. Experimental investigations conducted in a two-layer fluid with varied stratification conditions were employed to evaluate the applicability of the aHOU and MCC models. The validation of this approach involved examining the stability of generated ISWs by comparing experimental waveforms with theoretical predictions, demonstrating good agreement with prior research. Furthermore, evaluation of the modified wave generation method included an analysis of dimensionless phase velocity and characteristic frequency. The study also explored the quasi-linear relationship between the designed wave amplitude and the actual wave amplitude, establishing a polynomial fit between the actual wave amplitude and the layer thickness ratio. This approach offers a new method for stable and controllable laboratory generation of ISWs. Under finite water depth conditions, the method can produce ISWs that propagate stably over long distances and effectively control parameters such as wave amplitude and wave profile across a broad range of wave amplitudes and stratifications. These results confirm the effectiveness of the modified method and underscore its practical applicability in ISWs generation.

On propagation behavior of shear wave in piezoelectric-sandwiched structure

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.

Phase velocity analysis by multi-parametric variations in a highly heterogeneous sandwich plate structure embedded in the Pasternak foundations with viscoelastic interlayer

This investigation explores the vibrational response of a sandwich plate with material parameter nonhomogeneity and a viscoelastic core, incorporating Pasternak foundations. The study views the equation of motion from an anti-plane shear perspective, presenting a generalized exact dispersion relation (GEDR). It analyzes the impact of parameters like material nonhomogeneity, viscoelasticity, and Pasternak foundation properties on the dimensionless phase velocity against wave number. Findings reveal decreasing phase velocity with increasing wave number, with nonhomogeneity and Pasternak parameters exerting substantial influence. The study offers valuable insights into composite material wave behavior, benefiting design methodologies for diverse applications.

Study of the dynamic electro-mechanical and microstructural behaviour on the elastic wave in FGM/FGPM composite structure: WKB asymptotic approach

This paper presents a theoretical investigation of the horizontally polarized shear wave in a composite structure. The assumed composite is composed of Functionally graded piezoelectric material (FGPM) layer constrained between an FGM (Functionally graded material) layer and a couple stress half-space with size-dependent microstructural effect. The variation in rigidities and densities are considered parabolic and linear in the upper and constrained layers, respectively. An analytical WKB (Wentzel–Kramers–Brillouin) asymptotic approach has been adopted for obtaining the dispersion relation. Also, a finite difference scheme (FDS) has been introduced to calculate the phase velocity and group velocity of the SH-wave. If waves travel in the time domain, it is necessary to check the accuracy and stability requirements. So that FDS has been adopted because of its accuracy, reliability, and flexibility. For the purpose of numerical calculation, three sets of FGPMs are considered namely, PZT−4, PZT−5H ceramic, and ceramic. Graphs have been plotted by means of dimensionless phase velocity against dimensionless wave number to show the effect of various parameters on the propagation of SH-wave. Numerical results demonstrated the accuracy and versatility of the phase and group velocity depending on the stability ratio of the FDS.

Wave propagation of the viscoelastic FG-GPLRPC microplate via sinusoidal shear deformation theory (SSDT) and modified coupled stress theory (MCST)

This is the first research on the wave propagation analysis of the viscoelastic functionally graded graphene platelet reinforced piezoelectric composite (FG-GPLRPC) microplate exposed to the electromagnetic field. Uniform distribution (UD) and two types of functionally graded distribution patterns of GPL reinforcements are considered. Kelvin Voigt’s model is engaged in providing the realistic material property of the viscoelastic system. The viscoelastic FG-GPLRPC microplate is embedded in the orthotropic Visco Pasternak foundation. Halpin–Tsai micromechanics model and the rule of mixture (ROM) is applied to formulate the effective Young's modulus, density, and Poisson's ratio of viscoelastic FG-GPLRPC microplate. Governing equations are derived using nonlocal modified coupled stress theory (MCST) and sinusoidal shear deformation theory (SSDT). After validating the results, the influence of different parameters, including three pattern types of functionally graded distributions of GPLs, the weight fraction of GPLs, various foundation models, magnetic field, the geometrical aspect ratio of the system, and damping coefficient, are carried out. The results illustrate that adding 1% weight fraction of GPLs leads to an increment of 28.57% in the dimensionless phase velocity of the structure. It is hoped that the results of this study will be useful in improving the design of smart systems.

Experimental study of crossflow instability in a Mach 6 delta wing flow

In this paper, the traveling crossflow instability in the boundary layer on the windward side of a delta wing is studied. The experiments are carried out in a Mach 6 low-noise wind tunnel, with the angles of attack of the model being 5° and 10°, and the Reynolds number being in a range of 2.43 × 10<sup>6</sup>–14.21 × 10<sup>6</sup> m<sup>–1</sup>. The wall fluctuation pressure is measured by fast-response Kulite pressure transducers. The power spectrum density (PSD) analysis is conducted to obtain the disturbance waves' development process in the boundary layer. The temperature-sensitive paints (TSPs) and nano-tracer based planar laser scattering (NPLS) technique are also used. From the TSP results, the boundary layer transition near the leading edge of the delta wing is smooth and parallel to the leading edge. A peak around 10 kHz in power spectrum density is detected by the fast-response pressure sensor, which may be caused by the traveling crossflow waves. To verify this dominant mode, an NPLS image in the plane of <i>n</i> = 36 mm is obtained. The shapes of vortex structures correspond to the shapes of the crossflow vortices from the numerical simulation. Only when the boundary layer is laminar can the traveling crossflow wave signal be observed from the PSD curves. When the boundary layer is at a transitional or turbulent phase, the low-frequency component is dominant in the PSD curve. With the increase of Reynolds number, the characteristic frequency of the crossflow wave increases, and the wave’s amplitude first increases and then decreases. Moreover, the angle of attack effect is obtained. The increasing of the angle of attack can make the traveling crossflow wave grow faster and saturate, attenuate at the position closer to the leading edge of the delta wing or at a lower Reynolds number. By sensor pairs composed of three Kulite transducers, the phase velocity and the propagation angle of the traveling crossflow wave are investigated. The dimensionless phase velocities of the traveling wave are in ranges of 0.24–0.26 and 0.26–0.32 at 5° and 10° angles of attack, respectively. The propagation angles are at 50°–60° and 40°–55° at the angles of attack of 5° and 10°, respectively. At a larger angle of attack, the traveling wave’s propagation angel is smaller, but the phase velocity is bigger. It may be because the spanwise pressure gradient is higher at a larger angle of attack, and then the crossflow velocity is stronger.

Mechanics of 2D Elastic Stress Waves Propagation Impacted by Concentrated Point Source Disturbance in Composite Material Bars

Green’s function, an analytical approach in inhomogeneous linear differential equations, is the impulse response, which is applied for deriving the wave equation solution in composite materials mediums. This paper investigates the study of SH wave’s transmission influenced by concentrated point source disturbance in piezomagnetic material resting over heterogeneous half-space. Green function approach is used to solve differential equation and obtain the dispersion relation in determinant form and match with existing classical Love wave equation for the authenticity for the article. The properties of SH wave throughout the considered framework and their state of relying on varied geometrical and physical parameters are scrutinized. The simulated outcomes of disparate physical quantities viz., dimensionless phase velocity, elastic parameter, group velocity, initial stress, piezomagnetic/heterogeneity parameter and stress distribution of SH wave in the considered structure are investigated and used to regulate the behavior of dispersion characteristics of smart material waveguides.

Influence of Rigidity, Irregularity and Initial Stress on Shear Waves Propagation in Multilayered Media

The propagation of shear waves in an anisotropic fluid saturated porous layer over a prestressed semi-infinite homogeneous elastic half-space lying under an elastic homogeneous layer with irregularity present at the interface with rigid boundary has been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for shear waves is derived by using the perturbation technique followed by Fourier transformations. The dimensionless phase velocity is plotted against dimensionless wave number for the different size of ratios of depth of rectangular irregularity with the height of the layer and anisotropy parameters with the help of MATLAB graphical routines in presence and absence of initial stress. From the graphical results, it has been seen that the phase velocity is significantly influenced by the wave number, the depth of the irregularity, rigid boundary and initial stress. The acquired outcomes can be valuable for the investigation of geophysical prospecting and understanding the cause and evaluating of damage due to earthquakes.

Rigidity and Irregularity Effect on Surface Wave Propagation in a Fluid Saturated Porous Layer

The propagation of surface waves in a fluid- saturated porous isotropic layer over a semi-infinite homogeneous elastic medium with an irregularity for free and rigid interfaces have been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for Love waves is derived by simple mathematical techniques followed by Fourier transformations. It can be seen that the phase velocity is strongly influenced by the wave number, the depth of the irregularity, homogeneity parameter and the rigid boundary. The dimensionless phase velocity is plotted against dimensionless wave number graphically for different size of rectangular irregularities and homogeneity parameter with the help of MATLAB graphical routines for both free and rigid boundaries for several cases. The numerical analysis of dispersion equation indicates that the phase velocity of surface waves decreases with the increase in dimensionless wave number. The obtained results can be useful to the study of geophysical prospecting and understanding the cause and estimating of damage due to earthquakes.

Dispersion of Torsional Surface Wave in a Pre-Stressed Heterogeneous Layer Sandwiched Between Anisotropic Porous Half-Spaces Under Gravity

The study of surface waves in a layered media has their viable application in geophysical prospecting. This paper presents an analytical study on the dispersion of torsional surface wave in a pre-stressed heterogeneous layer sandwiched between a pre-stressed anisotropic porous semi-infinite medium and gravitating anisotropic porous half-space. The non-homogeneity within the intermediate layer and upper semi-infinite medium is assumed to rise up, because of quadratic variation and exponential variation in directional rigidity, pre-stress, and density respectively. The displacement dispersion equation for the torsional wave velocity has been expressed in the term of Whitaker function and their derivatives. Dispersion relation and the closed-form solutions have been obtained analytically for the displacement in the layer and the half-spaces. It is determined that the existing geometry allows torsional surface waves to propagate and the observe exhibits that the layer width, layer inhomogeneity, frequency of heterogeneity in the heterogeneous medium has a great impact on the propagation of the torsional surface wave. The influence of inhomogeneities on torsional wave velocity is also mentioned graphically by means plotting the dimensionless phase velocity against non-dimensional wave number for distinct values of inhomogeneity parameters.

Wave propagation analysis in viscoelastic thick composite plates resting on Visco-Pasternak foundation by means of quasi-3D sinusoidal shear deformation theory

In this research, the wave propagation in a viscoelastic composite thick plate resting on a Visco-Pasternak foundation is analyzed by means of sinusoidal shear deformation theory (SSDT). The viscoelastic properties of the plate are considered by using Kelvin-Voigt model. The material properties of composite plate are assumed viscoelastic based on Kelvin-Voigt model. The governing equations of motion are derived by Hamilton's principle. The analytical solution is applied to obtain the effects of the structural and foundation damping coefficients, wave number, aspect ratios, elastic properties and number of layers on the wave propagation behavior of the viscoelastic composite plate including the dimensionless phase velocity, cut-off and escape frequencies. The obtained results indicate that the dimensionless phase velocity and natural frequency decrease with increasing the damping coefficient. Also, it is observed that the effect of layups on the phase velocity becomes more sensible for small wave numbers. However, the effect of the damping coefficient on the dimensionless phase velocity and natural frequency is only observed at large dimensionless wave numbers.

Influence of Stress on Propagation of Shear Wave in Piezoelectric-Piezoelectric (PE-PE) Composite Layered Structure

Shear waves (SH) propagation in piezoelectric composite under the influence of initial stress is investigated analytically and numerically. The dispersion equation of shear waves propagation in direction normal to the layering is obtained in presence of initial stress. Numerical solutions were obtained for evaluating the effect of stress on dimensionless frequency and phase velocity. The effect of stress on stop band is discussed in this study. It can be concluded from the results that initial stress has significant effect on propagation characteristics of shear waves. The variation of initial stress has small effect on the phase velocity of shear waves. This study provides insight for development of piezoelectric composite structure under the influence of initial stress.

Dispersion and non-reciprocal elastic wave propagation in a membrane coupled with a uniform flow

In this paper, we carry out an analytical study to investigate the dispersive and non-reciprocal properties of harmonic elastic wave propagation in a membrane on an elastic foundation. One side of the membrane is in contact with a uniform inviscid and incompressible flow. The analysis shows that the frequency spectrum and the dispersion curve are not symmetric, therefore breaking the principle of reciprocity. We show that the dynamics of the wave propagation of the system depends on the dimensionless phase velocity of the membrane and the dimensionless stiffness of the elastic foundation. The system possesses one region where the phase velocity of the propagating waves in opposite directions is different, and another where the waves travel only in one direction (directional band gap). There also exist regions in which only evanescent and spatially growing waves are excited.

Shear Wave Propagation Due to a Point Source

The present paper is concerned with the propagation of shear waves in a heterogeneous isotropic layer lying over a semi-infinite homogeneous isotropic half-space due to a point source. The dispersion equation of shear waves has been established with the help of Green's function technique and Fourier transform. The deduced dispersion equation for this study agrees well with the classical Love wave equation in the absence of heterogeneity. Significant effect of heterogeneity on the phase velocity of shear wave has been observed. The dimensionless phase velocity against dimensionless wave number has been plotted and the influence of heterogeneity parameter is also revealed graphically through numerical computation.

Shear Wave Propagation in a Cylindrical Earth Model

In the present paper the study of shear wave propagation in a cylindrical fibre-reinforced earth model has been discussed in the presence of radial inhomogeneity. The dispersion equation of shear wave propagation has been derived by using Debye asymptotic expansion for upper layer and lower layer to be heterogeneous and homogeneous respectively. The oncoming results are verified with the classical result of Love wave in the absence of reinforcement and inhomogeneity parameter. The variation of dimensionless phase velocity has been plotted against dimensionless wave number to show the effect of inhomogeneity parameter, reinforcement and the ratio of radii.

The propagation of surface waves in a double layered medium over an anisotropic liquid saturated porous half space

A model of surface wave propagation in a transversely isotropic elastic solid layer lying between a homogeneous liquid layer and liquid saturated porous anisotropic half space has been considered. This appears to be a realistic model of interest as the bottom of ocean is likely to be anisotropic homogeneous to some kilometers. The frequency equation has been obtained in the form of ninth order determinant and gives complex velocities representing the attenuated waves when the liquidsaturated porous solid is dissipative. Some special cases have been discussed and numerical computations have been done by Symbolab Solutions with mathematical approximation method. The dimensionless phase velocity ratios have been plotted against the dimensionless wave number for different values of density and different values of ratio of anisotropy parameters C/F with the help of MATLAB graphical routines. Finally, conclusions have been drawn on the basis of analysis of results and graphs.

Wave propagation in FG-CNT-reinforced piezoelectric composite micro plates using viscoelastic quasi-3D sinusoidal shear deformation theory

Abstract This research deals with the nonlocal wave propagation analysis of embedded nanocomposite polymeric piezoelectric micro plates reinforced by single-walled carbon nanotubes (CNTs). For the CNT-reinforced piezoelectric composite (CNTRPC) micro plate, uniform distribution (UD) and three types of functionally graded (FG) distribution patterns of single-walled CNT reinforcements are assumed. The material properties of FG-CNTRPC micro plate are assumed orthotropic viscoelastic based on Kelvin–Voigt model. The viscoelastic FG-CNTRPC micro plate subjected to 2D electro-magnetic fields is embedded in an orthotropic Visco-Pasternak foundation. Quasi-3D sinusoidal shear deformation theory is employed to establish the governing equations in which the size effects are considered using Eringen's nonlocal theory. Analytical solution is applied in order to obtain the dimensionless phase velocity, cut-off and escape frequencies. A detailed parametric study is conducted to elucidate the influences of the small scale parameter, magnetic fields, FG distributions of CNTs, damping coefficient, aspect ratio, applied voltage and elastic medium on the wave propagation behavior of viscoelastic FG-CNTRPC micro plate. Results indicate that the dimensionless cut-off and escape frequencies decrease with increasing the magnitude of small scale parameter. Furthermore, it can be concluded that CNT distribution close to top and bottom is more efficient than those distributed nearby the mid-plane for increasing the stiffness of plates. Results of this investigation can be applied for optimum design of smart composite plates as micro-electro-magneto-mechanical sensors and actuators.

Modeling of SH-waves in a fiber-reinforced anisotropic layer

In this paper we investigate the existence of SH-waves in fiber-reinforced layer placed over a heterogeneous elastic half-space. The heterogeneity of the elastic half-space is caused by the exponential variations of density and rigidity. As a special case when both the layers are homogeneous, our derived equation is in agreement with the general equation of Love wave. Numerically, it is observed that the velocity of SH-waves decreases with the increase of heterogeneity and reinforced parameters. The dimensionless phase velocity of SH-waves increases with the decreases of dimensionless wave number and shown through figures.

Love wave propagation in a fiber-reinforced medium sandwiched between an isotropic layer and gravitating half-space

This paper is devoted to study of the dispersion equation of Love waves in a fiber-reinforced medium sandwiched between an isotropic layer and elastic half-space under the influence of gravity. The equations of motion have been discussed in each media. The frequency equation of a Love wave was obtained using the separation of variables method and Whittaker’s function expansion under a suitable assumption. The boundary conditions were introduced at interfaces of the upper layer, intermediate medium, and half-space. The dispersion equation was derived in closed form by means of Biot’s gravity parameter. The particular cases have been derived in the absence of reinforcement and gravitational force of the reinforced layer and half-space, respectively. Numerical solutions were discussed graphically to show the nature of wave propagation. Dimensionless phase velocity was obtained against non-dimensional wave number for different values of reinforced parameters, Biot’s gravity parameter, and thickness ratio of the upper layer and intermediate layer.

Propagation of shear waves in viscoelastic heterogeneous layer overlying an initially stressed half space

The present paper is concerned with the propagation of shear waves in an isotropic, viscoelastic, heterogeneous layer lying over a homogeneous half space under initial stress. For the layer the inhomogeneity associated to rigidity, internal friction and density is assumed to be linear function of depth. The dispersion equation of shear waves has been obtained in closed form. The dimensionless phase velocity and damping velocity have been plotted against dimensionless wave number for different values of inhomogeneity parameter and initial stress. The effects of inhomogeneity and initial stress have been shown in the dispersion curves.