Quasi-transverse Waves Research Articles

Reflection of coupled elastic waves in nonlocal rotating viscoelastic media

In this paper, propagation of homogeneous harmonic plane waves has been studied in an infinite homogeneous isotropic nonlocal viscoelastic rotating medium. Due to the rotational effects, two coupled plane waves, namely a quasi longitudinal wave and a quasi transverse wave are found in the medium under study. The dispersion equations is derived analytically and represented numerically. The problem of reflection of the quasi longitudinal wave at a stress-free solid half-space of the considered medium is also investigated. Various analytical results for the phase speed, attenuation coefficients, reflection coefficients and their corresponding energy ratios are depicted graphically for a particular model of interest to highlight the effect of nonlocal as well as rotational parameter.

Propagation and reflection of thermoelastic wave in a rotating nonlocal fractional order porous medium under Hall current influence

This investigation relates to the research on Hall current on propagation and reflection of elastic waves through non-local fractional-order thermoelastic rotating medium with voids. The system is split up into longitudinal and transverse components using the Helmholtz vector rule. It is observed that, through the frequency dispersion relation four coupled quasi-waves exist in the medium. The rotating solid modifies the nature of purely longitudinal and transverse waves toward the quasi-type waves. All the propagating waves are dispersive as they depend upon angular frequency. The quasi-longitudinal wave qP and quasi-transverse wave qSV faces cut-off frequencies. The nonlocal parameter affect all the waves except the quasi void wave. Analytically, the reflection coefficients of the wave are computed using suitable boundary conditions. MATLAB software is used to perform numerical computations for a chosen solid material. The amplitude ratios and the speed of propagation of the wave are plotted graphically for rotational frequency, nonlocal, fractional order, and Hall current parameter. The significant effect of the physical parameters on the computed results has been observed. The cut-off frequency of the waves is also presented graphically. The energy conservation law is proved in the form of energy ratios. The earlier findings in the literature are obtained as special case in the absence of rotation, Hall current parameter and porous voids.

Effect of Initial Stress and Impedance Boundary in Transversely Isotropic Materials

This paper aimed at studying the effect of initial stress and impedance boundary surface on the elastic waves propagation in transversely isotropic materials. The governing equations of transversely isotropic materials with initial stress are treated in the [Formula: see text]-plane to obtain the phase velocities of two waves, quasi-longitudinal ([Formula: see text]) and quasi-transverse ([Formula: see text]) waves. The normal mode operation is employed to obtain the expression of the displacement components and stress components. The problem of reflection of incident waves at the impedance boundary of transversely isotropic material is also investigated in the presence of initial stress to obtain the amplitude ratios of reflected waves. The variations of displacement and force stress are illustrated with respect to the axis of propagation by employing amplitude ratio expression. The effect of initial stress and impedance parameters on the expression of displacement and force stress as well as amplitude ratios of transversely isotropic materials are illustrated graphically for a particular model.

Reflection of inhomogeneous waves in a monoclinic magneto-thermoelastic rotating material

This paper presents the modeling of inhomogeneous plane waves reflecting from the stress free surface of a monoclinic magneto-thermoelastic rotating material. The effects of magnetic field and rotation on the phase speeds corresponding to quasi longitudinal, quasi thermal and quasi transverse-waves are examined. The amplitude and energy ratios corresponding to the reflected waves are derived with the help of boundary conditions. The effects of the incident angle, magnetic field and rotation on the amplitude and energy ratios are examined and discussed numerically. The sum of energy ratios has been examined and observed that it obeys the conservation law of energy.

Reflection of plane waves at the stress-free/rigid surface of a micro-mechanically modeled Piezo-electro-magnetic fiber-reinforced half-space

The development of fiber-reinforced composites (FRCs) is ever-increasing for better vibrational energy absorption within a material, reducing transmission of noise/vibration to neighboring structures, etc. The integrity of these structural components is tackled using Non-destructive testing (NDT)/Non-destructive evaluation (NDE) methods based on wave reflection through transducers. Owing to such factors, the present work has two primary objectives-firstly, to develop the micro-mechanics model of an orthotropic Piezo-Electro-Magnetic Fiber-Reinforced Composite (PEMFRC), which consists of BaTiO as fiber constituent and CoFeO as matrix constituent. Secondly, to analyze plane wave (qP/qSV) reflection at stress-free/rigid surface of a solid PEMFRC half-space. For an incident plane wave, four waves, namely quasi-longitudinal (qP), quasi-transverse (qSV), electroacoustic (EA), and magnetoacoustic (MA) waves, get reflected. The propagation directions of all reflected waves for incident qP/qSV wave are graphically demonstrated. Electrically Open Magnetically Open (EOMO), Electrically Short Magnetically Short (ESMS), Electrically Open Magnetically Short(EOMS), and Electrically Short Magnetically Open (ESMO) boundaries, for both Stress-free and Rigid surfaces, are considered. Using secular equations along with suitable boundary conditions, the amplitude ratios are derived using Cramer's rule. Furthermore, using the energy flux relation and expressions of amplitude ratios, the energy ratios of all reflected waves, interaction energy, and net energy are derived, which exhibit the influence of the existing parameters. Some special cases of the problem are discussed, and the Law of Conservation of Energy is validated.

Surface plasmonic waveguide and ultra-wideband bandpass filter using double-layered glide symmetric corrugated lines

In this paper, an ultra-wideband high-efficiency bandpass filter based on a surface plasmonic waveguide (SPW) is proposed. The novel SPW consists of double-sided glide symmetric periodic corrugated metal. The dispersion characteristics of the double-layered glide symmetric SPW are analyzed. By using glide symmetry technology, the dispersion curve for the two lowest-order modes of the proposed SPW is a degeneracy at the Brillouin zone boundary, resulting in a higher propagation constant than the traditional symmetric structure with the same geometry. The dispersion relation of the SPW when glide symmetric conditions are broken is also investigated. Based on the proposed double-layered glide symmetric SPW, we design a bandpass filter working in an ultrawide range of frequencies. To realize the high-efficient transmission of the bandpass filter, the matching structure composed of double-layer grooves with gradient variation is designed for the effective mode conversion of quasi-transverse electromagnetic waves and spoof surface plasmonic polariton. The upper cutoff frequency of the passband can be tuned by adjusting the geometric parameters of the corrugated metal unit, and the lower cutoff frequency can be controlled by modifying the coupling distance with the bottom layer. A prototype of an ultra-wideband bandpass filter has been manufactured and measured, showing a reasonable agreement with simulations. The proposed novel UWB bandpass filter with glide symmetry can be widely used in microwave and millimeter wave related communication systems, and may play an important role in the fabrication of advanced plasma functional devices and circuits.

A Broad Dual-Band Bandpass Filter Design Based on Double-Layered Spoof Surface Plasmon Polaritons

In this work, a broad dual-band bandpass filter is designed by applying double-layered spoof surface plasmon polaritons (DLSSPPs) as the main transmission line (MTL) and loading combined-stub dual-mode resonators (CSDMRs) onto the MTL with certain spaces. Each CSDMR consists of an open stub and a short stub that are connected in parallel. Efficient mode conversion between the quasi-transverse electromagnetic waves in the microstrip line and the spoof surface plasmon polaritons (SSPPs) on the double-layered surface plasmon waveguide is realized using gradient double-layered metal gratings and via the sector structure impedance matching technique. A parametric study of the CSDMR demonstrates that center frequencies and bandwidths can be controlled by varying the stub lengths and widths of the CSDMRs. A second-order dual-band filter is designed and fabricated, and simulated and experimental S-parameters agree well. A lower loss of the passband is achieved compared with the filters that apply single-layered SSPPs. The space between two CSDMRs is shortened because of the slow-wave effect of the DLSSPPs. The lowpass performance of the DLSSPPs exhibits good rejection from the cutoff frequency above.

Electro-Thermo-Mechanical multiple fields coupled wave propagation through piezoelectric semiconductor sandwich structure

Based on the electro-thermo-mechanical multiple physical fields coupling model, the propagation of coupled elastic waves through a piezoelectric semiconductor sandwich structure is studied. Due to the consideration of non-Fourier heat conduction (G-N III-type) and non-Fick diffusion, there are totally five kinds of coupled waves in the piezoelectric semiconductor, i.e. quasi-longitudinal elastic wave, quasi-transverse elastic wave, charge carrier wave, thermal wave and piezopotential wave. The state vector is appropriately defined and the transfer matrix of state vector in the piezoelectric semiconductor is derived from the coupled equations which govern the piezopotential, charge carrier, thermal and mechanical multiple physical fields. The mathematic model of reflection/transmission through the piezoelectric semiconductor sandwich structure is finally established by considering the continuous condition of the state vectors at two interfaces. The reflection/transmission coefficients, the energy flux allocation and dissipated energy flux are studied numerically. The effects of steady carrier density, lifetime of carrier, thermal-elastic coupling parameters and the interlayer thickness on the dispersion and attenuation of coupled waves as well as the reflection transmission behavior are discussed based on the numerical results.

Reflection of plane waves in a functionally graded thermoelastic medium

In this paper, the reflection phenomenon of plane harmonic waves in a functionally graded thermoelastic medium is studied based on the generalized theory of thermoelasticity. The boundary is assumed to be stress free and thermally insulated. For the incidence of quasi-longitudinal (QL) wave or quasi-transverse (QT) type wave, there may exist three types of reflected waves. For each reflected wave, the corresponding slowness vector is resolved to define its phase speed and reflected angle. Further, the effect of the functionally graded factor on the phase speeds, reflected angles as well as the reflection coefficients for the incidence of QL or QT wave were investigated and shown graphically.

Analysis of plane wave reflection phenomenon from the surface of a micro-mechanically modeled piezomagnetic fiber-reinforced composite half-space

In the present article, firstly, the micro-mechanical model of piezomagnetic fiber-reinforced composite (PMFRC), composed of CoFe 2 O 4 fiber-epoxy matrix combination, is presented employing the Strength of Materials (SM) and Rule of Mixtures (RM) techniques. Secondly, the impacts of varying fiber-volume fractions ( Ω f ) on the energies carried by different reflected waves in the PMFRC are analytically studied. Due to the incidence of a quasi-longitudinal wave, three reflected waves viz. quasi-longitudinal (qP), quasi-transverse (qSV), and magneto-acoustic (MA) waves are generated in the PMFRC half-space. Propagation angles of all reflected waves are analyzed considering incident qP and qSV waves, and the existence of critical angles is established for the latter case. The closed-form expressions of amplitude ratios of all reflected waves are derived by employing appropriate magneto-mechanical boundary conditions and using Cramer's rule. In order to validate the numerical results, the expressions of energy ratios of all reflected waves and interaction energy are derived, which exhibit the influence of existing parameters. In doing so, the Law of Conservation of Energy is also established. The existence of a critical value of Ω f is discovered in the range ( 0.6 , 0.8 ) , beyond which the magnitudes of energies carried by the reflected waves change drastically.

Shock response of single-crystal boron carbide along orientations with the highest and lowest elastic moduli

The response of monocrystalline boron carbide to planar shock loading has been investigated using molecular-dynamics simulations, along crystal orientations with the highest and lowest elastic moduli. While shocks of intensity lower than the Hugoniot elastic limit (HEL) generate quasilongitudinal and quasitransverse waves, an elastic precursor trailed by inelastic waves is observed when HEL is exceeded. Bond breakage, accompanied by temperature rise, is observed to be the primary mode of deformation under the inelastic waves. Higher shock intensities (particle velocity, ${U}_{p}>2.5\phantom{\rule{0.16em}{0ex}}\mathrm{km}/\mathrm{s}$) generate a deformation shock front, which induces loss of shear strength along with a considerable loss of crystalline order. Boron carbide is also revealed to exhibit two distinct deformation regimes. While shear strength increases with ${U}_{p}$ in the first regime $({U}_{p}\ensuremath{\le}2.5\phantom{\rule{0.16em}{0ex}}\mathrm{km}/\mathrm{s})$, a monotonic reduction is observed in the second $({U}_{p}>2.5\phantom{\rule{0.16em}{0ex}}\mathrm{km}/\mathrm{s})$. The latter regime is also characterized by a convergence in the shock Hugoniot curves obtained along the two loading directions, indicating that the Hugoniot state of boron carbide may be independent of crystal orientation for ${U}_{p}>2.5\phantom{\rule{0.16em}{0ex}}\mathrm{km}/\mathrm{s}$. Finally, it is shown that the simulation-derived hydrostat curve presented in this work is coherent with experimental data up to 140 GPa and provides an accurate basis for assessing residual strength of boron carbide under shock conditions.

Magnetic and rotational effects on the reflection of inhomogeneous waves in a fiber-reinforced thermoelastic material

The problem of reflection of inhomogeneous plane waves from the free surface of a fiber-reinforced magneto-thermoelastic rotating material has been investigated. The phase speeds of quasi longitudinal, quasi transverse and quasi thermal waves are derived. The reflection coefficients and the energy ratios are obtained. The magnetic and rotational effects on the reflection coefficients and energy ratios are computed numerically and presented graphically. It is found that the magnetic field and rotation influence the reflection coefficients and energy ratios significantly. Critical angles are observed for incident quasi transverse wave. The sum of energy ratios has been verified to validate the problem.

Analysis of plane wave reflection and transmission phenomenon at the interface of two distinct micro-mechanically modeled rotating initially stressed piezomagnetic fiber-reinforced half-spaces

Analyzed the influence of normal/shear initial stresses and rotation on reflection/transmission characteristics of waves propagating at the interface of two distinct micro-mechanically modeled piezomagnetic fiber-reinforced composite(PMFRC) half-spaces composed of CoFe2O4 fiber-epoxy matrix combination. An incident quasi-longitudinal(qP) wave generates reflected/transmitted quasi-longitudinal(qP), quasi-transverse(qSV), and magneto-acoustic(MA) waves, whose propagation directions are illustrated graphically. Transmitted qP wave has critical angles for considered initial stresses and rotation. Energy ratios of reflected/transmitted waves, interaction energy, and net energy are obtained, which satisfy the Law of Conservation of Energy, thereby validating this problem. Influences of incident angle, initial stresses, and rotation on amplitude/energy ratios are meticulously analyzed.

Reflection and transmission of waves at the common interface of piezoelectric half-spaces with microstructure

The present article deals with the reflection and transmission of waves at an interface of piezoelectric (ALN & PZT-5T) half-spaces with microstructures. Unlike the classical piezoelectric material, in the considered media, five coupled waves (2 bulk and 3 surface) [namely the Quasi-longitudinal wave (QP), Quasi-transverse wave (QSV), Electric-acoustic wave (EA), P-type surface wave (SP) and S-type surface wave (SS)] are generated in response to an oblique incident Quasi plane wave. The main objective of this study is to investigate the influence of the characteristic length of microstructure, the inertial characteristic length and flexoelectric coefficients on the reflection and transmission coefficients. For this purpose, the linear algebraic equation, continuity conditions at the common interface are contracted. The linear system of equations comprising the reflection and transmission coefficients is derived, which is solved by using the Cramer's rule. The consequence of this electromechanical phenomenon may be advantageous in certain engineering applications that involve smart nano-composites.

Effect of grain boundaries on elastic shock wave in graphene

Effect of grain boundaries (GBs) on elastic shock wave in graphene is investigated by molecular dynamics simulations. Bicrystal graphenes with symmetrical GB are shocked along directions perpendicular and parallel to GB. For perpendicular shock loadings, double elastic shock waves emerge in form of quasilongitudinal (QL) and quasitransverse (QT) waves, since the loading direction is neither zigzag nor armchair. GB attenuates the QL wave and gives rise to new QT waves propagating into grains. Transverse particle motion in the elastic shocks can induce small lattice rotations and different oriented regions, whose number increases upon the passage of waves through GB. Upon shock loadings along GB, transverse particle motions of opposite direction generate in the two grains, and change the pressure distribution right behind wavefront, and then result in deviation of shock wave from planar loading or “V” shaped wavefront turning at GB. The above phenomena are attributed to the turn of grain orientation at GB and transverse particle motions induced by lattice symmetry reduction upon shock compression.

Impact of interfacial imperfections on the Reflection and Transmission phenomenon of plane waves in a Porous-Piezoelectric model

Reflection and transmission of plane waves are extensively used to conduct non-destructive testing(NDT) or non-destructive evaluation(NDE) of composites for characterizing/mapping subsurface defects and assessing the in-situ condition of structural components without reforming the original features of the composites in a non-tarnish way. These materials composed of more than one base material are the major components in the construction and modelling of air-crafts, space-crafts, military & defense applications, and nuclear industry. Thus, the present work deals with a mathematical model focused on the phenomenon of reflection and transmission of an incident plane wave at an imperfect interface between two different Porous-Piezoelectric(PP) half-spaces. According to the nature of the PP material, an incident plane wave (I-qP1 wave) results in five reflected and transmitted waves, namely reflected and transmitted quasi-longitudinal and quasi-transverse waves in the solid phase(qP1 and qSV, respectively), quasi-longitudinal wave in the fluid phase(qP2), and electro-acoustic waves in solid and fluid phases(EA1 and EA2, respectively). Due to reasons like the presence of interfacial defects owing to accumulative damages, half-spaces are generally not perfectly bonded. Mechanical and electrical interfacial defects fundamentally affect the performances of structural components that are utilized in several fields. Thus, reflection and transmission of different waves are studied for six distinct interfaces, viz. normally stiff interface, transversely stiff interface, electrical imperfection, slip interface, complete debonding, and welded interface. With the aid of secular equations and boundary conditions, a system of algebraic equations is obtained, from which the amplitude ratios are derived. Furthermore, the energy ratios of these waves are obtained, along with the interaction energy among various waves, using the energy flux relations and amplitude ratios. The conservation of total energy at the interface of the two media and some exclusive cases of this problem validate the study. For graphically illustrating the effects of these interface conditions on the reflection and transmission phenomenon, numerical data of PP BaTiO3 and PZT−7H materials are adopted. The energy ratios of various reflected and transmitted waves are plotted against the angle of incidence as well as against wave number.

Influence of varying fiber volume fractions on plane waves reflecting from the stress-free/rigid surface of a piezoelectric fiber-reinforced composite half-space

Wave reflection phenomenon at the stress-free/rigid surface of a piezoelectric fiber-reinforced composite (PFRC) half-space is studied. The PFRC is micro-mechanically modeled using Strength of Materials (SM) and Rule of Mixtures (RM). Some of its electro-mechanical data are graphically shown and its advantages are discussed. An incident quasi-longitudinal (qP) wave generates reflected quasi-longitudinal (qP), quasi-transverse (qSV), and electroacoustic (EA) waves, whose propagation angles are graphically demonstrated. Closed-form expressions of energy ratios of reflected waves and interaction energy are obtained, which satisfy the Law of Conservation of Energy, thus validating this problem. Influences of incident angle, varying fiber volume fractions, and stress-free/rigid surfaces on amplitude/energy ratios are discussed.

Response of Two-Temperature on the Energy Ratios at Elastic-Piezothermoelastic Interface

In the present investigation the reflection and transmission phenomenon of plane waves between two half spaces elastic and orthotropic piezothermoelastic with two-temperature theory is discussed. A piezothermoelastic solid half space is assumed to be loaded with an elastic half space. Due to the phenomenon, four qausi waves are obtained; quasi longitudinal (qP) wave, quasi transverse (qS) wave, quasi thermal (qT) wave and electric potential wave (eP). It is found that the amplitude ratios of various reflected and refracted waves are functions of angle of incidence, frequency of incident wave and are influenced by the piezothermoelastic properties of media. The energy ratios are computed numerically using amplitude ratios for a particular model of graphite and cadmium selenide (CdSe). The variations of energy ratios with angle of incidence are shown graphically depicting the effect of two-temperature. The conservation of energy across the interface is justified. A particular case of interest is also deduced from the present investigation.

Transient Green's functions of a buried pulse in a constrained transversely isotropic half-space

In this paper, transient surface Green's functions (GFs) excited by a general dynamic pulse buried in a constrained transversely isotropic (TI) half-space are derived in analytical forms. The constrained transverse isotropy is defined by an explicit relation that expresses one of the five elastic constants in terms of the other four independent constants so that no coupled P-SV wave exists. Use is made of the solutions available for general TI materials in Hankel–Laplace transformed domain in order to extract the corresponding response functions for the constrained material. Under this constraint, the coupled fourth-order wave operator, which represents the convolved motion of the quasi-longitudinal and quasi-transverse waves, is decoupled into two separated second-order wave operators describing the motion of the pure dilatational (P) and pure shear (SV) waves. The involved Laplace transform inversion is carried out using the novel Cagniard scheme so that the final displacement GFs are expressed in terms of the elementary line integrals over a finite interval. The GF solution is valid for the entire range of the constrained TI material including material isotropy as its special case, and clearly illustrates the disturbances due to different stress waves including, P, SV, SH, Rayleigh and diffracted SP waves. Moreover, the GFs show that in this constrained TI material, the compressional and horizontally polarized waves, excited by a source located at an arbitrary depth, propagate towards the surface with direction-dependent velocities. The explicit formulas for these velocities of the waves are obtained in terms of the inclination angle of the wave normal with respect to the axis of material symmetry. On the other hand, the vertically polarized wave and the diffracted SP wave propagate with eigen velocity, independent from the direction of the propagation. Two critical epicentral distances, at which mode conversion in ray diagram occurs, are detected for this constrained TI material. One critical distance marks the phenomena of total reflection of SV-waves where the incident SV-wave is totally reflected and the diffracted SP-wave travels along the free surface. The other marks the distance where the SH- and SP-waves become coalescent, and furthermore, before this epicentral distance the SH-wave is faster, and after this distance, the SP-wave is faster. To show the relevance of this constrained TI material in engineering and material modeling applications and its relation to the physics of TI materials, we also demonstrate that, in addition to its mathematical simplification, this reduced anisotropy can well approximate the elastic coefficients of some real TI materials, particularly those encountered in exploration geophysics and seismology.

Shock Loading of Heteromodular Elastic Materials under Plane-Strain Condition

The paper discusses the results of mathematical modeling the two-dimensional nonlinear dynamics of heteromodular elastic materials. The resistance of these materials under tension and compression is various. The deformation properties of the heteromodular medium are described within the framework of the isotropic elasticity theory with stress-dependent elastic moduli. In the plane strain case, it is shown that only two types of the nonlinear deformation waves can appear in the heteromodular elastic materials: a plane-polarized quasi-longitudinal wave and a plane-polarized quasi-transverse wave. Basing on obtained properties of the plane shock waves, two plane self-similar boundary value problems are formulated and solved.