Propagation Of Rayleigh Surface Waves Research Articles

Size-dependent effect on the interaction of surface waves in micropolar thermoelastic medium with dual pore connectivity

This research tackles a critical knowledge gap in Rayleigh surface wave propagation. It offers a comprehensive analysis that surpasses previous limitations. A size-dependent micropolar medium with unique void distributions and thermal effects is considered in this work. The constitutive relations and equations of motion for a nonlocal micropolar thermoelastic medium with double voids (MTMWDV) have been established by using Eringen’s nonlocal elasticity theory. Employing the three-phase-lag thermoelasticity theory (TPLTE), the study utilizes a wave-mode method to derive analytical solutions for Rayleigh waves in a nonlocal MTMWDV. To gain a comprehensive understanding of wave behavior, we solve the characteristic equation and analyze its roots, applying a filter based on the surface wave decay condition. A medium with stress-free and isothermal boundaries is explored through computational simulations to determine the attenuation coefficient and phase velocity. Furthermore, particle motion analysis is conducted to complement the analytical and computational approaches. Moreover, the influence of the nonlocal parameter and various thermoelastic models on these wave phenomena is investigated. The validity of the current mathematical model is confirmed through the derivation of particular scenarios.

Impact of memory-dependent heat transfer on Rayleigh waves propagation in nonlocal piezo-thermo-elastic medium with voids

PurposeThis paper addresses a significant research gap in the study of Rayleigh surface wave propagation within a piezoelectric medium characterized by piezoelectric properties, thermal effects and voids. Previous research has often overlooked the crucial aspects related to voids. This study aims to provide analytical solutions for Rayleigh waves propagating through a medium consisting of a nonlocal piezo-thermo-elastic material with voids under the Moore–Gibson–Thompson thermo-elasticity theory with memory dependencies.Design/methodology/approachThe analytical solutions are derived using a wave-mode method, and roots are computed from the characteristic equation using the Durand–Kerner method. These roots are then filtered based on the decay condition of surface waves. The analysis pertains to a medium subjected to stress-free and isothermal boundary conditions.FindingsComputational simulations are performed to determine the attenuation coefficient and phase velocity of Rayleigh waves. This investigation goes beyond mere calculations and examines particle motion to gain deeper insights into Rayleigh wave propagation. Furthermore, this investigates how kernel function and nonlocal parameters influence these wave phenomena.Research limitations/implicationsThe results of this study reveal several unique cases that significantly contribute to the understanding of Rayleigh wave propagation within this intricate material system, particularly in the presence of voids.Practical implicationsThis investigation provides valuable insights into the synergistic dynamics among piezoelectric constituents, void structures and Rayleigh wave propagation, enabling advancements in sensor technology, augmented energy harvesting methodologies and pioneering seismic monitoring approaches.Originality/valueThis study formulates a novel governing equation for a nonlocal piezo-thermo-elastic medium with voids, highlighting the significance of Rayleigh waves and investigating the impact of memory.

Tri-axial ground-borne vibration measurements during rail pass-bys

Ground-borne vibrations from rail pass-bys, transmitted from train wheels rolling on the rails, have the potential to cause various adverse effects at nearby receptors, such as annoyance and re-radiated noise. To assess the impact of rail pass-bys, surface-level vibration can be characterized in three components: one vertical and two horizontal directions. Prior experience, best-practice guidelines from the Federal Transit Administration Transit Noise and Vibration Impact Assessment Manual, and theory of propagation of Rayleigh surface waves indicate that the vertical component dominates the horizontal components, such that vibrations from rail pass-bys can be adequately characterized by the vertical component only. This purpose of this study is to assess the sufficiency of characterizing the impact of ground-borne vibrations caused by rail pass-bys based solely in the vertical direction. Tri-axial vibration measurements were conducted for freight and passenger trains in Ontario, Canada, using a multi-channel signal analyzer for simultaneous measurement of multiple-axis vibration levels. The measured levels were then examined across the three components.

Rayleigh waves in thermoelasticity: Triple porous media in local thermal non-equilibrium

Assuming the hypothesis of local thermal non-equilibrium, this work investigates the propagation of Rayleigh surface waves in a thermoelastic half-space, isotropic, homogeneous and structured with a triple level of porosity. Its surface is supposed to be stress-free, thermally insulated and characterized by null pressure boundary conditions. A class of wave solutions is highlighted for the differential system of the model, each solution satisfying suitable asymptotic conditions in the depth of the considered half-space. Then, the Rayleigh wave solution is sought as a linear combination of the elements of this class, and, moreover, by means of the selected boundary conditions, the associated secular equation is found. By solving the secular equation, the characteristics of the wave solution are determined: the propagation speed as well as the damping in time. With the purpose of clearly highlighting the characteristics of the model, the secular equation is solved numerically and significant graphical representations are provided, using the software packages Mathematica and MATLAB. This suggests an increase of the Rayleigh wave propagation speed, corroborated with the appearance of the damping in time of its amplitude.

Eigenvalue approach to study Rayleigh waves in nonlocal orthotropic layer lying over nonlocal orthotropic half-space with dual-phase-lag model

In this present article, we deal with the propagation of Rayleigh surface waves in the nonlocal orthotropic thermoelastic layer which is lying over a nonlocal orthotropic thermoelastic half-space in the context of the dual-phase-lag model. This problem is considered in the context of Eringen’s nonlocal elasticity theory. A vector-matrix differential equation is obtained which is solved by an eigenvalue approach. The frequency equation of Rayleigh surface waves is derived and various particular cases are discussed. The different characteristics namely attenuation coefficient, specific loss, penetration depth, and phase velocity are presented graphically with respect to frequency.

Analysis of thermal effect on propagation of Rayleigh surface waves in a composite structure

Analysis of thermal effect on propagation of Rayleigh surface waves in a composite structure

Numerical analysis of the dispersion of acoustic Rayleigh waves in a Functionally Graded Piezoelectric half-Space

Considerable attention has been given to the study of the propagation of surface waves in order to improve the efficiency and lifetime of the surface acoustic wave devices such as transducers. In this paper, an investigation of the Rayleigh waves in functionally graded piezoelectric material is presented. The Rayleigh surface wave propagation is assumed to take place in a transversely isotropic graded piezoelectric half-space with material properties varying continuously along the thickness direction. The obtained results have shown that dispersive Rayleigh waves can propagate on the surface of the FGPM half-space with characteristics that depend on the graded variation of the material parameters. Based on the dispersion relations, the phase velocity for both the electrically open and shorted cases at the free surface is deduced. The displacement magnitudes and the corresponding decay variations are plotted and discussed.

A Power-Law of Two Kernels in Reductive Nonlinear Rayleigh Equation for Isotropic Elastic Materials

We reinvestigate theoretically a propagation of the nonlinear Rayleigh surface waves (NRSW) on isotropic elastic materials to understand nonlinear characteristics of the reductive nonlinear Rayleig...

Rayleigh wave propagation at the boundary surface of dry sandy ($SiO_2$) thermoelastic solids

PurposeThe purpose of study to this article is to analyze the Rayleigh wave propagation in an isotropic dry sandy thermoelastic half-space. Various wave characteristics, i.e wave velocity, penetration depth and temperature have been derived and represented graphically. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form.Design/methodology/approachThe present article deals with the propagation of Rayleigh surface wave in a homogeneous, dry sandy thermoelastic half-space. The dispersion equation for the proposed model is derived in closed form and computed analytically. The velocity of Rayleigh surface wave is discussed through graphs. Phase velocity and penetration depth of generated quasi P, quasi SH wave, and thermal mode wave is computed mathematically and analyzed graphically. To illustrate the analytical developments, some particular cases are deliberated, which agrees with the classical equation of Rayleigh waves.FindingsThe dispersion equation of Rayleigh waves in the presence of thermal conductivity for a dry sandy thermoelastic medium has been derived. The dry sandiness parameter plays an effective role in thermoelastic media, especially with respect to the reference temperature for η = 0.6,0.8,1. The significant difference in η changes a lot in thermal parameters that are obvious from graphs. The penetration depth and phase velocity for generated quasi-wave is deduced due to the propagation of Rayleigh wave. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form.Originality/valueRayleigh surface wave propagation in dry sandy thermoelastic medium has not been attempted so far. In the present investigation, the propagation of Rayleigh waves in dry sandy thermoelastic half-space has been considered. This study will find its applications in the design of surface acoustic wave devices, earthquake engineering structural mechanics and damages in the characterization of materials.

Propagation and attenuation of Rayleigh and pseudo surface waves in viscoelastic metamaterials

The development of seismic metamaterials has attracted much research interest in the past decade. Efforts have been made by using experimental and theoretical approaches to isolate buildings and structures susceptible to elastic surface wave damage. However, most seismic metamaterials were designed without considering the viscoelastic effect that widely exists in nature. In this work, we investigate the propagation and attenuation of the Rayleigh and pseudo surface waves (PSWs) in two types of viscoelastic seismic metamaterials, namely, pillared and inclusion-embedded metamaterials, by analyzing the complex band structures and transmission spectra. The complex band structure developed in this work reveals for the first time the existence of PSWs and their propagation properties in inclusion-embedded metamaterials at the surface. These PSW modes are hidden in the traditional ω(k) technique, therefore showing the usefulness of the complex band structure approach. Introducing viscosity to the substrate of both types of seismic metamaterials will enhance the attenuation of both the Rayleigh wave and PSW. For inclusion-embedded metamaterials, the viscoelastic effect in the soft coating layer can have a specific influence only on the PSW. PSWs show advantages to minimize the relative attenuating effect in general. The results in this work will open up great possibilities for designing and optimizing seismic metamaterials in practice.

Rayleigh waves in porous nonlocal orthotropic thermoelastic layer lying over porous nonlocal orthotropic thermoelastic half space

ABSTRACT The present paper deals with the propagation of Rayleigh surface waves in a nonlocal thermoelastic orthotropic layer which is lying over a nonlocal thermoelastic orthotropic half space. The problem is considered in the context of Green-Naghdi type III model of hyperbolic thermoelasticity and Eringen’s nonlocal elasticity theory in the presence of voids. The problem is solved using eigenfunction expansion method. Frequency equation of Rayleigh waves is derived and different particular cases are also deduced. The effects of voids and nonlocality on different characteristics of Rayleigh waves are presented graphically.

Rayleigh waves in porous orthotropic medium with phase lags

The present article deals with the propagation of Rayleigh surface waves in homogeneous orthotropic medium. This thermoelastic problem is studied under the purview of three-phase-lag model of hyperbolic thermoelasticity in the presence of voids. The normal mode analysis is employed to obtain a vector matrix differential equation which is then solved by eigenvalue approach. The frequency equations for different cases are derived. In order to illustrate the analytical developments, the numerical solution is carried out and the computer simulated results in respect of phase velocity and attenuation coefficient are presented graphically. Phase velocity and attenuation coefficient decreases in the presence of voids. The present problem is the most general one as other problems can be obtained as special cases from it.

Propagation of Rayleigh wave in initially-stressed compressible hyperelastic materials

In this paper, propagation of Rayleigh surface wave in a compressible half-space solid with initial stress is discussed. The basic formulation of the problem includes the non linear theory of elasticity and theory of invariants. The equations governing infinitesimal motions superimposed on a finite deformation are used to study the combined effect of initial stress and finite deformation on wave speed. Secular equation governing the wave speed of a surface wave is presented and analyzed in detail. Various conditions are found for the existence and uniqueness of the wave speed. Furthermore, to understand the physical behavior of surface wave propagation, the theoretical results are plotted and analyzed for various numerical values of parameters involved in a prototype model. It is concluded that the surface wave speed is considerably affected by compression and tension as well as due to the stretch ratios of deformation. Moreover, for various choices of numerical values of governing parameters, the admissible numerical values of initial stress components and stretch ratios are also illustrated graphically.

Surface waves in piezothermoelastic transversely isotropic layer lying over piezothermoelastic transversely isotropic half-space

In this article, the propagation of Rayleigh surface waves in a piezothermoelastic transversely isotropic layer lying over a piezothermoelastic transversely isotropic half-space is investigated in the context of the Green–Naghdi model type III of hyperbolic thermoelasticity. The secular equation of Rayleigh surface waves is derived, and different cases are discussed. Phase velocity, attenuation coefficient and specific loss of surface waves are computed and presented graphically with respect to frequency, and a comparison of different wave characteristics for classical and generalized thermoelastic models is presented in the figures.

Rayleigh waves in a magneto-thermoelastic anisotropic half-space

The aim of the present article is to study the propagation of Rayleigh surface waves in homogeneous transversely isotropic medium. The problem is considered under the purview of three-phase-lag model in an initially stressed magneto-thermoelastic half-space. Normal mode analysis is employed to the considered equations and eigenvalue approach is used to obtain the expressions for the displacements, stresses, and temperature. The frequency equations of Rayleigh surface waves are derived, and different cases are discussed. The effect of magnetic field and initial stress on the phase velocity and attenuation coefficient of Rayleigh waves are presented graphically.

Impact of damage on the effective properties of network materials and on bulk and surface wave propagation characteristics

We analyze in this contribution the propagation of bulk and Rayleigh surface waves in periodic architectured materials undergoing internal damage. An elastic damageable continuum-based model is developed in the framework of the thermodynamics of irreversible processes, whereby the displacement experiences a jump across the faces of the propagating crack. The crack propagation involves an enhancement of the displacement field associated with embedded discontinuities, which remain localized within each (triangular type) finite element. The displacement discontinuity is regulated by the traction separation behavior described by an exponential cohesive model with damage hardening followed by softening. The effective mechanical properties of the overall network are evaluated versus the increasing damage. The phase velocities for the longitudinal and transverse modes are then computed continuously versus the amount of damage, considering successively the situations of symmetrically and unsymmetrically distributed damage occurrence and propagation. Simulation results show that although the crack pattern is different in these two situations, it has no impact on the evolution of the effective moduli versus global damage. The phase velocities computed based on the effective moduli decrease as damage propagates within the network; thus, it is an indicator of the amount of global damage.

Surface waves in porous nonlocal thermoelastic orthotropic medium

The present article deals with the propagation of Rayleigh surface waves in a homogeneous orthotropic medium based on Eringen’s nonlocal thermoelasticity. This thermoelastic problem is studied under the purview of Green–Naghdi model type III of hyperbolic thermoelasticity in the presence of voids. The normal mode analysis is employed to obtain a vector matrix differential equation which is then solved by an eigenvalue approach. The frequency equations for different cases are derived. The path of surface particles during Rayleigh wave propagation is found to be elliptical. In order to illustrate the analytical developments, the numerical solution is carried out and the computer-simulated results with respect to phase velocity, attenuation coefficient and specific loss are presented graphically.

Surface waves in nonlocal thermoelastic medium with state space approach

In this paper, a new model based on Eringen’s nonlocal thermoelasticity is constructed. The propagation of Rayleigh surface waves in homogeneous isotropic medium is considered under the purview of this new nonlocal thermoelasticity theory in the context of energy dissipation theory. The normal mode analysis is employed to the considered equations to obtain vector matrix differential equation which is then solved by state space approach. The frequency equations for different cases are derived. The phase velocity, attenuation coefficients, specific loss and penetration depth of Rayleigh surface waves are computed numerically and presented graphically with respect to frequency and the effects of non-locality on the considered parameters are presented in the figures.

To the problem of the propagation of Rayleigh surface waves in preliminarily stressed bodies with curvilinear boundaries

To the problem of the propagation of Rayleigh surface waves in preliminarily stressed bodies with curvilinear boundaries

Rayleigh surface wave propagation in an orthotropic rotating magneto-thermoelastic medium subjected to gravity and initial stress

The prime objective of the present article is to analyze the effects of rotation and initial stress on the propagation of Rayleigh surface waves in a homogeneous, orthotropic magneto-thermoelastic half space subjected to gravity field. The frequency equations in closed form are derived and the amplitude ratios of surface displacements, temperature change during the Rayleigh wave propagation on the surface of half space have been computed analytically. The highlights of this study are the effects of different parameters (rotation, magnetic field, initial stress, and gravity) on the velocity of Rayleigh waves. Variation in phase velocity of Rayleigh waves against a wave number is shown graphically. Some particular cases have been deduced. Also, the classical Rayleigh wave equation is obtained as a special case of the present study. Numerical example has been carried out and represented by the means of graphs. Impacts of various involved parameters appearing in the solutions are carefully analyzed. In fact, in the absence of various parameters, these equations are in agreement with the results for isotropic medium.