Breather propagation in a damped oscillatory chain with Hertzian nearest-neighbour coupling is investigated. The breather propagation exhibits an unusual two-stage pattern. The first stage is characterized by power-law decay of the breather amplitude. This stage extends over finite number of the chain sites. Drastic drop of the breather amplitude towards the end of this finite fragment is referred

We construct the exact nonlinear wave solutions of the Nonlinear Schrödinger equation on the period wave background instead of on a constant background. By using Darboux-Bäcklund transformation, soliton and breather solutions on two types of cnoidal wave backgrounds are given. The density evolutions of these solutions are given under different parameters to study their wave structures and dynamical

The theoretical study by the perturbation method of the acoustic effects at the degenerate parametric interaction of a strong high-frequency and a weak low-frequency longitudinal elastic waves in microinhomogeneous solids with a quadratically-bimodular nonlinearity is presented. The amplitude dependences for the following nonlinear effects are revealed and analyzed: generation of second and fourth

The multi-component AB system, which appears in the ultra-short optical pulse field and the geophysical fluid dynamics, is investigated via the Darboux transformation technique. Combining the special vector solutions for the Lax pair and the corresponding Darboux transformation, the higher-order semirational solutions for the AB system are constructed. Besides, the semirational solutions are discussed

This paper reports on a theoretical framework to analyse coupled wave propagation in magnetoelectroelastic solids of hexagonal symmetry. The constitutive equations contain the effective properties of micromechanics to model piezoelectric–piezomagnetic composites. The Mori–Tanaka scheme is used. The governing equations include the elastodynamic equations of motions and unique forms of the Maxwell equations

We investigate structured arrays and rings in elasticity to design elastic platonic circuits that utilise resonant phenomena. Creating ring resonators, and understanding their coupling to input and output arrays, allows for the development of platonic circuits including add–drop filters (ADFs) and coupled resonator elastic arrays (CREAs), and hence we envisage integrated platonic devices. Structured

In this paper we established a numerical method for Equal Width (EW) Equation using Polynomial Scaling Functions. The EW equation is a simpler alternative to well known Korteweg de Vries (KdV) and regularized long wave (RLW) equations which have many applications in nonlinear wave phenomena. According to Polynomial scaling method, algebraic polynomials are used to get the orthogonality between the

This paper focuses on quasi-two-dimensional integral surface method in order to estimate the propagation of two-dimensional acoustic waves. In this approach, the required surface data is generated by replication of a two-dimensional data curve along the third out-of-plane dimension. For this purpose, a two-dimensional monopole acoustic source is employed and the Farassat integral surface approach is

Several months of seafloor-mounted, pressure-transducer data collected in Mordvinova Bay off the south-east coast of Sakhalin Island in the Sea of Okhotsk are used to interpret surface-gravity waves across a wide range of periods, during intervals when the sea surface was free of sea ice, covered by drift ice of 0.5–1 m thickness, and when both drift ice and consolidated shore fast sea ice was present

An approximate solution for the steady linear internal wave field generated by a localized, horizontally moving source in a thermocline is derived using ray and WKB (Wentzel–Kramers–Brillouin) theory. The waves are assumed to be steady in a reference frame moving with the source velocity. This solution is shown to agree in the limit of propagating waves with an existing solution that is expressed in

In this work, the regularized and the modified regularized long wave equations are solved using an improvised cubic B-spline collocation technique. Posteriori corrections are made in the cubic B-spline interpolant by forcing it to satisfy some specific interpolatory and end conditions, which results in the formation of improvised B-spline collocation technique. For temporal domain discretization, strong

We report our experimental observation of a single and stable defect mode arising in the non-Bragg bandgap of surface water waves by introducing a defect element into a water channel with periodically corrugated sidewalls. By investigating the existence of the non-Bragg defect mode and its frequency shifting, we find that unlike the Bragg defect mode which arises within an extended region around the

This paper investigates methods of band gap formation in two-dimensional locally resonant elastic metamaterials and proposes a technique for computing such gaps as algebraic functions of integrated Bloch modes and metamaterial parameters. Mode shapes associated with the deformation of unit cells consisting of a hard matrix, soft filler, and hard resonator are investigated near the lower and upper bounds

We study the coherent propagation and incoherent diffusion of in-plane elastic waves in a two dimensional continuum populated by many, randomly placed and oriented, edge dislocations. Because of the Peierls–Nabarro force the dislocations can oscillate around an equilibrium position with frequency ω0 . The coupling between waves and dislocations is given by the Peach–Koehler force. This leads to a wave

Returning to Manne et al. (2000), wherein a class of hyperbolic reaction-diffusion-acoustic models is considered, we show that the inexact transport equation derived by these authors becomes the exact equation for the propagation of second-sound (i.e., thermal waves) in a rigid solid when reformulated under the modified internal energy model, one of several formulations of what has come to be known

The interaction of oblique incident waves with a floating porous plate has been investigated using the matched eigenfunction expansion method (MEEM). The porous boundary condition based on Darcy’s law is applied at a floating porous plate (Zhao et al. (2009)). Depending on the presence of a vertical rear wall, the wave energy dissipation by a floating porous plate is evaluated with two analytical models:

Scattering of electromagnetic plane waves normally incident on a flat perfect electric conductor strip in arbitrary rotational motion in its own plane is investigated in the context of Hertzian Electrodynamics. This canonical problem is an analytical-asymptotic approach that reveals the parametric dependence of interference of electromagnetic waves with rotating blades, a subject which is known as

The propagation of electromagnetoacoustic SH surface waves (called briefly EMA-SH waves) in non-dispersive piezoelectric media was investigated by Li (1996). Romeo (2004) has derived a formula for the wave velocity. However, it is not valid for all values of material parameters belonging to the existence domain of EMA-SH waves. In this paper, a new formula for the velocity of EMA-SH waves has been

We construct a solution to the initial–boundary value problem, called the Lamb-Danilovskaya problem, for the half-space occupied by a thermo-viscoelastic medium with memory. The viscoelastic medium is described by the Biot model, whereas the thermal influence is described by the Gurtin–Pipkin model. The solution is obtained using Cagniard-de Hoop method. Based on that solution, we describe various

This paper develops a variational formulation for two-dimensional (2-D) vibro-acoustic analysis of a circular ring in unbounded acoustic domain. The Reissner–Naghdi’s generalized shell theory is adopted to formulate the energy functional of the circular ring, while the Helmholtz equation is used to derive the stored energy in the acoustic domain. A modified variational principle combined with a domain

Based on the Legendre orthogonal polynomial series expansion and the partial wave theory, a Legendre orthogonal polynomial method (LOPM) is proposed to calculate the reflection and transmission coefficients of plane waves at the liquid/solid interface of a liquid-loaded functionally gradient material (FGM) plate. The displacement solutions in FGM plate are fitted approximately by Legendre orthogonal

The ray-based generalized Radon transform (GRT) inversion/migration strategy is studied in this paper for acoustic transversely isotropic media with a vertical symmetry axis (VTI media) represented by the P-wave normal moveout velocity, Thomsen parameter δ, anelliptic parameter η, and density. The multi-parameter GRT inversion solutions for multi-shot/multi-offset acquisition geometries are derived

Though lightweight sandwich structures have been extensively applied in practical engineering, it remains a challenge to control wave propagation and vibration in these structures in a low-frequency range. In this work, the band structure of flexural waves in a metamaterial sandwich beam (MSB) with hourglass lattice truss core is investigated using the transfer matrix method (TMM). The hourglass truss

The steady-state vibro-acoustic behavior of a plate–cavity system under harmonic excitations and static temperature loads is investigated using a Wave Based Method (WBM). The solutions of the governing equations of the vibro-acoustic problem considering thermal effects are derived. The coupled wave based model is constructed based on wave functions and particular solution functions for the acoustic

In this study, the Scaled Boundary Finite Element Method (SBFEM) was used to perform analyses and evaluate the objective function in shape optimization of devices relying on acoustic wave propagation. Similar to the Boundary Element Method (BEM), the SBFEM requires only the discretization of the boundary of the computational domain. However, unlike BEM, there is no need for a fundamental solution;

The role of a floating elastic plate on the hydrodynamic instability of a gravity-driven flow down an inclined plane is examined in the linear and nonlinear regimes. Linear instability of the system with respect to infinitesimal disturbances is captured using normal-mode analysis. The critical conditions for instability are obtained analytically utilizing the small film aspect ratio. The bifurcation

In this paper, the Mth-order lump solutions for the (2+1)-dimensional Kadomtsev–Petviashvili I equation are studied. Firstly, the Nth-order wronskian determinant solutions of the Hirota bilinear form of the (2+1)-dimensional Kadomtsev–Petviashvili I equation are given. Then, the 1st-order lump solution is obtained by making elementary transformations and taking limit to the 2nd-order wronskian determinant

Supersonic flows past the morphing cavities with different ramp angles of the trailing wall are studied by the direct numerical simulation (DNS) method. As the ramp angle increases, the sound pressure level of the dominant mode and overall sound pressure level gradually decrease at the last monitor point. The number of the feedback shock waves and the size of the large-scale vortices also gradually

This study derives solitons solutions of the reverse-time nonlocal Davey–Stewartson III equation by the Kadomtsev–Petviashvili hierarchy reduction method and Hirota’s bilinear method. The solutions are expressed as N×N Gram-type determinants with different parametric reduction conditions. N-soliton and line breather solutions on both constant and periodic backgrounds are derived. The dynamics of these

A multi-component semi-discrete nonlinear integrable system associated with the relevant third-order auxiliary linear problem is claimed to be the prototype system for several reduced integrable systems formulated in terms of true dynamical field variables. The main conservation laws related to the prototype system are found in the framework of generalized recurrent approach. The two-fold Darboux–Bäcklund

The present study focuses on analysing the behaviour of wave propagation in carbon nanotubes along with the characterization of the buckling phenomenon. The carbon nanotubes are modelled as continuum shells that utilize the nonlocal theory of elasticity as these consider the small effects of the nano structures. The expression for the dispersion relation of the wave propagation in single-walled carbon

The scope of the present work is to elucidate the reverberations of propagating guided waves through delaminated regions confined in composite plate structures. As it is well known, delamination between consequent plies is the most common type of damage in composite structures. A mean of investigation of delamination cracks is through guided wave propagation. It has been observed that either type of

Metamaterials are generally known for their waves attenuation capabilities. This behaviour, which is related to the microstructure composing these materials, can be due to a Bragg-type scattering mechanism or to local resonances. The objective here is to exploit the two phenomena for generating a system able to localize the energy carried by propagating elastic (or acoustic) waves. To this purpose

This article deals with the dynamic response of laterally unbounded, horizontally layered plates subjected to dynamic sources applied at arbitrary locations, which is ultimately a classical problem. This response is most often obtained via a modal superposition in terms of the complex Lamb modes by casting the equations in the frequency–space domain, followed by a Fourier inversion into the space–time

This study proposes an analytically unprecedented model of a meta-lattice truss with local resonators to generate a broader low-frequency bandgap. By leveraging the mass–spring model, a new equivalent meta-unit cell considering the elastic shear springs is developed to accurately predict the performance of the meta-lattice truss in suppressing stress wave propagations. Theoretical analyses and numerical

We consider the effective wave motion, at spectral singularities such as corners of the Brillouin zone and Dirac points, in periodic continua intercepted by compliant interfaces that pertain to e.g. masonry and fractured materials. We assume the Bloch-wave form of the scalar wave equation (describing anti-plane shear waves) as a point of departure, and we seek an asymptotic expansion about a reference

This work considers the propagation of bending waves along the free edge of a semi-infinite piezoelectric plate perfectly bonded with a metal strip plate of the same thickness within the framework of the first-order Reissner–Mindlin refined plate theory. The three-dimensional coupled equations for displacement fields are solved with the help of the solution to electric potential for a plate of infinite

Periodic structures can be designed to exhibit elastic wave propagation band gap behaviour by varying material or geometrical properties, i.e. phononic crystals, or by periodically distributed resonators or boundary conditions, i.e. acoustic metamaterials, with various applications in passive noise and vibration control. However, variability in the manufacturing process causes material and geometry

In this paper, we give an integrable four-field lattice hierarchy associated to a new discrete spectral problem. We obtain our hierarchy as the compatibility condition of this spectral problem and an associated equation, constructed herein, for the time-evolution of eigenfunctions. The Hamiltonian representation of the four-field lattice hierarchy are constructed by using the trace identity. We consider

It is shown that Bound States in the Continuum (BSC) exist in an elastic structure consisting of a periodic double array of thin (subwavelength) cylindrical scatterers embedded in a background material, where the distance between the arrays is taken to be large in comparison to both the wavelength and the period of the array. The background medium supports waves with all polarizations, one longitudinal

We analyze soliton solutions and verify the Hirota N-soliton condition for the B-type Kadomtsev–Petviashvili equation, within the Hirota bilinear formulation. A weight number is used in an algorithm to check the Hirota condition while transforming the Hirota function in N wave vectors to a homogeneous polynomial. Soliton solutions are presented under general dispersion relations.

Flexural edge waves in a Kirchhoff plate, carrying periodically spaced spring–mass​ resonators at its edge and laid on a Winkler foundation, are considered. A spectral element method is applied on a representative unit cell to develop the dynamic stiffness matrix of the structure. In light of structural periodicity, Bloch wave theorem is used to derive a quadratic eigenvalue problem of the wave propagation

We present a semi-analytical method for computing the reflection and transmission coefficients at joints connecting an arbitrary number of semi-infinite orthotropic plates based on the line-junction approximation. We use a wave approach and describe reflection, transmission and mode conversion between eigenmodes of the vibro-acoustic equations for orthotropic plates. A detailed derivation is presented

We propose a multi-harmonic numerical method for solving wave scattering problems with moving boundaries, where the scatterer is assumed to move smoothly around an equilibrium position. We first develop an analysis to justify the method and its validity in the one-dimensional case with small-amplitude sinusoidal motions of the scatterer, before extending it to large-amplitude, arbitrary motions in

We consider two ‘Classical’ Boussinesq type systems modelling two-way propagation of long surface waves in a finite channel with variable bottom topography. Both systems are derived from the 1-d Serre–Green–Naghdi (SGN) system; one of them is valid for stronger bottom variations, and coincides with Peregrine’s system, and the other is valid for smaller bottom variations. We discretize in the spatial

Gravity waves of the Stokes-type in a system of two horizontal layers of inviscid, stratified and miscible fluids are studied by applying a Lagrangian description of fluid motion. It is shown that for the total vertically-integrated Stokes drift (the Stokes flux) to become zero, the density must be continuous at the interface. This is not the case in a system of two immiscible homogeneous layers of

This manuscript describes the derivation of systems of equations for weakly nonlinear gravity waves in shallow water in the presence of constant vorticity. The derivation is based on a multi-layer generalization of the traditional columnar Ansatz. A perturbative development in a nonlinear parameter and a dispersive parameter allow us to obtain sets of equations, for the horizontal fluid velocity and

We propose a novel approach to design a tunable acoustic channel drop filter based on a fluid–fluid phononic crystal (PnC), using two ring resonators. A square lattice of infinitely long cylindrical water inclusions is embedded in the mercury matrix to characterize the PnC structure. We show that the output resonant frequency can be ultra-tuned by changing the location of each ring, and the quality

Particles or cells in suspension and exposed to ultrasonic waves experience an acoustic radiation force (FR) which, under certain conditions, drives them toward positions of acoustic equilibrium. In this paper, we present a three-dimensional model of the particle motions within the acoustic field generated by ultrasonic standing waves. This model allows a theoretical study of the three-dimensional

Propagation of acoustic waves is considered in a system consisting of two stiff quarter-spaces connected by a planar soft layer. The two quarter-spaces and the layer form a half-space with a planar surface. In a numerical study, surface waves have been found and analyzed in this system with displacements that are localized not only at the surface, but also in the soft layer. In addition to the semi-analytical

A generalized analytical approach for the propagation of Bleustein–Gulyaev wave in a piezoelectric material loaded on its surface with a viscoelastic fluid is established in this paper. The Bleustein–Gulyaev waveguide surface is subjected to various glycerol concentrations. The Maxwell and Kelvin–Voigt models are used to describe the viscoelasticity of this fluid. Exact dispersion equation is obtained

A ray dynamics describing wave transport on curved and smooth thin shells can be obtained from the underlying wave equations via the Eikonal approximation. We analyse mid-frequency effects near the ring frequency for curved plates consisting of a cylindrical region smoothly connected to two flat plates. Using classical shell theory, we treat a corresponding ray-tracing limit derived in the short wavelength

The propagation characteristics of feature guided waves (FGWs) in topographical waveguides, such as welded joints, have been widely investigated. However, most of these investigations analyzed linear acoustic characteristics. Considering the high sensitivity of nonlinear ultrasonic techniques in the nondestructive evaluation of microscopic defects in materials, such as identifying micro-defects at

The detection and evaluation of closed cracks are of prime interest in industry. Whereas conventional ultrasonic methods fail to detect these defects, nonlinear methods based on activation of the nonlinear behavior of closed cracks constitute an interesting alternative. The aim of this article is to give a better understanding of interactions between cracks and a longitudinal elastic wave for a quantitative

In this work, we examine generalized equal width (GEW) equation which is a highly nonlinear partial differential equation and describes plasma waves and shallow water waves. Nonlinearity of the equation is tackled by a linearization technique and finite difference approach is utilized for time derivatives. For spatial derivatives we first introduce delta-shaped basis functions which are relatively

We use the bilinear Kadomtsev–Petviashvili (KP) hierarchy reduction method for deriving new families of explicit lump–soliton solutions to the PT-symmetric nonlocal Fokas system. These lump–soliton solutions are semi-rational solitons that are classified into three different species under appropriate parametric restrictions: line solitons, rational lumps, and semi-rational lump–soliton solutions. There

In this work we study the effect caused by the so called Holian conjecture (HC) on the rarefied gases shock-wave structure under the continuum approach. This conjecture which was introduced to study hard spheres takes the longitudinal temperature to calculate the viscosity and thermal conductivity, a fact which makes the shock-wave structure be modified by the explicit lack of isotropy. We generalized

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

In this study, the propagation of surface water waves initially displaced by a tectonic seafloor deformation of arbitrary geometry was obtained considering the rupture kinematics. The developed solution was applied to a set of problems for wave generation by bottom motion with arbitrary spatiotemporal variations. First, a single bottom motion with different uplift speeds was considered; results showed