For the sake of lowering the locally resonant bandgap without additional mass or softer springs, a multi-resonator periodic hybrid structure with an ultralow-frequency band gap is proposed. The hybrid structure is composed of quasi-zero-stiffness (QZS) mechanical systems and multiple mass-in-mass (MIM) lattice systems. A theoretical model is established to investigate the dispersion relation of the

Rational solutions to the modified Korteweg–de Vries (mKdV) equation are given in terms of a quotient of determinants involving certain particular polynomials. This gives a very efficient method to construct solutions. We construct very easily explicit expressions of these rational solutions for the first orders n=1 until 10.

We propose an algorithm based on the Method of Difference Potentials (MDP) for the numerical solution of multiple scattering problems in three space dimensions. The propagation of waves is assumed time-harmonic and governed by the Helmholtz equation. The latter is approximated with 6th order accuracy on a Cartesian grid by means of a compact finite difference scheme. The shape of the scatterers does

The research of the derivative nonlinear Schrödinger equation (DNLS) has attracted more and more extensive attention in theoretical analysis and physical application. The improved physics-informed neural network (IPINN) approach with neuron-wise locally adaptive activation function is presented to derive the data-driven localized wave solutions, which contain rational solution, soliton solution, rogue

In this paper, the existence and stability of solitons in parity-time (PT)-symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with fourth-order diffraction (FOD) coefficient and higher-order nonlinearities have been investigated. For the linear case, we have demonstrated numerically that, the FOD parameter can alter the PT-breaking points. Exact analytical

The current paper concerns to develop an efficient and robust numerical technique to solve the shallow water equation based on the generalized equal width (GEW) model. The considered model i.e. the generalized equal width (GEW) equation is a PDE that it can be classified in the category of hyperbolic PDEs. The solution of hyperbolic PDEs is similar to a fixed or moving wave. Thus, for solving these

The present analysis confers the propagation characteristics of horizontally polarized​ shear (SH) wave through a heterogeneous transversely isotropic fluid-saturated poroelastic sandwiched layer of finite width embedded between two heterogeneous isotropic elastic half-spaces due to the impact of an impulsive line source. The dissipation of energy caused by the relative fluid flow is neglected in transversely

We investigate on controlling quantum localized structures in a 1D Heisenberg spin chains containing a large number of quanta via the magic angle, where the dynamics of modulated waves is be modeled by the equation of motion, obtained by means of time-dependent Hartree approximation and time-dependent variational method. Through the linear stability analysis, the criterions of appearance of modulation

The scattering of scalar waves by a periodic row of inclusions is theoretically and numerically investigated. The wavelength in the background medium is assumed to be much larger than the typical sizes of the inclusions. The latter are also much softer than the matrix, yielding localized resonances within the microstructure. Previous works in the inviscid case have concerned: (i) the derivation of

A WKB solution to the cochlear wave equation is derived, which results from the interaction between the passive dynamics of the basilar membrane and the 1D fluid coupling in the scalae, including both fluid viscosity and compressibility. The effect of various nondimensional parameters on the form of this solution is discussed. A nondimensional damping parameter and a nondimensional phase-shift parameter

The scattering of gravity waves by a rigid floating dock in the presence of an array of porous and non-porous breakwaters of different configurations is analysed under the framework of linear potential flow theory. The waves passing the submerged porous structures are assumed to follow Darcy’s law. Two independent physical problems such as the array of porous and non-porous breakwaters, placed (i)

We address the numerical simulation of periodic solids (phononic crystals) within the framework of couple stress elasticity. The additional terms in the elastic potential energy lead to dispersive behavior in shear waves, even in the absence of material periodicity. To study the bulk waves in these materials, we establish an action principle in the frequency domain and present a finite element formulation

The high-order Absorbing Boundary Condition proposed by Hagstrom and Warburton was applied to various models as the wave equation, dispersive, convected with stratified materials. We propose an other way to expand the use of this condition with Domain Decomposition Method. We apply it here to a Stratified Dispersive Wave Model not just to limit the real unbounded domain but to use a non-overlapping

This paper provides a time domain model for the propagation of transient ultrasonic waves in a self-similar porous material having a rigid frame. This model is based on the formalism of Stillinger–Palmer–Stavrinou, which consists in modeling the fractal material as a porous medium with a non-integer dimensional space. This paper is devoted to the time-domain analytical calculus of the reflection and

We formulate resolution enhancement as a modified Backus–Gilbert inverse problem and determine the optimal complex weights that improve focusing of waves in space and time. The optimization corrects for receiver geometry. If we accurately know the location of a control point in the subsurface we can use the corresponding optimal weights to achieve enhanced focusing in a prescribed target zone surrounding

We propose in this work a model of a continuum with a structure described by an infinite-order equation of motion. The resulting equation of motion provides dispersion for P and S waves, and there are parameter intervals where the wave velocities can decrease and increase with the average size of the microstructure. There are parameter intervals for which the velocity ratio of VS∕VP is high enough

Homogenisation theory is used to derive Wood’s formula for the speed at which a pressure wave can propagate in an air/water mixture. The smallness of the impedance ratio between air and water results in a dramatic lowering of the wave speed of the mixture and, when the air fraction is small, the possibility of regions of persistent ringing in the vicinity of the boundary where the pressure is applied

The acoustical problem dealing with the interaction of a plane wave propagating along the liquid-filled cylindrical cavity with an elastic spherical shell filled, in turn, with the compressible liquid is solved. An axisymmetric case is studied. The boundary problem for simultaneous solution of the wave equations describing the motion in the fluid filling the vessel as well as in the fluid contained

Materials with asymmetric microstructure can constitutively couple macroscopic fields from different physics. Examples include piezoelectric materials that couple mechanical and electric fields and Willis materials that anomalously couple dynamic and elastic fields, for example velocity and stress. Recently, it was shown that anomalous coupling between the elastodynamic and electric field emerges when

Exact solutions of the linear water-wave problem describing oblique waves over a submerged horizontal cylinder of small (but otherwise fairly arbitrary) cross-section in a two-layer fluid are constructed in the form of convergent series in powers of the small parameter characterizing the “thinness” of the cylinder. The terms of these series are expressed through the solution of the exterior Neumann

A laminar flow of a thin layer of mud down an inclined plane under the action of gravity is considered. The instability of a film flow and the formation of finite amplitude waves are studied within the framework of both two-dimensional governing equations of a power-law fluid and its depth-averaged hyperbolic simplification. The conditions of the existence of roll waves for these models are formulated

We adopt a robust numerical continuation scheme to examine the global bifurcation of periodic travelling waves of the capillary–gravity Whitham equation, which combines the dispersion in the linear theory of capillary–gravity waves and a shallow water nonlinearity. We employ a highly accurate numerical method for space discretization and time stepping, to address orbital stability and instability for

The objective of the present study is to suppress the large amplitudes of a continuous spinning shaft under an active vibration control. For this purpose, the Positive Position Feedback (PPF) control with time-delays are applied to the system via Macro-Fiber-Composite (MFC) sensors and actuators. The nonlinear dynamics of the system is explored analytically utilizing the perturbation method in the

We investigate the modulation instability and higher-order rogue waves for the Gerdjikov–Ivanov equation. Based on the theory of the linear stability analysis, the modulation instability is the condition of the existence of the rogue waves. With the help of Darboux transformation and a variable separation technique, the formula of the higher-order rogue wave solutions is given explicitly. The kinetics

The time-dependent motion of flexural waves generated by the vibration of an elastic plate resting on a variable Winkler foundation with compression is studied. The physical problem is analysed under the assumption of small amplitude structural response in two dimensions. The dispersion equation is analysed in detail, and points of wave blocking are shown to exist. The time-dependent propagation is

For wave propagation over a finite array of cycloidal bars or trenches, an analytical solution of wave reflection in terms of Frobenius series to the modified mild-slope equation (MMSE) is given. First, the present solution related to cycloidal bars is validated against experimental data and two numerical solutions for wave reflection by rectified cosinoidal bars with the bar parameters same to those

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

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

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

A generalized Poisson summation formula produces an explicit expression for the surface current on a plane that radiates a set of preselected plane waves. Specifically, the surface current is expressed as an integral in the complex plane of a function whose poles determine the plane-wave directions of propagation and whose residues determine the corresponding plane-wave amplitudes. When only a finite

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

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

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

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

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