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Biodegradable polymers find an increasing number of applications in different fields of engineering and medicine due to their environmental-friendly degradation. The process of degradation of biodegradable polymer constituents and the bonding quality between the constituents in composites can be identified by the analysis of the phononic band structure. The present article considers a layered composite, in which the matrix degradation is modeled by a multitude of layers with decreasing values of their mechanical properties. Bonding between the inclusion and the degrading matrix is taken into account by a linear elastic bonding model in the first case and by a viscoelastic model in the second case. [ABSTRACT FROM AUTHOR]

The influence of viscoelastic ocean beds on the characteristics of surface waves passing through mangrove forests is analyzed under the assumption of linearized water wave theory in two dimensions. The trunks of the mangroves are assumed to be in the upper-layer inviscid fluid domain, whilst the roots are inside the viscoelastic bed. The associated equation of motion is obtained by coupling the Voigt’s model for flow within the viscoelastic medium with the equation of motion in the presence of mangroves. The modified dynamic conditions are coupled with the kinematic conditions to obtain the boundary condition at the free surface and the interface of the two fluids consisting of the upper layer inviscid fluid and the viscoelastic fluid bed. To understand the effects of bed viscosity as well as elasticity on energy dissipation, the complex dispersion relation associated with the plane progressive wave is derived and analyzed. Effect of physical parameters associated with mangroves and viscoelastic bed on wave motion in surface and internal modes are computed and analyzed to understand their roles in attenuating wave effects. The present model will be useful in the better understanding of wave propagation through mangroves in the coastal zone having muddy seabed. [ABSTRACT FROM AUTHOR]

The properties and accuracy of the linearized version of the fully dispersive and nonlinear wave model developed in Yates and Benoit (2015) and Raoult et al. (2016) are analyzed for both flat and variable bottom bathymetries. This model considers only a single layer of fluid and uses a basis of orthogonal Chebyshev polynomials to project the vertical structure of the potential. This approach results in an exponential convergence rate with the maximum degree of the Chebyshev polynomial, denoted N T , while only first- and second-order derivatives in space need to be evaluated. For the constant water depth case, the linear dispersion relation of the model is derived analytically, and expressions are established for N T ranging from 2 to 15. The analysis shows a rapid increase in accuracy in the deep water range with increasing N T . For instance, the relative error in the calculated wave celerity (in comparison with Stokes’ analytical solution) remains smaller than 2.5% for deep water cases with k h up to 100 using N T ≥ 9 ( k and h are the representative wavenumber and water depth, respectively). The wave kinematics, vertical profiles of the horizontal and vertical orbital velocities, converge to the Stokes profiles for k h up to 60 when using a sufficiently high value of N T . The vertically-averaged relative errors of the horizontal and vertical velocities remain below 6% and 3%, respectively, for k h up to 60 when using N T ≥ 11 . The presented model shows better dispersive properties in deep water than several high-order Boussinesq-type models. For variable bottom bathymetries, the shoaling properties of the model are studied numerically, exhibiting good agreement with results from Stokes linear theory in the case of mild bottom slopes, using a sufficiently high value of N T with respect to the offshore relative water depth. For an offshore water depth of k h = 10 (i.e. more than 3 times the deep water limit), accurate wave heights in shallow water ( k h = 0 . 25 ) are obtained with N T = 6 (or higher). Finally, the linear version of the model is validated with comparisons to analytical solutions of the reflection and transmission coefficients of regular waves over Roseau-type bathymetric profiles. Two bottom profiles are considered, including one with a steep slope, whose maximum value reaches about 1:0.7 (i.e. an angle of about 54.9 deg.). Using N T = 7 , small differences ( < 0 . 4 % ) with the analytical solution are observed for the four considered cases, confirming the ability of the linear model to represent accurately the effects of steep bottom gradients on wave propagation dynamics. [ABSTRACT FROM AUTHOR]

The paper investigates waves generated by the moving loads on ice plates floating on an incompressible fluid. Two different viscoelastic approximations are considered for the ice cover: A model depending on the strain-relaxation time, and a model including a hereditary delay integral. The problem is formulated in terms of the exact dispersion relation and the Dirichlet–Neumann operator connected to the fluid motion. Weakly nonlinear and linear approximations are derived by truncating the Dirichlet–Neumann operator. The Laplace transform is used to find the exact solutions of the linearized problems for the two viscoelastic models considered. • Visco-elastic effects on waves generated by moving loads on ice sheets. • Exact solutions of the linearized problem. • Study of wave response in practical cases. [ABSTRACT FROM AUTHOR]

Using Biot’s consolidation theory, effect of poroelastic bed on flexural gravity wave motion is analyzed in both the cases of single-layer and two-layer fluids. The model for the flexural gravity waves is developed using linear water wave theory and small amplitude structural response in finite water depth. The effects of permeability and shear modulus of poroelastic bed and time period on flexural gravity wave motion are studied by analyzing the dispersion relation, phase speed, plate deflection, interface elevation and pressure distribution along water depth. Various results for surface gravity waves are analyzed as special cases. The study reveals that bed permeability retards the hydrodynamic pressure distribution along the water depth significantly compared to shear modulus whilst, floating plate deflection decreases significantly with change in shear modulus compared to permeability of the poroelastic bed. The present study can be generalized to analyze various wave–structure interaction problems over poroelastic bed. [ABSTRACT FROM AUTHOR]

The results of a previous paper (Muracchini et al., 1992) are generalized by considering a hyperbolic system in one space dimension with multiple eigenvalues. The dispersion relation for linear plane waves in the high-frequency limit is analyzed and the recurrence formulas for the phase velocity and the attenuation factor are derived in terms of the coefficients of a formal series expansion in powers of the reciprocal of frequency. In the case of multiple eigenvalues, it is also verified that linear stability implies λλ-stability for the waves of weak discontinuity. Moreover, for the linearized system, the relationship between entropy and stability is studied. When the nonzero eigenvalue is simple, the results of the paper mentioned above are recovered. In order to illustrate the procedure, an example of the linear hyperbolic system is presented in which, depending on the values of parameters, the multiplicity of nonzero eigenvalues is either one or two. This example describes the dynamics of a mixture of two interacting phonon gases. [ABSTRACT FROM AUTHOR]

Acoustic-gravity wave propagation under a compressed ice-shelf is mathematically modelled under the assumption of small ice-shelf deflection, linearised compressible water wave theory, and ocean floor elasticity. The dispersion relation associated with the acoustic-gravity modes is derived. Special cases of the free surface gravity wave motion with a rigid and elastic bottom, and flexural-gravity wave motion with rigid ocean bottom are approximated by utilising the dispersion relation. The effect of ice-shelf thickness and compressive stress on the propagation speed is investigated for different acoustic-gravity modes. The pressure distribution along the water column and the ice-shelf due to different acoustic-gravity modes are illustrated. While ice thickness significantly alters the phase speed and pressure distribution, the compressive force generally has a negligible effect on the phase speed of acoustic-gravity modes. However, the compression has significant effect on the pressure distribution. A separate treatment for relatively low frequencies shows a significant impact of the compressive force on the spatial pressure distribution. The dominance of the leading acoustic-gravity modes on different physical characteristics is evident from their graphical representations. An orthogonality property for the depth-dependent functions of the velocity potential in the water region is established along with a few approximate forms. This mathematical model can be treated as a more general one that can unify several well-established models of acoustic-gravity wave propagation. • Small amplitude linear acoustic-gravity waves under a compressed ice-shelf are studied. • The ocean floor is elastic and dilatation and rotational potential functions are considered. • The effect of ice-shelf thickness on the phase speed is investigated. • The impact of the different compressive stress acting on the ice-shelf is studied. • The leading acoustic-gravity mode changes more significantly than other modes. [ABSTRACT FROM AUTHOR]

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 isotropic fluid-saturated poroelastic sandwiched layer. The heterogeneities in layer and half-spaces are considered with the respective spatial quadratic and exponential type variations in the elastic constants and densities. Green's functions are obtained for this sandwiched layered structure by considering a charge-density/line-force (Dirac-delta function) at lower bonding surface of layer and half-space. Dispersion relation for the propagation of SH wave in aforesaid structure has been obtained with well-known properties of Green's functions, Fourier's transformation and appropriate boundary conditions. The obtained dispersion relation is reduced for a structure with a heterogeneous transversely isotropic fluid-saturated poroelastic layer of finite width overlying a heterogeneous isotropic elastic half-space in the particular case of problem. Moreover, the obtained dispersion relations are validated and matched with pre-established standard and classical results. The effect of various affecting parameters viz. anisotropy of layer, porosity of layer and heterogeneities of layer and half-spaces on phase velocity of propagating wave in said structure are shown graphically through numerical computations. Further, a comparative study of distinct cases of heterogeneous/homogeneous structures is also performed which serves as the major highlight of the present study. • SH wave propagation in a poroelastic sandwiched layer due to an impulsive source. • Green's function method is used to drive dispersion relation in closed form. • Obtained results are validated with pre-established and standard results. • Numerical simulation is done to show the effect of affecting parameters graphically. [ABSTRACT FROM AUTHOR]

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 simulated for the case of both constant and variable properties. For the case of varying properties, it is shown that the wave amplitude near the blocking point for this class of flexural waves satisfies the hyper-Airy differential equation, which is solved analytically in terms of the fourth-order Airy function. Further, the asymptotic solution of the hyper-Airy differential equation is derived by employing the WKB method to match the far-field solution with the near-field solution. The results obtained analytically are compared with a novel time-domain simulation based on a spectral method. • The time-domain solution is calculated for a Winker foundation with compression. • The asymptotic solution is calculated in terms of the Airy and hyper-Airy function. • A novel numerical method is derived using a spectral method. • The asymptotic solution is validated by comparison. • The time-domain simulation is presented as a movie. [ABSTRACT FROM AUTHOR]

Abstract: We derive exact dispersion relations for axial and flexural elastic wave motion in a rod and a beam under finite deformation. For axial motion we consider a simple rod model, and for flexural motion we employ the Euler–Bernoulli kinematic hypothesis and consider both a conventional transverse motion model and an inextensional planar motion model. The underlying formulation uses the Cauchy stress and the Green–Lagrange strain without omission of higher order terms. For all models, we consider linear constitutive relations in order to isolate the effect of finite motion. The proposed theory, however, is applicable to problems that also exhibit material nonlinearity. For the rod model, we obtain the exact analytical explicit solution of the derived finite-deformation dispersion relation, and compare it with data obtained via numerical simulation of nonlinear wave motion in a finite rod. For the beam model, we obtain an approximate solution by standard root finding. The results allow us to quantify the deviation in the dispersion curves when exact large deformation is considered compared to following the assumption of infinitesimal deformation. We show that incorporation of finite deformation following the chosen definitions of stress and strain raises the frequency branches for both axial and flexural waves and consequently also raises the phase and group velocities above the nominal values associated with linear motion. For the beam problem, only the inextensional planar motion model provides an accurate description of the finite-deformation response for both static deflection and wave dispersion; the conventional transverse motion model fails to do so. Our findings, which represent the first derivation of finite-strain, amplitude-dependent dispersion relations for any type of elastic media, draw attention to (1) the tangible effect of finite deformation on wave dispersion and consequently on the speed of sound in an elastic medium and (2) the importance of incorporating longitudinal–transverse motion coupling in both static and dynamic analysis of thin structures subjected to large nonlinear deformation. [Copyright &y& Elsevier]

Abstract: This paper addresses the characteristics of shear waves in a transversely isotropic poroelastic layer under a free or rigid boundary and lying over an elastic layer. Based on Biot’s theory, the dispersion equation for shear waves was derived analytically, taking boundary conditions and geometry into account. Detailed numerical simulations are provided to illustrate graphically the phase and group velocities plotted against the dimensionless wave number. Such illustrations allow the identification and comparison of the effects of the thickness ratio of the layer, two different boundary conditions, porosity, and anisotropy. It was observed that the phase and group velocities increase as thickness ratio and porosity increase. In addition, the phase and group velocities increase or decrease as anisotropy increases. In the rigid boundary condition, phase velocity increases to a greater extent than it does in the free boundary condition. [Copyright &y& Elsevier]

Abstract: A new nonlinear evolution equation is derived for surface solitary waves propagating on a liquid–air interface where the wave motion is induced by a harmonic forcing. Instead of the traditional approach involving a base state of the long wave limit, a base state of harmonic waves is assumed for the perturbation analysis. This approach is considered to be more appropriate for channels of length just a few multiples of the depth. The dispersion relation found approaches the classical long wave limit. The weakly nonlinear dispersive waves satisfy a KdV-like nonlinear evolution equation with steeper nonlinearity. [Copyright &y& Elsevier]

Abstract: The effect of dust charge fluctuation on the existence and propagation of dust acoustic waves in unmagnetized dusty plasma is studied. Dispersion relation for the dust acoustic waves with temporal dust charge fluctuations is calculated based on the reductive perturbation technique. By considering two different limiting cases of the dust charging frequency, it is shown that the dusty plasma system gives rise to linear or nonlinear dust acoustic waves. The well-known collisionless damping of two existing normal modes and one purely damped mode are recovered when the dust charging frequency is comparable to the dust acoustic wave frequency. On the other hand, when the dust charging frequency is considerably higher than the wave frequency, it is then possible to derive a nonlinear Schrödinger type equation with envelope soliton as solution. [Copyright &y& Elsevier]

Abstract: The effect of viscosity on dispersion of capillary–gravity waves becomes significant when the attenuation coefficient is greater than about 2.5% of the wave number. For low viscosity fluids such as water this condition is met at frequencies greater than about 5kHz in which case direct measurement of wavelength is difficult. For higher viscosity fluids the effect appears at much lower frequencies but direct measurement of wavelength becomes difficult since viscosity causes severe attenuation of surface waves. We have overcome the measurement difficulties by using a new miniature laser interferometer, which directly measures the wavelength of standing capillary waves with the requisite precision to yield reliable dispersion data for viscous fluids. Here we review the effect of viscosity on the dispersion relation and present new experimental data on dispersion of capillary waves in several water-glycerol mixtures. Our data provides direct experimental verification of the theoretical analysis. [Copyright &y& Elsevier]

Abstract: This paper considers flexural wave propagation in a spatially periodic structure consisting of identical beams of finite length, as a unit, connected to adjoining ones by couplers giving restoring moment at junctions, and extending to both infinity. Motions of the beam are restricted in a plane, and two cases are considered in linear theory. One is concerned with rigid beams and the other elastic beams. For the former case, the difference and differential equations for the displacements are derived from the equations of motions for translation and rotation of each beam with boundary conditions at the junctions, and a linear dispersion relation is obtained. For the latter, the Bernoulli–Euler equation for flexural motions of each beam is solved with boundary conditions at the junctions. Then a transmission matrix is derived, which relates deflection in each unit to the one in adjoining units. By examining eigenvalues and eigenvectors of the matrix, propagation characteristics are discussed and Bloch wave functions as elementary functions for the deflection are obtained. It is shown that the dispersion relations exhibit stopping bands for the frequency, which is not found in the case of the rigid beams. Continuum approximation of the articulated beams is discussed to derive legitimate beam equations for long waves. Also discussed is the physical interpretation of the cutoff frequencies for the stopping bands. [Copyright &y& Elsevier]

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 extent. The exact dispersion relation of bending edge waves is obtained. The propagation of bending edge waves in such a composite plate demonstrates multi-mode due to the presence of the metal strip plate. This wave has properties analogous to the surface wave in an elastic half-space covered by a thin layer within the theory of plane strain. The number of propagation modes depends on the width–thickness ratio of the metal plate and increases as this width–thickness ratio increases. The phase velocity of the bending edge wave in a piezoelectric composite plate is much lower than that of pure piezoelectric plate. Effect of the dimension of the metal strip plate on dispersion curves of bending edge waves is limited. • Bending edge wave in piezoelectric composite plate demonstrates multi-mode propagation. • The number of propagation modes depends on the width-thickness ratio of metal plate. • The edge wave speed is much lower than that of pure piezoelectric plate. • Effect of the dimension of the metal strip plate on phase velocity is limited. [ABSTRACT FROM AUTHOR]