Description: Publication date: Available online 28 June 2018 Source: Wave Motion Author(s): J. Brizar Okaly, Alain Mvogo, R. Laure Woulaché, T. Crépin Kofané The nonlinear dynamics of DNA molecular chain is studied for longitudinal and transversal motions through a microscopic zigzag discrete helicoidal model with four degrees of freedom. Taking into account Stokes and hydrodynamical viscous forces, we use the semi-discrete approximation and show that the coupled nonlinear partial differential equations for the longitudinal and transversal out-of-phase motions can be reduced to the nonlinear Schrodinger equation with complex coefficients allowing analytical breather soliton solution. We found analytically as well as numerically that increasing the damping constant reduces the amplitude and increases the width of the soliton. When the zigzag angle decreases, the height of the soliton increases but its width remains constant. The linear stability analysis of the system is performed, the growth rate of the instability and the instability regions are discussed as a function of damping constant, zigzag angle and system parameters.

Description: Publication date: Available online 25 June 2018 Source: Wave Motion Author(s): D. Pölz, M.H. Gfrerer, M. Schanz We propose a space–time boundary element method for the dynamic simulation of elastic truss systems. The considered truss systems consist of several members, where in each elastic rod the dynamic behaviour is governed by the 1D wave equation. The time domain fundamental solution and boundary integral equations are used to establish the dynamic Dirichlet-to-Neumann map for a single rod. Thus, we are able to reduce the problem to the nodes of the truss system and therefore only a temporal discretization at the truss nodes is necessary. We introduce a stepwise solution strategy with local step size which ensures stability. Furthermore, the discretization within each of these time steps can be refined adaptively to reduce the approximation error efficiently. The optimal convergence of the method is demonstrated in numerical examples. Due to adaptive refinement, this optimal convergence rate is retained even for non-smooth solutions. Finally, the method is applied to study typical truss systems.

Description: Publication date: Available online 23 June 2018 Source: Wave Motion Author(s): Armand Wirgin The present study originated in the forward problem of the prediction of the effects of seismic waves (generated by impulsive deep-down sources) in urban areas. The traditional, numerically-intensive approaches to this problem have not, until now, given rise to simple theoretical paradigms which might explain how and why the (often-destructive) response of cities is conditioned by factors such as the city density, building average height, average building composition, site geometry and composition, and characteristics of the solicitation such as incident angles, polarization and frequency. We propose to homogenize the city in order to simplify, and make possible the understanding of, the site-city-solicitation interaction. This homogenization is treated as an inverse problem, i.e., by which we: (1) generate near-field response data for a ’real’ city, (2) replace (initially by thought) the city by a homogeneous (surrogate) layer above, and in firm contact, with the underlying site, (3) compute the response of the surrogate layer/site response for various trial constitutive properties, (4) search for the global minimum of the discrepancy between the response data and the various trial parameter responses (5) attribute the homogenized properties of the city to the surrogate layer for which the minimum of the discrepancy is attained. We carry out this five-step procedure for a host of ’real’ city and solicitation parameters, notably the frequency. The result is that: (i) for low frequencies and/or large city densities, the effective constitutive properties are their static equivalents, i.e., the effective shear modulus is the product of a factor related to the city density with the shear modulus of a generic substructure of the city and the effective complex velocity is equal to the complex velocity of the said generic substructure, (2) at higher frequencies and/or smaller city densities, the effective constitutive properties are dispersive and do not take on a simple mathematical form, with this dispersion compensating for the discordance between the ways the inhomogeneous city structure and the homogeneous surrogate layer respond to the seismic wave. For typical seismic solicitation frequencies, the city, represented as a layer with static homogenized properties, is quite adequate to account for the principal features of the response (notably those of the time-domain response). The model of the layer with dispersive homogenized properties is more suitable to account for such features as resonances due to the excitation of surface wave modes.

Description: Publication date: Available online 20 June 2018 Source: Wave Motion Author(s): S.V. Kuznetsov The paper is devoted to correcting structure of the representation for Rayleigh waves at non-semisimple degeneracy of the fundamental matrix. The incorrect representation was given in a paper “Implicit and explicit secular equations for Rayleigh waves in two-dimensional anisotropic media” by Cerv and Plesek (2013) .

Description: Publication date: Available online 20 June 2018 Source: Wave Motion Author(s): Felix Bob Wijaya, Shahrokh Sepehrirahnama, Kian-Meng Lim The movement of the particles in acoustophoresis is driven by the acoustic radiation force acting on the particles. Particles with positive contrast factor tend to agglomerate once they are pushed by the primary force to the vicinity of the pressure node. The main driving force of this agglomeration is the interparticle force. In this study, the boundary element method is used to calculate the interparticle force and torque acting on a pair of spheroidal particles. The numerical results show that the interparticle force is dominant over the primary force when the spheroids are near the pressure nodal plane, similar to the case of two spheres. On contrary, the interparticle torque is insignificant compared to the primary torque, even when the spheroids are close to each other. The results also provide a preliminary study about how biological cells, which are mostly not spherical in shape, agglomerate and orient themselves in the vicinity of the pressure node.

Description: Publication date: July 2018 Source: Wave Motion, Volume 80

Description: Publication date: September 2018 Source: Wave Motion, Volume 81 Author(s): Pinbo Ding, Bangrang Di, Ding Wang, Jianxin Wei, Lianbo Zeng Rocks in the Earth’s crust contain cracks in variable amounts and on variable scales. Depending on the in situ stress level, cracks are always distributed in a common normal direction (so-called aligned cracks). In this study, we focus on the velocity and anisotropy of perfectly aligned cracks (parallel cracks). The theoretical model is introduced to calculate the elastic properties of cracked rocks based on solid matrix properties, crack parameters, and fluid properties. The theoretical results using high- and low-frequency limits and intermediate frequency for velocities and anisotropy are compared with experimental data measured in the laboratory, where rocks are saturated with water and air. We used four synthetic rocks with different crack densities (0.0, 0.0243, 0.0486, and 0.0729) in this study. The comparison shows that the results for high, low, and intermediate frequencies provide good predictions of the shear velocities and anisotropy for saturated cracked rocks. Quantitatively, the results of the P-wave velocity and anisotropy for intermediate frequency fit the measured data better than that for the high- and low-frequency limits. Compared with water saturation, dry cracks with high compliance have a strong influence on the total compliance of rock. The water saturation results in high P-velocities and a low P-anisotropy, while dry cracks induce much lower P-velocities and a high P-anisotropy. The shear wave anisotropy is fluid-independent, theoretical results fit the measured data well in both water saturation and the dry case.

Description: Publication date: Available online 22 May 2018 Source: Wave Motion Author(s): V.L. Preobrazhensky, V.V. Aleshin, P. Pernod In this paper, we theoretically describe a magnetoelastic system with an explosive instability in which the magnetic energy can be converted into the mechanical one via an extremely efficient channel. The principle is based on the amplification of acoustic waves traveling in an antiferromagnetic crystal under the action of transversal electromagnetic pumping. It is known that such parametric interaction can produce an exponential acoustic wave amplification. Our finding consists in the addition of another pumping channel by means of a discrete resonant acoustic mode whose impact is similar to the Feshbach resonance observed in another physical system (ultra-cold gazes). The addition of the second pumping mechanism results in the explosive instability having the dynamics of a singularity at a finite time instead of the exponential growth. In our example the traveling waves are Lamb waves in an antiferromagnetic plate, and the additional pumping is a shear resonance. We establish equations governing the considered three-phonon parametric instability, theoretically analyze the instability conditions, and give a relevant numerical example illustrating the explosive magneto-acoustic dynamics. It is shown that the explosive scenario can occur with a very low signal level i.e. Lamb waves amplitudes comparable to spontaneous noise in the system.

Description: Publication date: Available online 5 May 2018 Source: Wave Motion Author(s): Shuwei Xu, Jingsong He, K. Porsezian The breather solutions of the Maxwell-Bloch equations in a two-level resonant system associated with the self-induced transparency phenomenon are constructed by the Darboux transformation. After constructing the formulas of the second-order breather solutions, the double degeneration and hybrid solutions are studied by the analytical form as well as figures. Our results might be helpful in such application or prevention of the rogue waves from breather solution interactions and degeneration in the nonlinear optical systems associated with the Maxwell-Bloch equations.

Description: Publication date: Available online 27 April 2018 Source: Wave Motion Author(s): Xiyue An, Hualin Fan, Chuanzeng Zhang The vibration properties of two-dimensional (2D) finite acoustic metamaterials (AMs) consisting of discrete masses and springs are investigated in this paper. In order to clarify the mechanisms of the bandgaps in AMs, the infinite symmetrical systems are also studied, especially the impact of the physical asymmetry caused by the discrepant stiffness coefficients of the springs connecting the unit-cells. Although the asymmetry cannot change the bandgap width, the change of the phase velocity and the generation of the shear mode have been proven analytically. To study the vibration properties of the finite AM model, the effective mass of each unit-cell is used. The effective mass properties of the unit-cell with single resonator and multi-resonators in 2D AMs subjected to a time-harmonic excitation are discussed. The effects of the number of the unit-cells, multi-resonators in each unit-cell, graded resonators in the finite AM model on the vibration suppression are thoroughly examined by the frequency response analysis. Numerical results show that the degree of the vibration attenuation is related to the size of the model and the number of the bandgaps changes corresponding to the disorders of the local resonators. Furthermore, imperfections or defects are introduced into the finite AM system. Wave propagation and guiding in a finite model for straight waveguide are investigated and discussed. The defect states induced by changing the central resonator of a supercell are demonstrated. Defect bands are obtained and their location is illustrated.