المؤلفون: Guo, Ming-Juan¹ (AUTHOR), Wen, Xiao-Yong¹ (AUTHOR) xiaoyongwen@163.com, Liu, Xue-Ke¹ (AUTHOR)

المصدر: Wave Motion. Feb2024, Vol. 125, pN.PAG-N.PAG. 1p.

مصطلحات موضوعية: *KORTEWEG-de Vries equation, *ACOUSTIC wave propagation, *DARBOUX transformations, *ROGUE waves, *WATER waves, *SOUND waves

مستخلص: Under consideration is the second-order integrable discretization of complex modified Korteweg-de Vries (mKdV) equation which is regarded as the discrete counterpart of the mKdV equation having an essential role in describing the propagation behavior of water waves and acoustic waves in nonlinear media. First of all, based on the known linear spectral problem, the discrete generalized (n , N − n) -fold Darboux transformation is constructed to derive various types of discrete exact localized wave solutions, including soliton and semi-rational soliton solutions on vanishing background, breather, rogue wave and hybrid interaction solutions on plane wave background, and rational soliton solution on constant background, and the relevant evolution structures are studied graphically. Secondly, the asymptotic analysis is used to discuss the elastic interaction for two-soliton solutions and limit states for rational soliton solutions. Finally, the numerical simulation is utilized to investigate the dynamical behavior and propagation stability of some exact solutions. The findings presented in this paper may contribute to explaining physical phenomena described by the mKdV equation. • The discrete generalized (n, N -n)-fold Darboux transformation is first constructed. • Various types of discrete exact localized wave solutions are derived. • Diverse discrete wave structures are analyzed and discussed graphically. • The limit states are invesigated via asymptotic analysis technique. • The numerical simulation is used to discuss dynamical behaviors. [ABSTRACT FROM AUTHOR]

المؤلفون: de Reboul, Silouane^1,2,3 (AUTHOR) silouane.de-reboul@utc.fr, Perrey-Debain, Emmanuel¹ (AUTHOR) emmanuel.perrey-debain@utc.fr, Zerbib, Nicolas² (AUTHOR) nze@esi-group.com, Moreau, Stéphane³ (AUTHOR) stephane.moreau@usherbrooke.ca

المصدر: Wave Motion. Aug2023, Vol. 121, pN.PAG-N.PAG. 1p.

مصطلحات موضوعية: *ACOUSTIC wave propagation, *THEORY of wave motion, *FINITE element method, *WAVE equation

مستخلص: A numerical method is presented to solve the propagation of sound waves in a two-dimensional domain in the presence of rotating obstacles without flow. It relies on a domain decomposition whereby rotating components are all embedded in a circular domain and the Arbitrary Lagrangian Eulerian framework which consists in writing the wave equation in the rotating reference frame. The transmission conditions at the interface between both domains is accomplished via the Frequency Scattering Boundary Conditions which, after classical discretization with the Finite Element Method (FEM), give rise to a series of coupled problems associated with a discrete set of frequencies. The performances of the method are demonstrated through several test cases of increasing complexity. • A numerical method to solve wave propagation in a rotating domain is presented. • The global system may be solved with classical frequency domain solver. • It involves a frequency coupling between the fixed and rotating domain. • The performances of the method are demonstrated through several test cases. [ABSTRACT FROM AUTHOR]

المؤلفون: Dvořák, Radim^1,2 (AUTHOR) radimd@it.cas.cz, Kolman, Radek¹ (AUTHOR) kolman@it.cas.cz, Fíla, Tomáš^1,2 (AUTHOR) filatoma@fd.cvut.cz, Falta, Jan^1,2 (AUTHOR) faltaja2@fd.cvut.cz, Park, K.C.^1,3 (AUTHOR) kcpark@colorado.edu

المصدر: Wave Motion. Aug2023, Vol. 121, pN.PAG-N.PAG. 1p.

مصطلحات موضوعية: *ELASTIC wave propagation, *ELASTIC waves, *YOUNG'S modulus, *LAGRANGE multiplier, *FINITE element method, *ANALYTICAL solutions, *ASYNCHRONOUS learning

مستخلص: This is a presentation of robust and accurate explicit time-stepping strategy for finite element modeling of elastic discontinuous wave propagation in strongly heterogeneous, multi-material and graded one-dimensional media. One of the major issues in FEM modeling is the existence of spurious numerical stress oscillations close to theoretical wave fronts due to temporal-spatial dispersion behavior of FE discretization. The numerical strategy presented for modeling of 1D discontinuous elastic waves is based on (a) pushforward-pullback local stepping — ensuring the elimination of dispersion due to different critical time step sizes of finite elements, (b) domain decomposition via localized Lagrange multipliers — to satisfy coupling kinematics and dynamic equations , (c) asynchronous time scheme — ensuring the correct information transfer of quantities for the case of integer ratios of time step size for all domain pairs. Dispersion behaviors, existence of spurious stress oscillations, and sensitivity of the dispersion to time step size are then suppressed. The proposed method is numerically tested with regard to the rectangular step pulse elastic propagation problem considering in-space varying Young's modulus. To prove robustness and accuracy, a comparison with results from commercial software, an analytical solution, and experimental data from partial assembly of a split Hopkinson pressure bar (SHPB) setup is provided. • Explicit asynchronous time scheme with local push-forward stepping is suggested. • One-dimensional strong heterogeneous cases on irregular FE meshes are solved. • The method of Localized Lagrange multipliers for domain decomposition is used. • Proposed asynchronous integrator does not dissipate energy on the interfaces. • Nominated time strategy produces the results without spurious stress oscillations. [ABSTRACT FROM AUTHOR]

المؤلفون: Jaberzadeh, Mehran¹ (AUTHOR), Li, Bing¹ (AUTHOR), Tan, K.T.¹ (AUTHOR) ktan@uakron.edu

المصدر: Wave Motion. Jun2019, Vol. 89, p131-141. 11p.

مصطلحات موضوعية: *ELASTIC wave propagation, *THEORY of wave motion, *ACOUSTIC wave propagation, *DENSITY, *NUMERICAL calculations

مستخلص: The effect of anisotropic mass density on wave propagation in acoustic/elastic metamaterials is presented in this research. The use of microstructures to achieve mass anisotropy in metamaterials is an intensive field of study. In this work, a numerical continuum model, based on a recently developed cantilever-in-mass model, is proposed. Mass anisotropy in this model is derived based on analytical calculations of a two-dimensional (2D) 'mass-in-mass'-spring lattice system. The mass–spring lattice is able to portray anisotropic effective mass density in two orthogonal principal directions. Effective mass density along each direction is frequency-dependent. A strong "effective mass anisotropy" is accomplished within the frequency band gap or just below the frequency range of negative effective mass. The proposed mass–cantilever continuum model is used to examine 2D wave propagation. Results show that wave attenuation in a metamaterial with 2D anisotropic mass density is dependent on both input frequency and wave input angle. This study demonstrates a case whereby wave attenuation is achieved by selecting wave input frequency in the band gap region to enact "negative effective mass density", thereby mitigating wave propagation. In this case, the most efficient attenuation performance is achieved at an input wave angle of 0°. This study also illustrates another case whereby wave attenuation is obtained by mass anisotropy at a frequency just below the local resonance frequency. Wave attenuation is achieved by redirecting wave propagation along the transverse direction, particularly prominent at an input wave angle of 70°. Both numerical calculations of mass–spring lattice model and continuum cantilever-in-mass model show excellent agreement with each other. • Frequency dependent mass anisotropy in elastic metamaterial is investigated. • Two directional mass anisotropy is achieved in a new mass–cantilever design. • Wave propagation depends on both frequency and wave input angle. • Within frequency band gap, wave is reflected along wave input angle of 0°. • Below local resonance frequency, wave redirection occurs at wave angle of 70°. [ABSTRACT FROM AUTHOR]

المؤلفون: Koutserimpas, Theodoros T.¹ (AUTHOR), Fleury, Romain¹ (AUTHOR) romain.fleury@epfl.ch

المصدر: Wave Motion. Jun2019, Vol. 89, p221-231. 11p.

مصطلحات موضوعية: *ACOUSTIC wave propagation, *ACOUSTICS, *THERMOELASTICITY, *STANDING waves, *TRANSMISSION of sound, *SOUND waves

مستخلص: In this paper, we present a complete analytical derivation of the equations used for stationary and nonstationary wave systems regarding resonant sound transmission and reflection described by the phenomenological coupled-mode theory. We calculate the propagating and coupling parameters used in coupled-mode theory directly by utilizing the generalized eigenwave-eigenvalue problem from the Hamiltonian of the sound wave equations for the problem of a one-dimensional isolated on-channel resonance. This Hamiltonian formalization could be beneficial and could potentially model and parameterize a broad range of acoustic wave phenomena. We demonstrate how to use this theory as a basis for perturbation analysis of complex resonant scattering scenarios. In particular, we form the effective Hamiltonian and coupled-mode parameters for the study of sound resonators with background moving media. Finally, we provide a comparison between coupled-mode theory and full-wave numerical examples, which validate the Hamiltonian approach as a relevant model to compute the scattering characteristics of waves by complex resonant systems. • Coupled-mode equations for stationary and nonstationary resonant sound systems. • Hamiltonian method approach for couple-mode theory parameters. • Perturbation analysis applied to the Hamiltonian of a nonstationary wave system. • Examples presented for stationary and nonstationary sound resonant problems. [ABSTRACT FROM AUTHOR]

المؤلفون: Bibi, Aysha¹ (AUTHOR), Liu, Huan^1,2 (AUTHOR), Xue, Jiu-Ling³ (AUTHOR), Fan, Ya-Xian² (AUTHOR), Tao, Zhi-Yong^1,2 (AUTHOR) zytao@hrbeu.edu.cn

المصدر: Wave Motion. May2019, Vol. 88, p205-213. 9p.

مصطلحات موضوعية: *ELASTIC wave propagation, *ELASTIC waves, *SURFACE geometry, *OPTIMAL control theory, *SURFACE plates, *DISPERSION relations

مستخلص: We demonstrate the manipulation of the first frequency bands by changing the periodic corrugations on the surfaces of elastic plates. Based on the Fourier analysis and Floquet theorem, we have derived the dispersion relations for elastic waves propagating in periodically corrugated plates with different geometric profiles, which can always lead to the creation of forbidden bands. The effects of corrugation profiles on the forbidden bands have been quantified by the introduced shape factor, which has been proved to be proportional to the bandwidth. The simulations have confirmed the effects of surface geometries on the bandwidth, which is linearly dependent on the shape factor and corrugation amplitude. The calculated shape factor from the simulated data is very close to its theoretical value, verifying the applicability of the proposed band manipulation mechanism. The theoretical and numerical results indicate that the desired forbidden band could be obtained by selecting the corrugation geometries with the optimal shape factor and corrugation amplitude, which provides an efficient way to realize elastic wave filters and band gap materials in vibration control engineering. • Wave propagation in an elastic plate with different corrugations is demonstrated. • The elastic wave spectrum forbidden bands are derived and simulated. • The effect of corrugation shape is quantified by the introduced shape factor. • The shape factor is estimated by the area under the curve related to wall profile. • The major Fourier components linearly affect the bandwidth with the shape factor. [ABSTRACT FROM AUTHOR]

المؤلفون: Pölz, D.¹ (AUTHOR) poelz@tugraz.at, Gfrerer, M.H.^1,2 (AUTHOR), Schanz, M.¹ (AUTHOR)

المصدر: Wave Motion. Apr2019, Vol. 87, p37-57. 21p.

مصطلحات موضوعية: *ELASTIC wave propagation, *TRUSSES, *BOUNDARY element methods, *IMPACT loads, *WAVE equation, *ELASTODYNAMICS, *APPROXIMATION error

مستخلص: Abstract 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. Highlights • Simulating elastodynamic rods via retarded potentials requires no spatial mesh. • The Dirichlet-to-Neumann map is the key tool in the proposed formulation. • Space–time discretizations facilitate stable and robust methods. • Adaptive refinement enables the simulation of impact loads. [ABSTRACT FROM AUTHOR]

المؤلفون: Hargreaves, Jonathan A.¹ (AUTHOR) j.a.hargreaves@salford.ac.uk, Lam, Yiu W.¹ (AUTHOR)

المصدر: Wave Motion. Apr2019, Vol. 87, p4-36. 33p.

مصطلحات موضوعية: *ACOUSTIC wave propagation, *WAVENUMBER, *INTEGRAL equations, *UNDERWATER acoustics, *SOUND wave scattering, *MATRIX inversion, *ARCHITECTURAL acoustics

مستخلص: Abstract In this paper, a new Boundary Integral Equation (BIE) is proposed for solution of the scalar Helmholtz equation. Applications include acoustic scattering problems, as occur in room acoustics and outdoor and underwater sound propagation. It draws together ideas from the study of time-harmonic and transient BIEs and spatial audio sensing and rendering, to produce an energy-inspired Galerkin BEM that is intended for use with oscillatory basis functions. Pivotal is the idea that waves at a boundary may be decomposed into incoming and outgoing components. When written in its admittance form, it can be thought of setting the Burton–Miller coupling parameter differently for each basis function based on its oscillation; this is a discrete form of the Dirichlet-to-Neumann map. It is also naturally expressed in a reflectance form, which can be solved by matrix inversion or by marching on in reflection order. Consideration of this leads to an orthogonality relation between the incoming and outgoing waves, which makes the scheme immune to interior cavity eigenmodes. Moreover, the scheme is seen to have two remarkable properties when solution is performed over an entire obstacle: (i) it has a condition number of 1 for all positive-real wavenumber k on any closed geometry when a specific choice of cylindrical basis functions are used; (ii) when modelling two domains separated by a barrier domain, the two problems are numerical uncoupled when plane wave basis functions are used — this is the case in reality but is not achieved by any other BIE representation that the authors are aware of. Normalisation and envelope functions, as would be required to build a Partition-of-Unity or Hybrid-Numerical-Asymptotic scheme, are introduced and the above properties are seen to become approximate. The modified scheme is applied successfully to a cylinder test case: accuracy of the solution is maintained and the BIE is still immune to interior cavity eigenmodes, gives similar conditioning to the Burton–Miller method and iterative solution is stable. It is seen that for this test case the majority of values in the interaction matrices are extremely small and may be set to zero without affecting conditioning or accuracy, thus the linear system become sparse - a property uncommon in BEM formulations. Highlights • New Boundary Integral Equation derived from energy considerations. • Decomposes waves into incoming and outgoing components. • Non-uniqueness due to cavity eigenmodes is avoided. • Physically separate problems are mathematically decoupled. • Matrices can be made sparse and iterative solution possible. [ABSTRACT FROM AUTHOR]

المؤلفون: Ahmetolan, Semra¹ (AUTHOR) ahmetola@itu.edu.tr, Peker-Dobie, Ayse¹ (AUTHOR), Deliktas-Ozdemir, Ekin² (AUTHOR), Caglayan, Esra³ (AUTHOR)

المصدر: Wave Motion. Jun2023, Vol. 119, pN.PAG-N.PAG. 1p.

مصطلحات موضوعية: *ELASTIC wave propagation, *LAMB waves, *THEORY of wave motion, *WAVENUMBER, *FREE surfaces, *DISPERSION relations, *ELASTIC waves

مستخلص: In this article, we investigate the problem of Lamb wave propagation in a layer composed of homogeneous, isotropic material with irregular free surfaces. It is assumed that the irregular free surfaces vary slowly in the direction of wave propagation. By employing an asymptotic perturbation method, a unique asymptotic solution for the amplitude function of Lamb waves is obtained. The dispersion relation is expressed as a function of phase velocity of waves, wave number and the direction of wave propagation. We examine the effect of irregularities of the boundary surfaces on the propagation of waves under the assumption that free surfaces have periodic properties. • Lamb wave propagation in a layer with irregular free surfaces is investigated. • The layer is composed of homogeneous and isotropic material. • A unique asymptotic solution for the amplitude of linear Lamb waves is obtained. • Dispersion relation is analysed. • Effects of periodic surfaces on wave propagation have been demonstrated graphically. [ABSTRACT FROM AUTHOR]

المؤلفون: Wang, Yi-Ze¹ wangyz@bjtu.edu.cn, Wang, Yue-Sheng¹

المصدر: Wave Motion. Apr2018, Vol. 78, p1-8. 8p.

مصطلحات موضوعية: *ELASTIC wave propagation, *PROPORTIONAL control systems, *PHONONIC crystals, *NONLINEAR systems, *APPROXIMATE solutions (Logic)

مستخلص: This work studies the active control effects on nonlinear phononic crystals by the piezoelectric spring model. Both negative and positive proportional control actions are considered. Based on the Lindstedt–Poincaré method, the approximate solution is derived and the stop band properties are presented. Numerical calculations show that the structural stiffness and negative proportional control of the piezoelectric spring can create a new stop band which is under the acoustic branch. But the positive proportional case has a different influence because of a critical wave number appearing. Moreover, the optic branch can be uplifted by the elastic wave amplitude. Different from the soft nonlinear characteristic, the hard nonlinear property can increase the stop band width. [ABSTRACT FROM AUTHOR]