The low frequency scatter of SH waves by a rough interface in an elastic plate

The study of the reflection and transmission of low frequency SH waves incident upon a rough interface in an elastic plate is undertaken by employing a theory of acoustic wave scattering from rough surfaces originally due to Biot and subsequently generalised to the case of elastic media. In this theory the interface is replaced by a distribution of voids/asperities whose individual size is small compared to the excitation wavelength. We plot the absolute values of the reflection and transmission coefficients versus frequency when a single symmetric SH plate mode is used as the input excitation. The different types of inclusions are used to simulate the rough surface are the hollow, fluid filled and aluminum spheres. Lastly, the loss of energy due to scattering is also estimated for the different inclusion distributions considered.     

Stochastic synchronization of rotating parametric pendulums

In this paper synchronization of two pendulums mounted on a mutual elastic single degree-of-freedom base is examined. The response of the pendulums is considered when their base is externally excited by a random phase sinusoidal force, thus leading to stochastic parametric excitation of the pendulums. The target is for the pendulums to establish and preserve rotary response since this study is motivated by a recently proposed ocean wave energy extraction concept where the heaving motion of waves excites a pendulum’s hinge point. Since the wave bobbing motion is random the system’s excitation is modelled as a narrow-band stochastic process. Mounting two pendulums on the same elastic base creates a coupling between them through their interaction with the base, providing a path for energy exchange between them. The dynamic response of the pendulums is numerically investigated with respect to establishment of rotations as well as identification of synchronization with the pendulums characteristics spanning along non-identical parameters.     

大延伸非均匀介质中地震波全弹性散射理论Ⅰ--弹性波单次散射理论

所描述的工作聚焦于大延伸非均匀介质中非均匀弹性地震波散射问题的研究.应用Born近似及等效源原理,推出了来自连续横向无界非均匀层的弹性散射波的通解.这一工作是解决大延伸非均匀介质的弹性地震波多次散射问题的基础.在上述通解的基础上,建立了适用于大延伸非均匀介质的全弹性散射理论.该理论可包容小尺度非均匀体、大延伸非均匀介质全弹性波单次弱散射理论及标量波单次弱散射理论,因此可视其为一个更为广义和统一的弱散射理论.     

Generation of Nonlinear Waves on a Viscoelastic Coating in a Turbulent Boundary Layer

Self–induced excitation of periodic nonlinear waves on a viscoelastic coating interacting with a turbulent boundary layer of an incompressible flow is studied. The response of the flow to multiwave excitation of the coating surface is determined in the approximation of small slopes. A system of equations is obtained for complex amplitudes of multiple harmonics of a slow (divergent) wave resulting from the development of hydroelastic instability on a coating with large losses. It is shown that three–wave resonant relations between the harmonics lead to the development of explosive instability, which is stabilized due to the deformation of the mean (Sover the wave period) shear flow in the boundary layer. Conditions of soft and hard excitation of divergent waves are determined. Based on the calculations performed, qualitative features of excitation of divergent waves in known experiments are explained.     

High frequency homogenization for structural mechanics

We consider a net created from elastic strings as a model structure to investigate the propagation of waves through semi-discrete media. We are particularly interested in the development of continuum models, valid at high frequencies, when the wavelength and each cell of the net are of similar order. Net structures are chosen as these form a general two-dimensional example, encapsulating the essential physics involved in the two-dimensional excitation of a lattice structure whilst retaining the simplicity of dealing with elastic strings.Homogenization techniques are developed here for wavelengths commensurate with the cellular scale. Unlike previous theories, these techniques are not limited to low frequency or static regimes, and lead to effective continuum equations valid on a macroscale with the details of the cellular structure encapsulated only through integrated quantities. The asymptotic procedure is based upon a two-scale approach and the physical observation that there are frequencies that give standing waves, periodic with the period or double-period of the cell. A specific example of a net created by a lattice of elastic strings is constructed, the theory is general and not reliant upon the net being infinite, none the less the infinite net is a useful special case for which Bloch theory can be applied. This special case is explored in detail allowing for verification of the theory, and highlights the importance of degenerate cases; the specific example of a square net is treated in detail. An additional illustration of the versatility of the method is the response to point forcing which provides a stringent test of the homogenized equations; an exact Green's function for the net is deduced and compared to the asymptotics.     

Wave propagation in elastic lattices subjected to a local harmonic loading. II. Two-dimensional problems

Steady-state and transient processes of elastic wave propagation in infinite 2D massless and material-bond lattices subjected to a local monochromatic excitation are studied. Anti-plane dynamics of rectangular and triangular lattices is considered. Mathematical models of lattices, dispersion properties of free waves, and results of transient problems solution are presented. Resonant excitations of lattices are explored. Asymptotic solutions are compared with the results of computer simulation. Special attention is given to the wave-beaming pattern in the case of the excitation frequency located within a pass-band.     

两种五零能模式材料单胞构型及其性能分析

五零能模式材料是一种新型的人工超材料,虽属于弹性材料,但组成其单胞的特殊构型使其宏观静态表现为仅能承载一种受力状态,动态表现为仅能传播一种弹性波。本文首先构造了两种五零能模式材料的单胞构型,其具有不同的弹性特性,其中一种材料可传播弹性膨胀波,另一种可传播弹性剪切波。然后分别采用代表体元法和均匀化法分析这两种单胞的等效弹性模量。五零能模式材料的分析分为两步更直观,开始从单胞桁架模型入手,检验单胞构型是否满足五零能模式的定义,然后分析单胞实体模型,考察单胞构型的结构参数与其等效弹性模量的关系。研究表明对于这种低密度弹性材料的分析,代表体元法更适合。     

Water waves in an elastic vessel

Linear and nonlinear analyses of water waves in an elastic vessel are carried out to study the dramatic phenomena of Dragon Wash as well as related controllable experiments. It is proposed that the capillary edge waves are generated by parametric resonance, which is shown to be a possible mechanism for both rectangular an circular vessels. For circular vessel, the normal geometric resonance is also operating, thus greatly enhance the dramatic effect. The mechanism of nonlinear mode-mode interaction is proposed for the generation of axisymmetric low-frequency gravity waves by the high- frequency external excitation. A simple model system is studied numerically to demonstrate explicitly this interaction mechanism.     

A mixture theory analysis for the surface-wave propagation in an unsaturated porous medium

The mixture theory is employed to the analysis of surface-wave propagation in a porous medium saturated by two compressible and viscous fluids (liquid and gas). A linear isothermal dynamic model is implemented which takes into account the interaction between the pore fluids and the solid phase of the porous material through viscous dissipation. In such unsaturated cases, the dispersion equations of Rayleigh and Love waves are derived respectively. Two situations for the Love waves are discussed in detail: (a) an elastic layer lying over an unsaturated porous half-space and (b) an unsaturated porous layer lying over an elastic half-space. The wave analysis indicates that, to the three compressional waves discovered in the unsaturated porous medium, there also correspond three Rayleigh wave modes (R1, R2, and R3 waves) propagating along its free surface. The numerical results demonstrate a significant dependence of wave velocities and attenuation coefficients of the Rayleigh and Love waves on the saturation degree, excitation frequency and intrinsic permeability. The cut-off frequency of the high order mode of Love waves is also found to be dependent on the saturation degree.     

Bifurcation and chaos of the circular plates on the nonlinear elastic foundation

According to the large amplitude equation of the circular plate on nonlinear elastic foundation , elastic resisting force has linear item , cubic nonlinear item and resisting bend elastic item. A nonlinear vibration equation is obtained with the method of Galerkin under the condition of fixed boundary. Floquet exponent at equilibrium point is obtained without external excitation. Its stability and condition of possible bifurcation is analysed. Possible chaotic vibration is analysed and studied with the method of Melnikov with external excitation . The critical curves of the chaotic region and phase figure under some foundation parameters are obtained with the method of digital artificial.     

On attenuation of free and forced waves in an infinitely long visco-elastic layer of a constant thickness

The conventional concepts of a loss factor and a complex-valued elastic module are used to study wave attenuation in a visco-elastic layer. The hierarchy of reduced order models is employed to assess attenuation levels of free and forced waves in various situations. First, the free waves are considered. In the low frequency limit, the attenuation of these waves is found to be in the excellent agreement with the existing knowledge. At high frequencies, predictions of the reduced order models fully agree with the solutions of exact Rayleigh–Lamb problem. Alternative excitation cases are considered for the forcing problem and a measure of the attenuation level is proposed and validated. The differences between two regimes, the low frequency one, when a waveguide supports only one propagating wave, and the high frequency one, when several waves are supported, are demonstrated and explained.     

Waves in microstructured solids and the Boussinesq paradigm

The emergence of soliton trains and interaction of solitons are analyzed by using a Boussinesq-type equation which describes the propagation of bi-directional deformation waves in microstructured solids. The governing equation in the one-dimensional setting is based on the Mindlin model. This model includes scale parameters which show explicitly the influence of the microstructure in wave motion. As a result the governing equation has a hierarchical structure. The analysis is based on numerical simulation using the pseudospectral method. It is shown how the number of solitons in emerging trains depends on the initial excitation. The head-on collision of emerged solitons is not fully elastic due to radiation but the solitons preserve their identity after collision and the speed of solitons is retained while the radiation keeps a certain mean value. That is why we have kept through this paper the notion of solitons.     

Reflection and transmission of elastic waves through a couple-stress elastic slab sandwiched between two half-spaces

The reflection and transmission of elastic waves through a couple-stress elastic slab that is sandwiched between two couple-stress elastic half-spaces are studied in this paper. Because of the couple-stress effects, there are three types of elastic waves in the couple-stress elastic solid, two of which are dispersive. The interface conditions between two couple-stress solids involve the surface couple and rotation apart from the surface traction and displacement. The nontraditional interface conditions between the slab and two solid half-spaces are used to obtain the linear algebraic equation sets from which the amplitude ratios of reflection and transmission waves to the incident wave can be determined. Then, the energy fluxes carried by the various reflection and transmission waves are calculated numerically and the normal energy flux conservation is used to validate the numerical results. The special case, couple-stress elastic slab sandwiched by the classical elastic half-spaces, is also studied and compared with the situation that the classical elastic slab sandwiched by the classical elastic half-spaces. Incident longitudinal wave (P wave) and incident transverse wave (SV wave) are both considered. The influences of the couple-stress are mainly discussed based on the numerical results. It is found that the couple-stress mainly influences the transverse modes of elastic waves.     

WAVELET METHOD FOR CALCULATING THE DEFECT STATES OF TWO-DIMENSIONAL PHONONIC CRYSTALS

Based on the variational theory, a wavelet-based numerical method is developed to calculate the defect states of acoustic waves in two-dimensional phononic crystals with point and line defects. The supercell technique is applied. By expanding the displacement field and the material constants （mass density and elastic stiffness） in periodic wavelets, the explicit formulations of an eigenvalue problem for the plane harmonic bulk waves in such a phononic structure are derived. The point and line defect states in solid-liquid and solid-solid systems are calculated. Comparisons of the present results with those measured experimentally or those from the plane wave expansion method show that the present method can yield accurate results with faster convergence and less computing time.     

The vibration of a half-space due to a buried mode I crack opening

The solution of a dynamic problem for calculation of a displacement field on a half-space surface caused by an internal mode I crack opening is presented. The problem is reduced to the system of boundary integral equations (BIEs). The equations of motion are solved with the use of Helmholtz potentials and applying Fourier integral transform. The effects of the crack size, the crack depth and the distance from the crack epicenter to the observation point on the parameters of elastic waves are investigated. It is established that the increasing of the defect size leads to narrowing bandwidth of elastic waves and to lowering of center frequency. The analysis given here can be used for identification of the crack growth during technical diagnostic of an industry objects and structural elements by AE method.     

Precursor waves associated with the motion of sources of variable intensity in a stratified fluid

When a source of variable intensity moves in a stratified fluid, several types of waves, possibly including waves that outstrip the source (precursor waves), are generated. By analyzing the expressions for the mean energy losses due to internal wave radiation per unit time it is shown that in fluids with convex wave dispersion curves up to four types of waves per mode are possible. One of these types, which vanishes under supercritical conditions, is related to the precursor waves. The angle dependence of these waves and their conditions of excitation with respect to source velocity are established. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 97–103, March–April, 1994.     

Mechanical wave momentum from the first principles

Axial momentum carried by waves in a uniform waveguide is considered based on the conservation laws and a kind of the causality principle. Specifically, we examine (without resorting to constitutive data) steady-state waves of an arbitrary shape, periodic waves which speed differs from the speed of its form and binary waves carrying self-equilibrated momentum. The approach allows us to represent momentum as a product of the wave mass and the wave speed. The propagating wave mass, positive or negative, is the excess of that in the wave over its initial value. This general representation is valid for mechanical waves of arbitrary nature and intensity. The finite-amplitude longitudinal and periodic transverse waves are examined in more detail. It is shown in particular, that the transverse excitation of a string or an elastic beam results in the binary wave. The closed-form expressions for the drift in these waves functionally reduce to the Stokes’ drift in surface water waves (a half the latter by the value). Besides, based on the general representation an energy–momentum relation is discussed and the physical meaning of the so-called “wave momentum” is clarified.     

Theory of water waves in an elastic vessel

Recent experiments related to the Dragon Wash phenomena showed that axisymmetric capillary waves appear first from excitation, and circumferential capillary waves appear after increase of the excitation strength. Based on this new finding, a theory of parametric resonance is developed in detail to explain the on-set of the prominent circumferential capillary waves. Numerical computation is also carried out and the results agree generally with the experiments. Analysis and numerical computation are also presented to explain the generation of axisymmetric low-frequency gravity waves by the high-frequency external excitation.