Material microstructure optimization for linear elastodynamic energy wave management

We describe a systematic approach to design material microstructures to achieve desired energy propagation in a two-phase composite plate. To generate a well-posed topology optimization problem we use the relaxation approach which requires homogenization theory to relate the macroscopic material properties to the microstructure, here a sequentially ranked laminate. We introduce an algorithm whereby the laminate layer volume fractions and orientations are optimized at each material point. To resolve numerical instabilities associated with the dynamic simulation and constrained optimization problem, we filter the laminate parameters. This also has the effect of generating smoothly varying microstructures which are easier to manufacture. To demonstrate our algorithm we design microstructure layouts for tailored energy propagation, i.e. energy focus, energy redirection, energy dispersion and energy spread.     

Development of a numerical wave tank for analysis of nonlinear and irregular wave field

A numerical wave-absorption filter has been developed for an open boundary condition in the analysis of nonlinear and irregular wave evolution. The filter is composed of a simulated sponge layer and Sommerfeld's radiation condition at the outer edge of the layer. The wave-absorption characteristics of the filter have been investigated by applying the linear potential theory and a two-dimensional nonlinear boundary element model. In both cases, the filter is found to he applicable for a wide range of wave parameters. In order to realize an idealized “numerical wave tank”, the present model also incorporates a nonreflective wave generator in the computational domain composed of a series of vertically aligned point sources. Numerous numerical experiments demonstrate that the present approach is effective in generating an arbitrary wave profile without reflection not only at the open boundaries but also at the wave generator.     

Curvature relation of wave front and wave changing in external field

Introduction ThestudiesofexcitablemediaconcernwithBZreaction,slimemoldaggregationand cardiactissue[1].Thepropertiesofthesemediaare:forsmallperturbationsthemediaquickly recovertotheirreststates,whileforstimuliexceedingathresholdthemediawillbeactivated andr…     

Velocity field after wave breaking

The velocity field in breaking water waves is considered in this paper. A numerical simulation describes in detail the transition from a primary overturning and consequent rebounding jets into a bore front, where the vorticity in the coherent large‐scale eddy structures devolves into turbulence. Spatial changes in the frequency spectra of the kinetic energy and the enstrophy are associated with the production, transport and dissipation of the Reynolds stress and the various wave and turbulent mixing length scales. Mean velocity fields and the wave and kinetic energy in a surf zone are evaluated. Fourier and wavelet spectral analysis is applied to study both the surface elevation and energy changes, and the distinction that must be made between spilling and plunging breakers is clarified in this paper. Copyright © 2002 John Wiley & Sons, Ltd.     

A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow

An overview of present understanding of microstructure in flowing suspensions is provided. An emphasis is placed on how the microstructure leads to observable bulk flow phenomena unique to mixtures. The bridge between the particle and bulk scales is provided by the mixture rheology; one focus of the review is on work that addresses the connection between microstructure and rheology. The non-Newtonian rheology of suspensions includes the well-known rate dependences of shear thinning and thickening, which have influence on bulk processing of suspensions. Shear-induced normal stresses are also measured in concentrated suspensions and include normal stress differences, and the isotropic particle pressure. Normal stresses have been associated with shear-induced migration, and thus have influence on the ultimate spatial distribution of solids, as well as the flow rate during processing; a second focus is on these uniquely two-phase behaviors and how they can be described in terms of the bulk rheology. An important bulk fluid mechanical consequence of normal stresses is their role in driving secondary flows.     

Symmetry conditions for third order elastic moduli and implications in nonlinear wave theory

Several results are presented concerning symmetry properties of the tensor of third order elastic moduli. It is proven that a set of conditions upon the components of the modulus tensor are both necessary and sufficient for a given direction to be normal to a plane of material symmetry. This leads to a systematic procedure by which the underlying symmetry of a material can be calculated from the 56 third order moduli. One implication of the symmetry conditions is that the nonlinearity parameter governing the evolution of acceleration waves and nonlinear wave phenomena is identically zero for all transverse waves associated with a plane of material symmetry.     

Unsteady RANS method for surface ship boundary layer and wake and wave field

Results are reported of an unsteady Reynolds‐averaged Navier–Stokes (RANS) method for simulation of the boundary layer and wake and wave field for a surface ship advancing in regular head waves, but restrained from body motions. Second‐order finite differences are used for both spatial and temporal discretization and a Poisson equation projection method is used for velocity–pressure coupling. The exact kinematic free‐surface boundary condition is solved for the free‐surface elevation using a body‐fitted/free‐surface conforming grid updated in each time step. The simulations are for the model problem of a Wigley hull advancing in calm water and in regular head waves. Verification and validation procedures are followed, which include careful consideration of both simulation and experimental uncertainties. The steady flow results are comparable to other steady RANS methods in predicting resistance, boundary layer and wake, and free‐surface effects. The unsteady flow results cover a wide range of Froude number, wavelength, and amplitude for which first harmonic amplitude and phase force and moment experimental data are available for validation along with frequency domain, linear potential flow results for comparisons. The present results, which include the effects of turbulent flow and non‐linear interactions, are in good agreement with the data and overall show better capability than the potential flow results. The physics of the unsteady boundary layer and wake and wave field response are explained with regard to frequency of encounter and seakeeping theory. The results of the present study suggest applicability for additional complexities such as practical ship geometry, ship motion, and maneuvering in arbitrary ambient waves. Copyright © 2001 John Wiley & Sons, Ltd.     

Real-time nonlinear cylinder wave force reconstruction in stochastic wave field considering second-order wave effects

This study provides a novel method for reconstructing real-time nonlinear wave forces on a large-scale circular cylinder by considering second-order wave effects. Potential theory is utilized for deriving the expression of wave forces with the measured data of wave elevation. Approximate expressions of quadratic transfer functions are built with undetermined coefficients, which are resolved by using the historical data of measured wave elevation. Two different algorithms, including fast Fourier transform (FFT) and recursive least squares (RLS), are adopted for real-time reconstruction. Hydrodynamic tests are conducted in the wave flume on a circular cylinder to examine the effectiveness of the nonlinear reconstruction method. Comparative results demonstrate that the accuracy of real-time reconstructed wave forces is significantly enhanced by the present method. The over-prediction errors at force crests and the under-prediction errors at force troughs have been reduced. Furthermore, comparative results show that the nonlinear method implemented by the FFT algorithm provides more accurate results, whereas the RLS algorithm is more time cost efficient.     

Dynamics of localized wave solutions for the coupled Higgs field equation

Nonlinear Dynamics - By virtue of Hirota bilinear form of the coupled Higgs field equation, some higher-order rogue wave, the Ma breather, the Akhmediev breather and the general breather solutions...     

Travelling wave solutions for a quasilinear model of field dislocation mechanics

We consider an exact reduction of a model of Field Dislocation Mechanics to a scalar problem in one spatial dimension and investigate the existence of static and slow, rigidly moving single or collections of planar screw dislocation walls in this setting. Two classes of drag coefficient functions are considered, namely those with linear growth near the origin and those with constant or more generally sublinear growth there. A mathematical characterisation of all possible equilibria of these screw wall microstructures is given. We also prove the existence of travelling wave solutions for linear drag coefficient functions at low wave speeds and rule out the existence of nonconstant bounded travelling wave solutions for sublinear drag coefficients functions. It turns out that the appropriate concept of a solution in this scalar case is that of a viscosity solution. The governing equation in the static case is not proper and it is shown that no comparison principle holds. The findings indicate a short-range nature of the stress field of the individual dislocation walls, which indicates that the nonlinearity present in the model may have a stabilising effect. We predict idealised dislocation-free cells of almost arbitrary size interspersed with dipolar dislocation wall microstructures as admissible equilibria of our model, a feature in sharp contrast with predictions of the possible non-monotone equilibria of the corresponding Ginzburg-Landau phase field type gradient flow model.     

Elastic-bound conditions for energetically optimal elasticity and their implications for biomimetic propulsion systems

Minimising the energy consumption associated with periodic motion is a priority common to a wide range of technologies and organisms. These include many forms of biological and biomimetic propulsion system, such as flying insects. Linear and nonlinear elasticity can play an important role in optimising the energetic behaviour of these systems, via linear or nonlinear resonance. However, existing methods for computing energetically optimal nonlinear elasticities struggle when actuator energy regeneration is imperfect: when the system cannot reuse work performed on the actuator, as occurs in many realistic systems. Here, we develop a new analytical method that overcomes these limitations. Our method provides exact nonlinear elasticities minimising the mechanical power consumption required to generate a target periodic response, under conditions of imperfect energy regeneration. We demonstrate how, in general parallel- and series-elastic actuation systems, imperfect regeneration can lead to a set of non-unique optimal nonlinear elasticities. This solution space generalises the energetic properties of linear resonance, and is described completely via bounds on the system work loop: the elastic-bound conditions. The choice of nonlinear elasticities from within these bounds leads to new tools for systems design, with particular relevance to biomimetic propulsion systems: tools for controlling the trade-off between actuator peak power and duty cycle; for using unidirectional actuators to generate energetically optimal oscillations; and further. More broadly, these results lead to new perspectives on the role of nonlinear elasticity in biological organisms, and new insights into the fundamental relationship between nonlinear resonance, nonlinear elasticity, and energetic optimality.

     

Homogenization for wave propagation in periodic fibre-reinforced media with complex microstructure. I—Theory

The effective elastic properties of periodic fibre-reinforced media with complex microstructure are determined by the method of asymptotic homogenization via a novel solution to the cell problem. The solution scheme is ideally suited to materials with many fibres in the periodic cell. In this first part of the paper we discuss the theory for the most general situation—N arbitrarily anisotropic fibres within the periodic cell. For ease of exposition we then restrict attention to isotropic phases which results in a monoclinic composite material with 13 effective moduli and expressions for each of these are determined. In the second part of this paper we shall discuss results for a variety of specific microstructures.     

应力波和动光弹等差条纹的分析与判读

介绍了动光弹的基本原理，并从理论上回答了动光弹应用中的一些问题，如惯性力可否忽略等．并在总结回顾动光弹等差条纹级次判读方法的基础上，提出了把应力波理论与等差条纹分析判读相结合的方法，这样不仅使条纹判读的概念更清晰，而且可提高条纹分析和级次判读的准确性．     

Mean field attenuation and amplitude attenuation due to wave scattering

We point out the inadequacy of two widely used approaches of formulating the amplitude attenuation of seismic waves, the formulation of mean-field attenuation and that of scattering coefficient under the single scattering approximation. Using a one-dimensional layered slab, we show that the attenuation of the mean field is merely a statistical effect caused by phase interference among different realizations of the random wave ensemble, and does not represent the amplitude attenuation. We will call the attenuation coefficient of the mean field as the randomization coefficient in order to distinguish it from the amplitude attenuation coefficient.We also show that the scattering coefficient method leads to the same result as the first order approximation to the renormalized perturbation series (or the bilocal approximation to Dyson's equation) of the mean field. Therefore these two approaches are equivalent to a certain degree. This is also shown by using the one-dimensional layered slab model as an example.After pointing out the incorrectness of comparing experiments on amplitude attenuation with the mean field formulation, we suggest and discuss some methods of obtaining the mean field in experiments. For one-dimensional problems, the samples must be taken along the whole propagation path in order to use a spatial average to substitute for ensemble average. For a three-dimensional wave field, measurements over a large seismic array can be used to obtain the mean field. The data from Lasa measured by Aki are used to compare with theory; the agreement between them is good. Finally we compare the mean-field attenuation (randomization) and the amplitude attenuation using the back-halfspace-integration approximation introduced by Wu, and compare them with the measured data by Aki. The comparison shows further the inability of the mean-field formulation in dealing with the problem of amplitude attenuation.     

Non-contact evaluation of the resonant frequency of a microstructure using ultrasonic wave

This paper presents a novel non-contact method for evaluating the resonant frequency of a microstructure, Firstly, the microstructure under test is excited by ultrasonic waves. This excitation method does not impose any undefined load on the specimen like the electrostatic excitation and also this is the first actual use of ultrasonic wave for exciting a microstructure in the literature. Secondly, the amplitudes of the microstructure are determined by image edge detection using a Mexican hat wavelet transform on the vibrating images of the microstructure. The vibrating images are captured by a CCD camera when the microstructure is vibrated by ultrasonic waves at a series of discrete high frequencies （〉30 kHz）. Upon processing the vibrating images, the amplitudes at various excitation frequencies are obtained and an amplitude-frequency spectrum is obtained from which the resonant frequency is subsequently evaluated. A micro silicon structure consisting of a perforated plate （192 × 192 μm） and two cantilever beams （76 × 43 μm） which is about 4 μm thickness is tested. Since laser interferometry is not required, thermal effects on a test object can be avoided. Hence, the setup is relatively simple. Results show that the proposed method is a simple and effective approach for evaluating the dynamic characteristics of microstructures.     

Moving shocks through metallic grids: their interaction and potential for blast wave mitigation

Numerical simulations and laboratory measurements have been used to illuminate the interaction of a moving shock wave impacting on metallic grids at various shock strengths and grid solidities. The experimental work was carried out in a large scale shock tube facility while computational work simulated the flow field with a time-dependent inviscid and a time-dependent viscous model. The pressure drop measured across the grids is a result of two phenomena which are associated with the impact of the shock on the metallic grids. First are the reflection and refraction of the incoming shock on the grid itself. This appears to be the main inviscid mechanism associated with the reduction of the strength of the transmitted shock. Second, viscous phenomena are present during the reflection and refraction of the wave as well as during the passage of the induced flow of the air through the grid. The experimental data of pressure drop across the grid obtained in the present investigation are compared with those obtained from computations. The numerical results slightly overpredict the experimental data of relative pressure drop which increases substantially with grid solidity at fixed flow Mach numbers. The processes of shock reflection and refraction are continuous and they can be extended in duration by using thicker grids that will result in lower compression rates of the structural loading and increase the viscous losses associated with these phenomena which will further attenuate the impacting shock. Preliminary theoretical analysis suggests that the use of a graded porosity/solidity material will result in higher pressure drop than a constant porosity/solidity material and thus provide effective blast mitigation.      

Rheological properties of PDMS/clay nanocomposites and their sensitivity to microstructure

The effect of microstructure on the rheology of clay/polymer nanocomposites is investigated using dispersions of organically treated clay in nearly Newtonian poly(dimethylsiloxane). Degree of dispersion and floc size are altered by using two different dispersion procedures and by changing the shear history. The scaling for dynamic moduli of attractive colloids applies, except for a possible relaxation mechanism at very low frequencies. The time to reach the crossover at a given frequency is found to be extremely sensitive to the dispersion procedure used. Hydrodynamic and elastic components of the steady state stress, on the other hand, evolve in a very similar fashion for the different systems. Although the relaxation times of the elastic stress components change drastically with flow-induced changes in structure, the dispersion process hardly has an effect at all. Intermittent start-up flows in the forward and reverse directions show that anisotropy persists long after the flow has been arrested, even at shear rates where no large reversible flocs are present. The degree of dispersion only had a limited effect on the anisotropy. Finally, the effect of shear on structure recovery has been studied. Very low shear rates are found to increase the rate of recovery, even for small strains.     

Opposed jets with small separations and their implications for the extinction of opposed flames

 Profiles of static pressure and the mean and rms of velocity fluctuations in opposed isothermal jets were measured with a combination of static-pressure probes, hot-wire and laser-Doppler velocimetry. The static pressures close to the axis at the outlet planes of the two jets increased as the separation was reduced below three diameters, with measurable and increasing radial flow below 0.8 diameters. This, in turn, reduced the mean axial velocity on the axis of symmetry. The mean strain rate along the stagnation plane was near constant over much of the impingement region for separations greater than 1.0 diameter and a maximum occurred at radial distances which increased as the jet separation was reduced below this value. The maximum values stemmed from the exit-plane profiles and were larger than the bulk strain rate by a factor which increased with radial distance from 2 to 5 for separations of 0.8 and 0.2 diameters. The non-uniform radial profile of mean strain rate caused local extinction of premixed flames to occur initially in the region of the maximum value and, with further increase in the bulk, and therefore in mean strain rate, it moved radially inwards to produce complete extinction. The bulk strain rate for complete extinction increased non-linearly with separation so that it was almost three times larger at 0.2 than at 0.8 diameters. Received: 8 May 2000/Accepted: 28 November 2000