Scattering from Rough Surfaces Using the"Shooting and Bouncing Rays" Technique

The “shooting and bouncing rays” (SBR) technique is used to analyze the electromagnetic scattering characters of ocean rough surfaces varying with time. Some numerical results are presented and compared with the method of moments, and some factors, such as the incident angle, polarization and frequency are investigated which influence on electromagnetic scattering characters of ocean rough surfaces.

Carpet Cloak Design for Rough Surfaces

Conventional carpet cloak structures have been utilized to conceal the objects located on a planar perfect electric conductor surface. We systematically investigate hiding arbitrarily shaped objects on a rough surface, as a more general and practical scenario. In addition, the required cloak is designed considering different boundary conditions for the surface beneath the object, despite the previous studies. To achieve an invisibility cloak, taking advantage of linear coordinate transformation, a simple homogeneous material is obtained to realize the cloak structure, facilitating the fabrication processes. Numerical simulations validate the performance of the proposed cloaking method. Therefore, the proposed structure is capable of cloaking in more general and complicated scenarios.

Research on synthetic aperture radar imaging technology of one-dimensional layered rough surfaces

A quick and exact imaging method for one-dimensional layered rough surfaces is proposed in this paper to study the scattering characteristics of a layered medium that exists widely in nature.The boundary integral equations of layered rough surfaces are solved by using the propagation-inside-layer expansion combined with the forward and backward spectral acceleration method（PILE＋FB-SA）,and the back scattering data are obtained.Then,a conventional synthetic aperture radar（SAR） imaging procedure called back projection method is used to generate a two-dimensional（2D） image of the layered rough surfaces.Combined with the relative dielectric permittivity of realistic soil,the random rough surfaces with Gauss spectrum are used to simulate the layered medium with rough interfaces.Since the back scattering data are computed by using the fast numerical method,this method can be used to study layered rough surfaces with any parameter,which has a great application value in the detection and remote sensing areas.

Fractal Prediction Model of Thermal Contact Conductance of Rough Surfaces

The thermal contact conductance problem is an important issue in studying the heat transfer of engineering surfaces, which has been widely studied since last few decades, and for predicting which many theoretical models have been established. However, the models which have been existed are lack of objectivity due to that they are mostly studied based on the statistical methodology characterization for rough surfaces and simple partition for the deformation formats of contact asperity. In this paper, a fractal prediction model is developed for the thermal contact conductance between two rough surfaces based on the rough surface being described by three-dimensional Weierstrass and Mandelbrot fractal function and assuming that there are three kinds of asperity deformation modes： elastic, elastoplastic and fully plastic. Influences of contact load and contact area as well as fractal parameters and material properties on the thermal contact conductance are investigated by using the presented model. The investigation results show that the thermal contact conductance increases with the increasing of the contact load and contact area. The larger the fractal dimension, or the smaller the fractal roughness, the larger the thermal contact conductance is. The thermal contact conductance increases with decreasing the ratio of Young＇s elastic modulus to the microhardness. The results obtained indicate that the proposed model can effectively predict the thermal contact conductance at the interface, which provide certain reference to the further study on the issue of heat transfer between contact surfaces.

Wear Resistance of 3Cr2W8V Rough Surfaces

Three types of rough surface were processed by laser irradiation on the 3Cr2W8V material hot-work die steel surface. The wear experiments with smooth surface and rough surface samples were repeated on the pin-tray wear machine. According to the wear results, we studied the regularity of wear resistance of different rough surface samples. The results indicated that bionic rough surface can improve the wear resistance of the material and the wear resistance can be increased 1-2 times, compared with the smooth surface. Also, the wear resistance of the rough surface was affected by laser current and duration of impulse. The bigger the laser current or the impulse duration, the better is the wear resistance. When the distance between the same kind of units which are distributed on the surfaces is changed, the wear resistance changes. The wear resistance of a bionic rough surface on which the grid units were distributed at spacing of 1 mm was the best. And we designed the wear models.

Preload-responsive adhesion of microfibre arrays to rough surfaces

Adhesion of bio-inspired microfibre arrays to a rough surface is studied theoretically. The array consists of vertical elastic rods fixed on a rigid backing layer, and the surface is modeled by rigid steps with a normally distributed height. Analytical expressions are obtained for the adhesion forces in both the approach and retraction processes. It is shown that, with the increasing preload, the pull-off force increases at first and then attains a plateau value. The results agree with the previous experiments and are expected helpful in adhesion control of the array in practical applications.

Study of MPI based on parallel MOM on PC clusters for EM-beam scattering by 2-D PEC rough surfaces

This paper firstly applies the finite impulse response filter （FIR） theory combined with the fast Fourier transform （FFT） method to generate two-dimensional Gaussian rough surface. Using the electric field integral equation （EFIE）, it introduces the method of moment （MOM） with RWG vector basis function and Galerkin＇s method to investigate the electromagnetic beam scattering by a two-dimensional PEC Gaussian rough surface on personal computer （PC） clusters. The details of the parallel conjugate gradient method （CGM） for solving the matrix equation are also presented and the numerical simulations are obtained through the message passing interface （MPI） platform on the PC clusters. It finds significantly that the parallel MOM supplies a novel technique for solving a two-dimensional rough surface electromagnetic-scattering problem. The influences of the root-mean-square height, the correlation length and the polarization on the beam scattering characteristics by two-dimensional PEC Gaussian rough surfaces are finally discussed.

Variational Approach to Scattering by Inhomogeneous Layers Above Rough Surfaces

In this paper, we study, via variational methods, the problem of scattering of time harmonic acoustic waves by unbounded inhomogeneous layers above a sound soft rough surface. We first propose a variational formulation and exploit it as a theoretical tool to prove the well-posedness of this problem when the media is non-absorbing for arbitrary wave number and obtain an estimate about the solution, which exhibit explicitly dependence of bound on the wave number and on the geometry of the domain. Then, based on the non-absorbing results, we show that the variational problem remains uniquely solvable when the layer is absorbing by means of a priori estimate of the solution. Finally, we consider the finite element approximation of the problem and give an error estimate.

VIBRATION OF CANTILEVERS WITH ROUGH SURFACES

We study the effect of surface roughness on the resonance frequency of micro-cantilever sensors. The analysis demonstrates that surface roughness can enhance, decrease or even annul the effect of surface stress on the resonance frequency, depending on the surface inclination angle and the Poisson ratio of the coating film on the cantilever.

Adhesive Contact of Elastic Solids with Self-Affine Fractal Rough Surfaces

The elastic adhesive contact of self-affine fractal rough surfaces against a rigid flat is simulated using the finite element method. An array of nonlinear springs, of which the force-separation law obeys the Lennard–Jones potential, is introduced to account for the interfacial adhesion. For fractal rough surfaces, the interfacial interaction is generally attractive for large mean gaps, but turns repulsive as the gap continuously shrinks. The interfacial interactions at the turning point corresponding to the spontaneous contact are shown for various surfaces. For relatively smooth surfaces, the probability density distributions of repulsion and attraction are nearly symmetric. However, for rougher surfaces, the simulation results suggest a uniform distribution for attraction but a monotonously decreasing distribution with a long tail for repulsion. The pull-off force rises with increasing ratio of the work of adhesion to the equilibrium distance, whereas decreases for solids with a higher elastic modulus and a larger surface roughness. The current study will be helpful for understanding the adhesion of various types of rough solids.

A new 3D plastoelastohydrodynamic lubrication model for rough surfaces

Plastoelastohydrodynamic lubrication of rough surfaces(R-PEHL)is a cutting-edge area of research in interface fluid-structure coupling analysis.The existing R-PEHL model calculates the elastic-plastic deformation of rough surface by the Love equation in a semi-infinite space smooth surface,which deviates from the actual surface.Therefore,it is an innovative work to study the exact solution of elastic-plastic deformation of rough surface and its influence on the solution results of R-PEHL model.In this paper,a new contact calculation model of plastoelastohydrodynamic lubrication(PEHL)with three-dimensional(3D)rough surface is proposed by integrating numerical method of EHL and finite element method.The new model eliminates an original error introduced by the assumption of semi-infinite space in contact calculation,providing wide applicability and high accuracy.Under the given rough surfaces and working conditions,the study reveals that:(1)the oil film pressure calculated by the new model is lower than that of the smooth surface in semi-infinite space by 200–800 MPa;(2)the Mises stress of the new model is 2.5%–26.6%higher than that of the smooth surface in semi-infinite space;(3)compared with the semi-infinite space assumption,the rough surface plastic deformation of the new model is increased by 71%–173%,and the local plastic deformation singularity may appear under the semi-infinite space assumption;(4)the plastic deformation caused by the first contact cycle on the rough surface of the new model accounts for 66.7%–92.9%of the total plastic deformation,and the plastic deformation of the semi-infinite space accounts for 50%–83.3%.This study resolves the contradiction between the smooth surface assumption and the rough surface in the existing R-PEHL model,establishing a solid logic foundation for the accurate solution of R-PEHL model.

Numerical Reconstruction of Locally Rough Surfaces with a Newton Iterative Algorithm

In this paper,we propose a Newton iterative algorithm to numerically reconstruct a locally rough surface with Dirichlet and impedance boundary conditions by near-field measurements of acoustic waves.The algorithm relies on the Frechet differentiability analysis of the locally rough surface scattering problem,which is established by reducing the original model into an equivalent boundary value problem with compactly supported boundary data.With a slight modification,the algorithm can be also extended to reconstruct the local perturbation of a non-local rough surface.Finally,numerical results are presented to illustrate the effectiveness of the inversion algorithm with the multi-frequency data.

Shear sliding of rough-walled fracture surfaces under unloading normal stress

Through high-precision engraving,self-affine sandstone joint surfaces with various joint roughness coefficients(JRC=3.21e12.16)were replicated and the shear sliding tests under unloading normal stress were conducted regarding various initial normal stresses(1e7 MPa)and numbers of shearing cycles(1 e5).The peak shear stress of fractures decreased with shear cycles due to progressively smooth surface morphologies,while increased with both JRC and initial normal stress and could be verified using the nonlinear Barton-Bandis failure criterion.The joint friction angle of fractures exponentially increased by 62.22%e64.87%with JRC while decreased by 22.1%e24.85%with shearing cycles.After unloading normal stress,the sliding initiation time of fractures increased with both JRC and initial normal stress due to more tortuous fracture morphologies and enhanced shearing resistance capacity.The surface resistance index(SRI)of fractures decreased by 4.35%e32.02%with increasing shearing cycles due to a more significant reduction of sliding initiation shear stress than that for sliding initiation normal stress,but increased by a factor of 0.41e1.64 with JRC.After sliding initiation,the shear displacement of fractures showed an increase in power function.By defining a sliding rate threshold of 5105 m/s,transition from“quasi-static”to“dynamic”sliding of fractures was identified,and the increase of sliding acceleration steepened with JRC while slowed down with shearing cycles.The normal displacement experienced a slight increase before shear sliding due to deformation recovery as the unloading stress was unloaded,and then enhanced shear dilation after sliding initiation due to climbing effects of surface asperities.Dilation was positively related to the shear sliding velocity of fractures.Wear characteristics of the fracture surfaces after shearing failure were evaluated using binary calculation,indicating an increasing shear area ratio by 45.24%e91.02%with normal stress.

Slip boundary conditions for rough surfaces

The velocity slip and temperature jump for a two-dimensional rough plate under hypersonic conditions were analyzed using the Direct Simulation Monte Carlo(DSMC)method.Surface roughness was explicitly modeled by introducing various structures on the flat plate.The influences of relative roughness height,which involves the roughness height,roughness spacing,incoming velocity,and the degree of rarefaction,were analyzed and discussed.It is found that with the increase of the relative roughness height,the jump temperature increases,while the slip velocity decreases gradually.The effects of surface roughness on the slip coefficients can be attributed to the change of accommodation coefficients.A new slip model for rough surfaces was established in this paper,which accounts for the coupling effects of gas rarefaction and surface roughness,without the effort to model the surface roughness explicitly.The nitrogen flows in the microchannel,and flows over a blunt cone and an axisymmetric bi-conic body,were simulated under the modified and conventional slip boundary conditions,respectively.The numerical solutions were validated with experimental data.It can be safely concluded that compared with the traditional first-order slip boundary conditions,the modified slip model improves the accuracy of macroscopic properties,especially the heat transfer coefficient.

High-order Bragg forward scattering and frequency shift of low-frequency underwater acoustic field by moving rough sea surface

Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition.Herein,underwater acoustic scattering modulation from a moving rough sea surface is studied based on integral equation and parabolic equation.And with the principles of grating and constructive interference,the mechanism of this acoustic scattering modulation is explained.The periodicity of the interference of moving rough sea surface will lead to the interference of the scattering field at a series of discrete angles,which will form comb-like and frequency-shift characteristics on the intensity and the frequency spectrum of the acoustic scattering field,respectively,which is a high-order Bragg scattering phenomenon.Unlike the conventional Doppler effect,the frequency shifts of the Bragg scattering phenomenon are multiples of the undulating sea surface frequency and are independent of the incident sound wave frequency.Therefore,even if a low-frequency underwater acoustic field is incident,it will produce obvious frequency shifts.Moreover,under the action of ideal sinusoidal waves,swells,fully grown wind waves,unsteady wind waves,or mixed waves,different moving rough sea surfaces create different acoustic scattering processes and possess different frequency shift characteristics.For the swell wave,which tends to be a single harmonic wave,the moving rough sea surface produces more obvious high-order scattering and frequency shifts.The same phenomena are observed on the sea surface under fully grown wind waves,however,the frequency shift slightly offsets the multiple peak frequencies of the wind wave spectrum.Comparing with the swell and fully-grown wind waves,the acoustic scattering and frequency shift are not obvious for the sea surface under unsteady wind waves.

Mechanical properties and fracture surface roughness of thermally damaged granite under dynamic splitting

In order to understand the mechanical properties and the fracture surface roughness characteristics of thermally damaged granite under dynamic splitting,dynamic Brazilian splitting tests were conducted on granite samples after thermal treatment at 25,200,400,and 600℃.Results show that the dynamic peak splitting strength of thermally damaged granite samples increases with increasing strain rate,showing obvious strain‐rate sensitivity.With increasing temperature,thermally induced cracks in granite transform from intergranular cracks to intragranular cracks,and to a transgranular crack network.Thermally induced damages reduce the dynamic peak splitting strength and the maximum absorbed energy while increasing the peak radial strain.The fracture mode of the thermally damaged granite under dynamic loads is mode Ⅱ splitting failure.By using the axial roughness index Z2 a,the distribution ranges of the wedge‐shaped failure zones and the tensile failure zones in the fracture surfaces under dynamic Brazilian splitting can be effectively identified.The radial roughness index Z_(2)^(r)is sensitive to the strain rate and temperature.It shows a linear correlation with the peak splitting strength and the maximum absorbed energy and a linear negative correlation with the peak radial strain.Z_(2)^(r)can be used to quantitatively estimate the dynamic parameters based on the models proposed.

A deterministic FE contact analysis of 3D rough surfaces with textures and comparison with classic statistical contact models

Accurate contact calculations of real rough surfaces are fundamental but complicated. The model-based methods are convenient and straightforward. But these methods ignore some factors and may lead to less accurate results. This is especially true when considering multi-scale topographic features of engineering rough surfaces. Based on artificially generated rough surfaces, the deterministic contact analysis of two 3D rough surfaces is conducted by the finite element method(FEM). The calculations show that when the separation between surfaces reduces, results of classic model-based methods are quite different from those of this study, especially when the roughness distribution and textures are considered. As friction pairs are working under increasing harsh conditions, the accurate contact calculation in this paper will be of great significance.

Study on the double transmission of ultrasonic waves through statistic rough surfaces

A model evaluating the signal loss of the double transmitted acoustic beams through random rough surfaces was established based on the Fresnel approximation and phase- screen approximation. A simple analytical solution was achieved using the exponential substi- tution approach to remove the nonlinear integral terms. The factors that affect the signal of double transmissions from random rough surfaces were analyzed. The research results demon- strated that the signal loss is not only related to the root-mean-squire height of the roughness, but also to the distance of wave traveling in the materials. The model can be very helpful for improving the reliability of NDT (Non-Destructive Testing).

A Theoretical Model for the Microwave Emissivity of Rough Sea Surfaces

When sea surface wavelengths are not larger than microwave wavelengths,the microwave emissivity of Gaussian rough sea surfaces can be investigated by applying effective media theory(EMT)of rough surfaces.For one-dimensional Gaussian sea surface,the microwave emissivity model is proposed by EMT,which regards the air-sea rough interface as a new effective medium of isotropic permittivity between the top layer of air and the bottom layer of seawater.The emissivity model is controlled by the root mean square deviation(RMSD)of the rough surface height and the correlation length of the rough surface.Results clearly show that the emissivity increases along with the RMSD increase if the latter is smaller than a critical value.Furthermore,excess emissivities and the brightness temperature increments for a wind-roughened sea surface can be estimated from those of flat surfaces by fitting the RMSD as a function of wind speed.Good agreements are obtained by comparing the results of our model with the satellite data at microwave frequencies of 1.4,6.8,18,21,and 37 GHz,respectively.Moreover,these findings imply that our method can be extended to retrieve the sea surface parameters,such as RMSD and the correlation length of the rough surface,from the satellite data.

Propagation of elastic waves in a plate with rough surfaces

The characteristics of Lamb wave propagating in a solid plate with rough surfaces are studied on the basis of small perturbation approximation. The Rayleigh-Lamb frequency equation expressed with SA matrix is presented. The Rayleigh-Lamb frequency equation for a rough surface plate is different from that for a smooth surface plate, resulting in a small perturbation △k on Lamb wave vector k. The imaginary part of △k gives the attenuation caused by wave scattering. An experiment is designed to test our theoretical predications. By using wedge-shape pipes, different Lamb wave modes are excited. The signals at different positions are received and analyzed to get the dispersion curves and attenuations of different modes. The experimental results are compared with the theoretical predications.