Rigid Rough Surface Research Articles

High-frequency diffraction corrections to backscattering cross sections from a rough three-dimensional surface

Diffraction corrections to scalar wave fields at perfectly free and rigid rough surfaces were derived by two iterations of the corresponding integral equations. These diffraction corrections to the pressure or normal velocity (which, in the geometrical optics limit, are doubled at perfectly rigid and free surfaces, respectively) were obtained with an accuracy of approximately 1k(2), where k is the wave number of incidence radiation. Based on these corrections to the surface fields, the backscattering cross sections at normal incidence from the statistically rough Gaussian surfaces were derived. It was found that for the gentle roughness, diffraction results in effective "smoothing" of roughness for rigid and free surfaces and increasing of the backscattering cross sections, but for a rigid surface with steep roughness, the "fictitious" surface can be more rough than the real one, and the diffraction corrections become negative.

Frictional Contact of Rubber on rough Surfaces

AbstractThe aim of this work is to investigate the frictional behaviour of rubber on rough rigid surfaces. Rubber friction is composed of hysteretic and adhesional effects. The main focus lies on the hysteresis theory which motivates rubber friction with the internal damping inside the viscoelastic material.It is necessary to perform a multiscale analysis to regard the roughness of the surface on all important length scales. The fractal surface is approximated by a superposition of harmonic functions. The simulations will start at the lowest wavelength and proceed to larger scales by replacing the smaller roughness with the ascertained friction law. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Oblique impact of inflated balls at large deflections

A planar theory for oblique impact of thin-walled spherical balls against a rough rigid surface has been developed on the basis of an assumed deformation field—an initially spherical ball is assumed to flatten against the constraint surface while the remainder of the ball remains undeformed. For inflated thin-walled balls, which are represented by these assumptions (basketballs, soccer balls, volleyballs, etc) the normal reaction force acting on the flattened contact patch is predominately due to the internal gas pressure—the reaction due to shell bending is insignificant in comparison with this gas force. During impact of a thin-walled ball there also is a non-conservative momentum flux reaction that is caused by the flow of momentum into and out-of the flattened contact patch. If the ball is translating as well as rotating about an axis perpendicular to the plane of motion, the distribution of the normal component of velocity for material entering and exiting the flattened contact patch results in a distribution of momentum flux force intensity around the periphery of the contact patch and consequently, a momentum flux torque acting on the flattened sphere. The effect of these reaction forces and torque on oblique impact of thin-walled spherical balls is calculated as a function of the ball deflection (or normal component of impact velocity). In comparison with rigid body calculations for oblique impact of a spinning ball against a rough surface at angles<45° from normal, the effect of maximum deflections as large as half the initial radius is to slightly accentuate the effect of friction on angle of rebound and moderately decrease the angular velocity of the ball. However, for angles >45° from normal, the final angular velocity can be as small as 40% of that predicted by rigid body theory. The most significant changes in rebound angle are for cases with initial backspin—a technique commonly used in many ball sports.

Dynamic analysis of single and cyclic indentation of an elastic–plastic multi-layered medium by a rigid fractal surface

Dynamic indentation of an elastic–plastic multi-layered medium by a rigid rough surface that exhibits fractal behavior was analyzed with the finite element method. A sufficiently large mesh was used to avoid the effects of the faster propagating dilatation waves after they were reflected from the artificial mesh boundaries. Single-indentation results illustrate the significance of the thickness of the surface layer and the indentation speed on the contact pressure distribution and subsurface stresses and strains. The initiation of yielding and the development of plasticity are interpreted in the context of results for the von Mises equivalent stress and equivalent plastic strain obtained during the loading and unloading phases of an indentation cycle. Cumulative plasticity and elastic shakedown are discussed in light of results revealing the evolution of deformation in the multi-layered medium due to cyclic indentation. The analysis provides insight into the importance of indentation speed, layer thickness, surface topography, and indentation cycle on the mechanical response of a multi-layered medium in dynamic contact with a rough surface exhibiting multi-scale (fractal) roughness.

Frictional contact of elastomer materials on rough rigid surfaces

AbstractThe frictional behavior of elastomer materials is still unexplored, but very important for many industrial applications. Special attention is turned to rubber friction on rough road tracks. Due to the non‐rigid material characteristics of the rubber it is not sufficient to use a constant friction coefficient like Coulombs law. The frictional qualities depend on many different influences like sliding velocity, applied normal stress, surface roughness, material properties and the temperature in the contact zone. (© 2004 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

A multiscale finite-element method for solving rough-surface elastic-contact problems

A novel multiscale finite-element method to investigate the elastic contact of two-dimensional rough surfaces is presented. The aim of the method is to find the microscopic curve that describes the deformed shape of a solid with a smooth boundary surface in frictionless contact with a rigid rough surface. In addition, the real contact area is studied through the surface deformation. The contact traction on the contact surface and the maximum shear stress around the contact region are analyzed. This method is based on the variational inequality approach for solving the elastic frictionless contact problem. The strategy is to separate a small slice within the contact region and solve it as an independent system. Then the contact traction is obtained through iterations between the solution of the independent small slice and the solution of the total solid body. We observe a much higher pressure than the result of Hertz theory around the asperities. The main conclusions are (1)~the actual contact area and surface traction are dependent on the wavelength and amplitude of the surface roughness, (2) there is a much higher pressure around the asperities than predicted by Hertz theory, and (3) the location of maximum shear stress tends to be shifted toward the surface as compared with the case of smooth-surface contact. The method has the potential to be extended to solve three-dimensional rough contact problems.PACS Nos.: 03.40.D, 46.30.P, 62.20.P

Contact of a viscoelastic body with a rough rigid surface and identification of friction coefficients

Abstract - The paper is concerned with the contact problem of a viscoelastic body with a rough rigid surface and the identification problem for the friction coefficient in the contact. Using a variational method, the authors give regularized solutions to the recovery problem, formulated as a minimization problem. A smoothness result for the fit-to-data functional is proved.

A new oblique impact test for motorcycle helmets

A new oblique impact test for motorcycle helmets is described, simulating a fall from a motorcycle on to the road surface or the windshield of a car. An instrumented headform falls vertically to impact a horizontally moving rigid rough or deformable surface. Both the impact site on the helmet, and the vertical and horizontal velocities, can be varied, while the headform linear and rotational accelerations are measured. The rig was used to compare a new helmet design with current helmets, which are designed to pass impact tests in which the impact force is perpendicular to the helmet surface. The new design, which has a low friction layer between the shell and the liner, reduced, by up to 50%, the rotational acceleration of the head compared with conventional designs.

Handling and Driving Characteristics for Six-Wheeled Vehicles

Handling performance of six-wheeled special-purpose vehicles is investigated in this study. Six-wheel drive (6WD) vehicles are believed to have good performance in off-the-road manoeuvring and to have fail-safe capabilities when one or two of their tyres are blown. However, the handling performance of six-wheel steering (6WS) vehicles is not yet well understood in the relevant literature. In this paper, six-wheeled vehicles are modelled as an 18 degree-of-freedom (DOF) system that considers non-linear vehicle dynamics, tyre models and kinematic effects. The vehicle model is constructed into a simulation tool using MATLAB/SIMULINK so that input/output and vehicle parameters can be changed easily using the modulated approach. Handling performance is analysed not only from the frequency domain but also from the time domain. Simulation results demonstrate that the effect of middle-wheel steering is not negligible from the viewpoint of handling characteristics such as yaw rate, lateral acceleration, etc. The simulation tool is also utilized for the manoeuvring analysis over a rough rigid surface, where the separation between the wheels and the road can be considered. In addition, a new 6WS control law is proposed in order to minimize the sideslip angle. Lane change simulation results show the advantage of 6WS vehicles with the proposed control law.

Handling and driving characteristics for six-wheeled vehicles

Handling performance of six-wheeled special-purpose vehicles is investigated in this study. Six-wheel drive (6WD) vehicles are believed to have good performance in off-the-road manoeuvring and to have fail-safe capabilities when one or two of their tyres are blown. However, the handling performance of six-wheel steering (6WS) vehicles is not yet well understood in the relevant literature. In this paper, six-wheeled vehicles are modelled as an 18 degree-of-freedom (DOF) system that considers non-linear vehicle dynamics, tyre models and kinematic effects. The vehicle model is constructed into a simulation tool using MATLAB/SIMULINK so that input/output and vehicle parameters can be changed easily using the modulated approach. Handling performance is analysed not only from the frequency domain but also from the time domain. Simulation results demonstrate that the effect of middle-wheel steering is not negligible from the viewpoint of handling characteristics such as yaw rate, lateral acceleration, etc. The simulation tool is also utilized for the manoeuvring analysis over a rough rigid surface, where the separation between the wheels and the road can be considered. In addition, a new 6WS control law is proposed in order to minimize the sideslip angle. Lane change simulation results show the advantage of 6WS vehicles with the proposed control law.

A T-MATRIX PERTURBATION FORMALISM FOR SCATTERING FROM A ROUGH FLUID-ELASTIC INTERFACE

A perturbative representation of the null field T-matrix for scattering a pressure wave from a fluid elastic interface with surface roughness is developed. It is shown that thenth order T-matrix may be calculated recursively and expressed in terms of the elements of a zeroth order T-matrix. Further, it is shown that the expression for thenth order T-matrix is general in form and may be specialized to scattering from rigid and soft rough surfaces and from the rough surface of a fluid sediment. The T-matrix for thenth order spectral amplitude of the scattered pressure field in the fluid is calculated and its diagrammatic representation is constructed. For sinusoidal surface roughness, the perturbative representation of the T-matrix is used to calculate the spectral amplitudes of the Floquet modes of the pressure field scattered in the fluid. The results are compared with those obtained from a non-perturbative representation of the T-matrix and the accuracy and region of applicability of the formalism is determined. Then the relative scattering amplitudes of some of the individual scattering processes that occur in the diagrammatic representation of the T-matrix are calculated through second order. It is shown that diagrams that correspond to scalar processes in which surface pressure fields are excited and propagated tend to dominate diagrams that correspond to vector and tensor processes in which surface displacement fields are excited and propagated. A “scalar” approximation to the perturbation series is defined in which only scalar diagrams in the perturbation series are maintained. Numerical results for the perturbation series in the scalar approximation to fourth order are compared with exact results and it is shown that the scalar approximation provides reasonably accurate results for some applications.

Nonlinear interaction of solids with rigid surfaces

A rigorous method is presented for the finite element analysis of the nonlinear large deflection interaction of solid bodies with rough rigid surfaces. At the points of interaction on the pre-deflned rigid surfaces, the equations for incremental interaction forces are assembled via static condensation, and are solved satisfying the force and displacement constraints at these points. The solution for these forces is then utilized for the complete incremental analysis of the problem. An automatic load-deformation control strategy is also incorporated to handle problems with turning load paths. Two example problems are solved using the method developed and the results are compared with previously established results.

Computer Simulation of Elastic Rough Contacts

A computer program is developed to analyze the contact of a rigid smooth plane and computer-simulated elastic rough surfaces. The simulated surfaces have isotropic Gaussian height distribution and bilinear autocorrelation function. Results of two cases are presented: (1) dry contact between a square elastic rough punch and a rigid smooth plane; (2) dry contact between an elastic rough half-space and a rigid smooth plane. Force-compliance relationship is compared with hat derived by Bush, Gibson, and Thomas. Real contact area ratio Ar is found to be approximately proportional to nominal contact pressure in the range 0.025 < Ar < 0.3. Presented at the 39th Annual Meeting in Chicago, Illinois May 7—10, 1984

The boundary layer in the flow of a plastic medium near a rough surface

High-speed flow of an incompressible plastic medium past a rigid rough surface with slippage along it is investigated. It is assumed that the ratio of the yield point of the medium to the dynamic pressure in the flow is small. An asymptotic representation of the solution is constructed, based on the assumption due to Lavrent'ev that in the case of flows with such properties the principal parts of the velocity and stress fields are represented by the corresponding fields of an ideal fluid. Equations are obtained describing the flow in the boundary layer. Group-theoretic analysis is used to find their solution for flows past wedges and cones. The thickness of the boundary layer is estimated.

Modified sound refraction near a rough ocean bottom

It is well established that there is a strong boundary wave during low-frequency grazing scatter at a rough rigid surface overlaid by a homogeneous medium. Tolstoy [J. Acoust. Soc. Am. 69, 1290–1298 (1981)] has also shown that when source and receiver are on the bottom and the velocity in the medium decreases away from the ocean bottom the boundary wave tunnels into the shadow zone. We consider the case when source and receiver are near the ocean surface. It is predicted that, under certain conditions of velocity gradient, frequency and bottom roughness, the addition of the boundary wave mode to the volume wave mode will change the path of the grazing specularly scattered ray above the rough bottom. As a result, an upward refracted ray will reach the surface at a skip distance significantly greater than for a smooth bottom. This modified refraction phenomenon should be detectable at sea, under suitable indicated experimental conditions.

Double refraction near a rough bottom in isothermal waters

The occurence of a boundary wave during low‐frequency grazing scatter from rough rigid surfaces has been described by Tolstoy and experimentally verified by Medwin et al. [J. Acoust. Soc. Am. 66, 1131–1134 (1979)] for a homogeneous medium overlying the surface. Tolstoy [J. Acoust. Soc. Am. 69, 1290–1298 (1981)] has also shown that, when the velocity in the medium decreases away from the ocean bottom, tunneling into the shadow zone takes place, for source and receiver on the bottom. We re‐examine this case but for the source and receiver near the ocean surface and for bottoms of lesser roughness. It is predicted that, under certain conditions of velocity gradient, frequency, and bottom roughness, the boundary wave mode causes a splitting of the limiting ray above the rough bottom. As a result, two refracted rays would reach the ocean surface: a primary ray (classical limiting ray for smooth bottom), and a secondary ray with a significantly greater skip distance. This double refraction phenomenon should be detectable at sea, under suitable experimental conditions. [Research supported by ONR.]

Cleaning of a Rough Rigid Surface: Removal of a Dissolved Contaminant by Convection‐Enhanced Diffusion and Chemical Reaction

A model is formulated with which one may calculate the rate of disappearance of a species dissolved in fluid trapped in a microscopic cavity of a surface. The model accounts for diffusion, convection, and chemical reaction. Solutions are carried out, and a numerical example is worked out in order to show the representative time scales of these interacting processes.

Non isothermal model of compressing a plastic disk under impact

A Inathematical model is considered for the thermal instability phenomenon of the axial s t ra in of a thin homogeneous disk f rom an incompressible viscoplast ic mater ia l with the inertial proper t ies taken into account of the fluxes originating under mechanical impact along the axis of symmet ry . These investigations are of interest for an analysis of technological mater ia l t rea tment p rocesses by a pulse load, the sensit ivity of explosives to impact by a p i le -dr iver , and many other cases where the sufficiently rapid (adiabatic) c o m press ion of a thin l ayer of substance between rigid rough surfaces is considered.

Scattering from a corrugated surface: Comparison between experiment, Helmholtz–Kirchhoff theory, and the facet-ensemble method

The facet-ensemble method is used to compute the complex field scattered by a corrugated surface with large roughness. The method employs in part the frequency transform of an asymptotic approximation to the exact impulse solution for diffraction from a rigid (or pressure release, if desired) ridge or trough [M. A. Biot and I. Tolstoy, J. Acoust. Soc. Am. 29, 381–391 (1957); A. D. Pierce, Acoustics (McGraw–Hill, New York, 1981), pp. 489–490.] In the method, the scattering surface is approximated by joining edge to edge long plane strips (facets). Each adjacent pair of facets makes up a ridge or trough. Theoretical scattered acoustic pressure amplitude values are then obtained by superposing the diffracted and reflected contributions from individual ridges and troughs. A similar method was introduced by Novarini and Medwin [J. C. Novarini and H. Medwin, J. Acosut. Soc. Am. 64, 260–268 (1978); H. Medwin and J. C. Novarini, J. Acoust. Soc. Am. 69, 108–111 (1981)]. A comparison is provided here between amplitude values measured in a water-tank, scattering experiment [G. A. Sandness, Ph.D. thesis, Univ. of Wisconsin, Madison (1971)] and values predicted using the facet-ensemble method. Agreement is good in general and remains so when the number of approximating facets per spatial wavelength of the surface is changed. Also provided is a comparison (for the experimental geometry) between the facet-ensemble method and numerical evaluation of the Helmholtz–Kirchhoff integral. Most of the scattering occurred near the normal direction, and the Helmholtz–Kirchhoff integral is accurate for that direction. Agreement in this case between the integral solution and the facet-ensemble method, therefore, is good. The facet-ensemble method shows promise for estimating accurately the complex field scattered from a rough rigid (or pressure release) surface for any number of receivers at any number of locations.

Boundary wave generation by coherent multiple scatter at a randomly rough rigid surface

In a series of papers starting in 1979 (J. Acoust. Soc. Am. 66, 1135–1144), I. Tolstoy has shown that the Biot boundary conditions for coherent scatter from a low roughness surface [J. Acoust. Soc. Am. 44, 1616–1622 (1968)] can be applied effectively to various deterministically rough interfaces such as hemispherical or ellipsoidal bosses between dissimilar fluids, or between a solid and a fluid. A boundary wave is predicted that is particularly strong at near grazing scatter provided that the low roughness criterion holds: ka < kh ⩽ 1, where a is the radius of the hemispherical bosses, h is the distance between them. Since it diverges cylindrically rather than spherically, the boundary wave can become stronger than a direct wave propagating over a smooth plane surface. Previously, this “Biot boundary wave” has been experimentally verified in the fluid over a rigid plane surface constructed of hemispherical scattering elements [H. Medwin et al., J. Acoust. Soc. Am. 66, 1131–1134 (1979)]. The Biot boundary...