Application of the isotropic road roughness assumption

Abstract Results of this paper are of interest in applications of the isotropic road roughness assumption [1] to problems of vehicle vibration. The cross-spectrum between heights of parallel profiles on a homogeneous and isotropic random surface is considered. Formulae involving single integrations are derived which express the cross-spectrum in terms of the spectrum of a single track. These show that the cross-spectrum at a particular wavenumber is independent of the single-track spectrum at lower magnitude wavenumbers, and provide some useful insight into the relationship between the spectra. Closed form solutions for the cross-spectra of the common single-track road roughness models are obtained. The limit behaviour of the cross-spectrum at small and large wavenumbers is also discussed.

[1]  K. Popp,et al.  Stochastic and Elastic Guideway Models , 1982 .

[2]  Peter C. Müller,et al.  Mathematical Methods in Vehicle Dynamics , 1982 .

[3]  K. M. Captain,et al.  Analytical Tire Models for Dynamic Vehicle Simulation , 1979 .

[4]  J. D. Robson,et al.  The application of isotropy in road surface modelling , 1978 .

[5]  S. Lang,et al.  An Introduction to Fourier Analysis and Generalised Functions , 1959 .

[6]  A. Yaglom,et al.  An Introduction to the Theory of Stationary Random Functions , 1963 .

[7]  J. D. Robson,et al.  Implications of isotropy in random surfaces , 1977 .

[8]  Ronald N. Bracewell,et al.  The Fourier Transform and Its Applications , 1966 .

[9]  J. D. Robson,et al.  Stochastic Road Inputs and Vehicle Response , 1976 .

[10]  D. N. Wormley,et al.  Dynamic Interactions Between Vehicles and Elevated, Flexible Randomly Irregular Guideways , 1977 .

[11]  N E Sussman.  STATISTICAL GROUND EXCITATION MODELS FOR HIGH SPEED VEHICLE DYNAMIC ANALYSIS , 1974 .

[12]  D. B. Macvean.  Response of vehicle accelerating over random profile , 1980 .

[13]  Robert F. Harrison,et al.  A systems approach to the characterization of rough ground , 1985 .

[14]  M. A. Dokainish,et al.  Nonlinear Random Response of Articulated Vehicles , 1979 .

[15]  David Cebon,et al.  Heavy vehicle vibration - a case study , 1985 .

[16]  G. Watson.  Bessel Functions. (Scientific Books: A Treatise on the Theory of Bessel Functions) , 1923 .

[17]  Robert F. Harrison,et al.  NONSTATIONARY RESPONSE OF VEHICLES ON ROUGH GROUND--A STATE SPACE APPROACH , 1981 .

[18]  J. D. Robson,et al.  The description of road surface roughness , 1973 .

[19]  David Cebon,et al.  THE ARTIFICIAL GENERATION OF ROAD SURFACE TOPOGRAPHY BY THE INVERSE FFT METHOD , 1984 .