J.D. Robson

THE DESCRIPTION OF ROAD SURFACE ROUGHNESS

It is shown that typical road surfaces may be considered as realizations of homogeneous and isotropic two-dimensional Gaussian random processes. Complete description of any such process is provided by a single autocorrelation function evaluated from any longitudinal track, and a single direct spectral density function therefore provides a road surface description which is sufficient for multi-track vehicle response analysis. A new road classification method is proposed which is based on this function.

The application of isotropy in road surface modelling

Abstract Road surface description forms the basis of vehicle response prediction, but in most cases precise description of a particular road is of less value than a description representative of a class of roads. In these circumstances an analytical road surface model has special advantages. In modelling a road surface—rather than a single road profile—the hypothesis of isotropy is shown to provide a useful basis, and the paper shows how a particular profile spectral density, together with the assumption of isotropy, can be used to define an effective surface model. Coherence functions derived from the proposed model are validated by comparison with coherencies based on measurement.

Implications of isotropy in random surfaces

Abstract Properties of isotropic random surfaces are considered, including relationships between their two-dimensional spectral densities and one-dimensional spectral densities of particular profiles. The former must be non-negative, and their volume integrals bounded; this is shown to imply additional restrictions on the admissible forms of one-dimensional profile spectra. A new spectral description f(n) is expressed in terms of the profile spectral density S(n). Restrictions on f(n) provide essential admissibility criteria for proposed forms of S(n). Use of these criteria is demonstrated and it is shown that some simple idealized profile descriptions are inadmissible. As an example of the practical application of the criteria the problem of describing effectively isotropic road surfaces by means of their profile spectra is considered. Approximate profile descriptions based on the law S(n) ∝ n−w are examined, and found to be admissible for realistic values of w. It is inferred that most good approximations to actual road descriptions will be admissible. The approach is general, however, and the criteria provide a means of testing any profile description whose admissibility is doubtful.

Response to profile-imposed excitation with randomly varying traversal velocity

Abstract Stationary response of a travelling system to profile-imposed excitation is investigated. The system is treated as linear and both the profile and traversal velocity of the system are considered to be stationary and Gaussian random functions of horizontal distance. The problem is formulated by means of a differential equation with random coefficients, and detailed analysis of vertical vibrations of the system travelling with small random velocity fluctuations is performed. An analytical expression for response spectral density is obtained in a relatively simple form for a general case, and this is used in calculation of the effect of randomly-varying velocity on a systems response in particular cases relevant to vehicle dynamics.

Response of an accelerating vehicle to random road undulation

Abstract The response of a simplified vehicle-model, accelerating across a randomly undulating surface, is computed for parameters typical of those of actual vehicles. It is shown that for practically-occurring values of forward acceleration, mean-square response differs little from that with zero acceleration. It is concluded that simple zero-acceleration analysis has a wider applicability than is generally realized.

Deductions from the spectra of vehicle response due to road profile excitation

Abstract Under certain circumstances response of a vehicle may be considered as a function of a single displacement imposed by the roadway: spectra of road profile and of vehicle response at various speeds are then simply related. It is shown here that in such a case the establishment of response spectra at two known vehicle velocities makes possible the prediction of response spectra at other speeds, and also the deduction of the form of the road profile spectrum.

A simplified quasi-Gaussian random process model based on non-linearity

Abstract The non-Gaussian response of a simple polynomial non-linear element to Gaussian excitation is investigated, and correlation functions and spectral densities up to the fourth order are established in terms of the second order correlation function and spectral density of the excitation. Suitable choice of excitation and non-linearity parameters then permits the response to be used, either in analysis as a well-described near-Gaussian random process, or as a good approximate model of any given near-Gaussian random process.

Interdependence of the spectral densities of multiple responses

Abstract The paper is concerned with the spectral densities (direct and cross) of the multiple response records of a linear system, such as a structure, subjected to multiple random excitation. The various spectral densities of a multivariate random process are in general independent, but the response characteristics of a linear structure impose certain relationships on the response spectral densities, and these are elucidated here. The relationships depend essentially on the numbers of excitation and response components. Special relationships are shown to apply in the common enough situation where the responses of a vibratory system may be taken to derive from the contributions of a finite number of normal modes.

The simulation of random vibration response by discrete frequency testing

Abstract The paper presents the theoretical basis for an analogue method whereby the random response of a structure may be inferred from measurements of its harmonic response when the excitations are replaced by discrete frequency forces or imposed motions. In the elementary case of a single random input, the method takes a particularly simple form. In the general multi-input case it is shown that the method may be used directly only when all the inputs are fully coherent. Otherwise a superposition technique involving multiple applications of sets of harmonic excitations is required. It is considered that the method may be of practical use as a tool in vibration testing and that, in addition, the underlying analysis contains results of considerable interest on the structure of multi-dimensional stationary random processes.