A State Space Approach to the Analysis of Nonstationary, Nonlinear Random Vibration with Particular Application to the Problem of Vehicles on Rough Ground,
SOUTHAMPTON UNIV (ENGLAND) INST OF SOUND AND VIBRATION RESEARCH
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The dynamic response of vehicles to uneveness in the underlying surface on which they are travelling is of obvious engineering interest both for reasons of ensuring structural integrity and to ensure safe handling and a comfortable ride. The problem has therefore received a great deal of attention in the literature over a number of years. The vehicle dynamics are modelled by ordinary differential equations in the time domain whilst the excitation process is modelled by a differential equation, cast in the spatial domain and driven by a spatially white process. The key novel feature is the linking of the two domains via the vehicles variable velocity enabling the dynamic equations to be augmented by the excitation ones having time variable coefficients. The link is made by drawing on some results from the theory of generalised functions. For linear systems, the analytical techniques referred to above become immediately applicable, in particular, differential equations governing the first two statistical moments may be derived for both single and multiple inputs. Furthermore, this augmented system, after some further analysis becomes amenable to evolutionary spectral representation i.e., decomposition of power in a signal over frequency at each time instant. Hitherto, the particular class of non-stationarity associated with the vehicle problem has not responded to this approach.