Nonstationary time-frequency characteristics of vehicle suspension systems based on evolutionary power spectral density

Improving the ride comfort for vehicles that travel at varying speeds is a nonstationary problem and has been an increasingly important topic for suspension system research. Accurate identification of frequencies associated with the resonant responses is needed for effective design of active suspension control strategies. However, traditional time-frequency (TF) methods have resolution limitations in either the time domain or the frequency domain. This paper proposes a new methodology to employ the evolutionary power spectral density (EPSD) to describe the responses of vehicles in the time-frequency domain. The key to calculate the responses in nonstationary cases is to derive the nonuniform modulation function which is obtained by the pseudo excitation method. To illustrate the applicability of the proposed method, an example of a seven-degree-of-freedom vehicle model is investigated in which the nonstationary excitations acting on the wheels are computed by the nonuniform modulation function and a precise integration method. Results show that resolutions obtained by the EPSD are more precise than the traditional TF methods with less than 0.2 Hz of bandwidth in both the lower frequency range at the first natural frequency of 1 Hz and in the higher frequency around 10 Hz. Moreover, the changing of the resonant frequency with varying speeds provides the insights, from the perspective of human body’s sensitivity to frequencies of vibration, to improve the ride comfort for vehicles under nonstationary driving conditions.