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The application of Green’s multidimensional function to investigate the stochastic vibrations of dynamical systems. (English) Zbl 0576.73084
Summary: The behaviour of stochastic vehicle vibrations published by W. Pȩkala and J. Szopa, (*) ibid. 54, 91-97 (1984; Zbl 0532.73081)], gives reason to doubt the correctness of the results. The characteristics of the variances shown in Figs. 2 to 7 of (*) are completely different from what is known from the literature [e.g. in K. Sobczyk and D. B. Macvean, Stoch. Probl. in Dyn., Symp. Univ. Southampton 1976, 412-434 (1977; Zbl 0383.70028)].
In this discussion the variances of the vehicle response will be calculated following two routes independent from each other: 1) similar to (*), Green’s multidimensional function method will be applied, however, the method is developped in view of state space analysis, and 2) a covariance analysis is performed. Here, the methods are not derived in full detail. For a detailed presentation see the references given.
MSC:
74H50 Random vibrations in dynamical problems in solid mechanics
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[1] Pcekala, W.; Szopa, J.: The application of Green’s multidimensional function to investigate the stochastic vibrations of dynamical systems. Ing.-Arch. 54 (1984) 91-97 · Zbl 0532.73081
[2] Hammond, J. K.; Harrison, R. F.: Nonstationary response of vehicles on rough ground ? a state space approach. J. Dyn. Syst., Meas. Control 103 (1981) 245-250
[3] Sobczyk, K.; Macvean, D. B.: Nonstationary random vibrations of systems travelling with variable velocity. In: Clarkson, B. L. (ed.): Stochastic problems in dynamics. London: Pitman 1977 · Zbl 0383.70028
[4] Müller, P. C.; Schiehlen, W. O.: Lineare Schwingungen. Wiesbaden: Akad. Verlagsgesellschaft 1976 · Zbl 0421.70001
[5] Masri, S. F.: Response of a multidegree-of-freedom system to nonstationary random excitation. J. Appl. Mech. 45 (1978) 649-656
[6] Rill, G.: Instationäre Fahrzeugschwingungen bei stochastischer Erregung. Diss. Univ. Stuttgart 1983
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