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The application of Green’s multi-dimensional function to investigate the stochastic vibrations of dynamical systems. (English) Zbl 0532.73081
Summary: In the paper is presented the application of Green’s multi-dimensional function to determine the probabilistic characteristics of the solutions of stochastic linear equations with time-variable coefficients, with random initial conditions and random excitations. The method is applied to calculate the variances of solutions for the vibrations of vehicle model (or suspension) accelerated over a random profile.

MSC:
74H50 Random vibrations in dynamical problems in solid mechanics
35R60 PDEs with randomness, stochastic partial differential equations
70J99 Linear vibration theory
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[1] Adomian, G.: Random operator equations in mathematical physics. J. Math. Phys. 11 (1970) 1069–1084, 12 (1971) 1944–1946, 1948–1955 · Zbl 0189.55401
[2] Beyn, W.-J.: Die Konvergenz der diskreten Greenschen Funktionen beim gewöhnlichen Differenzenverfahren. Z. Angew. Math. Mech. 59 (1979) T 47-T 49 · Zbl 0417.65043
[3] Bharucha-Reid, A. T.: Random integral equations. New York, London: Academic Press 1972 · Zbl 0327.60040
[4] Kreuzer, E.; Rill, G.: Vergleichende Untersuchung von Fahrzeugschwingungen an räumlichen Ersatzmodellen. Ing.-Arch. 52 (1982) 205–219 · Zbl 0496.73062
[5] Langer, J.: The parasitical damping in computer solutions of equations of movement. Arch. Land Eng. 25 (1979) 359–368 (in Polish)
[6] Macvean, D. B.: Response of vehicle accelerating over random profile. Ing.-Arch. 49 (1980) 375–380 · Zbl 0445.73053
[7] Masri, S. F.: Response of a multidegree-of-freedom system to nonstationary random excitation. J. Appl. Mech. 45 (1978) 649–656
[8] Matveev, N. M.: The methods of integration the ordinary differential equations. Moscow: Higher School 1963 (in Russian) · Zbl 0139.30203
[9] Müller, P. C.; Popp, K.: Kovarianzanalyse von linearen Zufallsschwingungen mit zeitlich verschobenen Erregerprozessen. Z. Angew. Math. Mech. 59 (1979) T 144-T 146 · Zbl 0425.70027
[10] Müller, P. C.; Popp, K.; Schiehlen, W. O.: Berechnungsverfahren für stochastische Fahrzeugeschwingungen. Ing.-Arch. 49 (1980) 235–254 · Zbl 0429.70023
[11] Müller, P. C.; Schiehlen, W. O.: Forced linear vibrations. CISM Vol. 172. Berlin, Heidelberg, New York: Springer 1973 · Zbl 0408.70018
[12] Newmark, N.: A method of computation for structural dynamics. J. Eng. Mech. Div., ASCE Vol. EM 3 (1959)
[13] Pękała, W.: RANGREENV – The system of problems for calculation the probabilistic characteristics of linear stochastic systems of variable parameters. IX. Sympozium ”The vibrations in physical systems”, Poznań-Błazejewko 1980 (in Polish)
[14] Pękała, W.; Szopa, J.: The numerical investigations of stochastic vibrations of multi-degree-of-freedom vehicle models. Proceedings of VI. Conference on Computer Methods in Mechanics of Structures. Białystok, 1983 (in Polish)
[15] Pękała, W.; Szopa, J.: The vibrations of double pendulum with length and mass changing under stochastic excitation. Zeszyty Nauk. Polit. Sl. Mathematics-Physics (in Polish) [in print]
[16] Pokojski, J.: Polyoptimization of linear vibration system of two-degree-of-freedom under stochastic excitation. Proceedings of III. Conference on Methods and Means of Automatic Design, Warsaw 19–21 November 1981 189–196 (in Polish)
[17] Rill, G.: Discussion related to the paper of D. B. Macvean: Response of vehicle accelerating over random profile in Ing.-Arch. 49 (1980) 375–380; Ing.-Arch. 52 (1982) 91–94
[18] Rill, G.: Grenzen der Kovarianzanalyse bei weißem Geschwindigkeitsrauschen. Z. Angew. Math. Mech. 62 (1982) T 70-T 72
[19] Sakata, M.; Kimura, K.: The use of moment equations for calculating the mean square response of a linear system to nonstationary random excitation. J. Sound Vib. 67 (1979) 383–392 · Zbl 0451.93067
[20] Skalmierski, B.; Tylikowski, A.: Stochastic processes in dynamics, Warsaw: PWN 1972 (in Polish) · Zbl 0504.60061
[21] Sobczyk, K.: Methods of statistical dynamics, Warsaw: PWN 1973 (in Polish) · Zbl 1194.74155
[22] Sobczyk, K.; Macvean, D. B.: Non-stationary random vibrations of road vehicle with variable velocity. Symposium on Stochastic Problems in Dynamics, University of Southampton, U.K., July 19th to 23 rd, 1976, 21.1–21.6
[23] Sobczyk, K.; Macvean, D. B.; Robson, J. D.: Response to profile – imposed excitation with randomly varying traversal velocity. J. Sound Vib. 52 (1977) 37–49
[24] Solodov, A. V.; Petrov, F. S.: Linear automatic systems with variable parameters. Moskwa: Izd. Nauka 1971 (in Russian)
[25] Szopa, J.: Application of Volterra stochastic integral equations of the II-nd kind to the analysis of dynamic systems of variable inertia. J. Techn. Phys. 17 (1976) 423–433 · Zbl 0363.60043
[26] Szopa, J.: Response of a multidegree-of-freedom system of variable coefficients to random excitation. Z. Angew. Math. Mech. 62 (1982) 321–328 · Zbl 0496.73078
[27] Szopa, J.; Wojtylak, M.: Numerical problems of determining probabilistic characteristics of solutions in stochastic nonlinear dynamic systems of variable inertia. Mech. Computer 4 (1981) 405–417 (in Polish) · Zbl 0621.65148
[28] Szopa, J.; Wojtylak, M.: On determination of probabilistic characteristics of solutions of double pendulum with varying length subject to random forcing. Theor. Appl. Mech. 17 (1979) 237–245 (in Polish) · Zbl 0415.70036
[29] Tsokos, Ch. P.: On a stochastic integral equation of the Volterra type. Math. Systems Theory 3 (1969) 222–231 · Zbl 0186.49902
[30] Tsokos, Ch. P.; Padgett, W. J.: Random integral equations with applications to stochastic systems. Berlin, Heidelberg, New York: Springer 1971. · Zbl 0225.60029
[31] Wicher, J.: The phenomenon of dynamic damping in a system being under random excitation. IFTR Raports 32 (1974) Warsaw (in Polish)
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