Engineering Transactions, 17, 2, pp. 269-280, 1969

Drgania Układu Liniowego Wywołane Procesem Przypadkowym o Jednostajnie Zmiennej Częstości

A. Tylikowski


The present work is devoted to change vibrations sustained by a force being a stochastic process. Forcing have been assumed in the form of a sum of harmonics with random amplitudes and phases. For the analysis a linear system has been taken, with one degree of freedom and viscotic damping. From the assumption of the uniform variability of frequency it results that the correlational function of a process so defined is of a nonstationary character. Therefore, the displacement is also a nonstationary stochastic process. The problem, as solved within the framework of the theory, consists of the determination of the variance of displacement as a function of time. The solution is expressed by functions of probability with a complex argument or related to it. The numerical calculations conducted enable to discover a number of interesting properties of the time courses of variance. The most marked feature of those curves is the occurrence of a sharp peak for time in the oscillating systems, in which equalization took place of the frequency forcing the process with the proper frequency. Analogously as in the deterministic case an increase of damping brings about an abrupt lowering of the level of variance.
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


F. M. LEWIS, Vibration during acceleration trough a critical speed, Trans. ASME, 54 (1932), 253-261.

А. П. Филипов, Вынужденные колебания линейной системы при прохождении через резонанс изменяющейся частотой, Изв. АН СССР, ОТН, № 12, 1958.

А. П, Филипов, Е. Г, Голосков, К вопросу о переходе через резонанс упругих систем, Труды Харьковского полит, инст., серия инж.-физ., 14 (1958).

W. J. STRONGE, Vibration due to an excitation with uniformly varying frequency, J. Appl. Mech, 2, 33, 462-463.

G. A. PIERSOL, Power spectra measurement for spacecraft vibration data, Spacecraft and Rockets, 12, 4, 1613-1617.

6. H. А. Николаенко* Вероятностные методы динамического расчета машиностроительных конструкций, Изд. Машиностроение, Москва 1967, 318-320.

I. I. GICHMAN, A. W. SKOROCHOD, Wstęp do teorii procesów stochastycznych, PWN, Warszawa 1968, 194-202.

[in Russian]

[in Russian]

[in Russian]

C. W. MARTZ, Tables of Complex Fresnel Integrals, NASA Report SP-3010, D. C. Washington, 1964.