Ein kinetisches Stabilitätsproblem bei stochastischer Erregung

Summary

An example is given for the kinetic instability of an elastic system under random time-dependent forces. A circular ring, loaded by forces of constant direction, is examined by means of the theory of stability of an elastic motion which was given byE. Mettler in 1947. If certain relations exist between the critical frequencies of the ring, the problem can be reduced to the solution of a differential equation with random coefficients already discussed byF. Weidenhammer. Stability occurs if damping is of order$\varepsilon ^2 (\varepsilon<< 1)$, while in deterministic cases damping must be of order ε¹, where ε denotes the magnitude of the excitation.