Vibration of linear structures due to jump‐discontinuous, non‐interrupted, stochastic processes

Abstract

SUMMARYThe solution of the problem of vibration of linearly elastic structures, caused by stochastic excitation of non-interrupted, jump-discontinuous character, is considered in the paper. Two types of excitation are examined. They form an enhancement of the continuous model which is most often used. The solution in the form of expected values, correlation functions and spectral densities of the deflection of the structure is formulated. Examples illustrating the solution are presented.

Stochastic stability of quasi-integrable and resonant Hamiltonian systems under parametric excitations of combined Gaussian and Poisson white noises

“…Suppose that ðn À1 þ αÞ-dimensional vector diffusion process β 0 is ergodic over the interval 0 r α r r 1; r ¼ 1; 2; …; n À 1; 0 r ψ v r 2π; v ¼ 1; 2; …; α and the stationary probability density of this vector process can be obtained from the reduced GFPK equation associated with the first n À 1 equations of Eq. (26) and the second equation of (18). The time averaging in Eq.…”

“…However, Mironowicz and Sniady [18] pointed out that the stochastic excitations are often combinations of continuous random process and random pulses. The combination of Gaussian and Poisson white noise excitations is one special case of such excitations.…”