H.-J. Starkloff

Random transverse vibrations of a one-sided fixed beam and model reduction

This paper is devoted to the computation of second-order moment functions of the solution of large-scale systems of linear random ODEs. Such systems result from the semi-discretization of PDEs describing continuous vibration systems with random excitation. Model reduction techniques are applied to find approximations of the desired moment functions of the large-scale system by computing them for a suitable low-dimensional system. Numerical results concerning transverse vibrations of a one-sided fixed beam subjected to a random excitation modeled by a random field are presented. Special attention is paid to e-correlated excitations characterized by a short correlation length.

Remarks on randomly excited oscillators

In the paper linear oscillators with stochastic excitation are considered. Explicit formulae for second-order characteristics of random solution processes for input processes which are wide-sense stationary or possess wide-sense stationary increments are given. Further, asymptotic expansions in the case of weakly correlated excitation processes are derived.

Asymptotic Expansions of Integral Functionals of Weakly Correlated Random Processes

In the paper asymptotic expansions for second-order moments of integral functionals of a family of random processes are considered. The random processes are assumed to be wide-sense stationary and c-correlated, i.e. the values are not correlated excluding an c-neighbourhood of each point. The asymptotic expansions are derived for e 0. Using a special weak assumption there are found easier expansions as in the case of general weakly correlated random processes. Expansions are given for integral functionals of real-valued as well as of complex vector-valued processes.

Stationary solutions of random differential equations with polynomial nonlinearities

The paper deals with systems of ODEs containing polynomial nonlinearities and random inhomogeneous terms. Applying perturbation method pathwise solutions are found in form of power series with respect to a parameter η controlling the nonlinearities. Under the assumption that for η=0 the system is stable and that the inhomogeneous terms are bounded the radius of convergence of the perturbation series is estimated. Further, it is proved that the perturbation series form stationary solutions if the inhomogeneous terms are stationary.