Systems of random differential equations and model reduction
Ralf Wunderlich
Habilitationsschrift, TU Chemnitz, 1999
Abstract :
This monograph is devoted to systems of ordinary differential equations with
stationary random excitation terms. For stable linear systems as well as
systems with polynomial nonlinearities the existence of stationary solutions
and the computation of their distribution characteristics as second-order
moment
functions are considered. Such questions arise in the investigation of the
long-time behaviour of the system response to permanently acting excitations.
The results can be directly applied to discrete vibration systems with damping
and an external random excitation.
The presented results are essentially based on the work of J. vom Scheidt
and his research group on weakly correlated random functions and their
application to random equations of mathematical physics.
They can be considered as extensions and generalizations of the work on random
vibration systems. In
particular, such topics are chosen where the author himself contributed to the
development: modeling of random excitations, higher-order expansions of
correlation functions, systems with polynomial nonlinearities and model
reduction. Several results have not been presented before.
The monograph is organized into 12 sections which form four chapters: