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Some dynamic load (excitation) processes have a nature of a train of impacts, shocks, or short duration loads (general pulses) occurring at random time instants.
Some dynamic load (excitation) processes have a nature of a train of impacts, shocks, or short duration loads (general pulses) occurring at random time instants. Sample functions of these excitations are discontinuous functions of time. These impulse process stochastic excitations are adequately characterized in terms of stochastic point processes, such as e.g. Poisson or renewal processes. Different impulse and pulse process stochastic excitations are characterized and the time-domain analysis for linear dynamic systems is briefly outlined.
For non-linear dynamic systems under an impulse process stochastic excitation (random train of impulses) the stochastic counterpart of the equations of motion is introduced in form of stochastic differential equations. Two classes of problems are discussed: Poisson impulse process excitations and more general renewal impulse process excitations. In the latter case the classical stochastic methods are not directly applicable because the original problem is non-Markov. It is demonstrated how, with the aid of suitable augmentation of the state space, the original problem can be converted into a Markov one. The following tools for the analysis of the response process are discussed: ordinary differential equations governing its statistical moments and partial integro-differential equations governing its probability density.
- Speaker
- Professor Radoslaw Iwankiewicz, Hamburg University of Technology, Germany
- Venue
- Fraser Noble Seminar Room