ABSTRACT
Dynamic systems under random trains of impulses driven by a generalized Erlang renewal process are considered. The interarrival times of the underlying renewal process are sums of two independent, negative exponential distributed random variables, with different parameters. The renewal driven train of impulses is exactly recast, with the aid of an auxiliary variable, into a Poisson driven train. The auxiliary variable is a Poisson driven stochastic variable, hence a non-Markov problem for an original state vector is converted into a non-diffusive Markov problem for a state vector augmented by the additional variable. The generalized Itô’s differential rule, valid for Poisson driven non-diffusive Markov processes, is used to derive the equations for response moments. Mean value and variance of the response of a linear oscillator, obtained from the equations for moments, are compared with those evaluated from classical integral expressions in terms of the renewal process product densities. For a non-linear oscillator the equations for response moments and the equation governing the time evolution of the response characteristic function are derived.
