Dynamical response of damped structural systems driven by jump processes

The consideration of uncertainties in numerical models to obtain probabilistic descriptions of vibration response is becoming more desirable for practical problems. In this paper a new method is proposed to obtain statistical properties of the response of damped linear oscillators subjected to Lévy processes. Lévy processes can be used to model physical phenomena that feature jumps. These types of problems are relevant to many civil, mechanical and aerospace engineering problems such as aircrafts subjected to sudden turbulence, wind turbines subjected to hurricanes and automobiles running over pot-holes. The mathematical theory behind Lévy processes is briefly discussed with various examples. These processes are then used to formulate the damped oscillator equation driven by Lévy noise. A relevant existence and uniqueness result for the solution of stochastic differential equations driven by Lévy noise is presented and an explicit form of the solution is found. An Euler scheme is proposed to calculate sample paths of the solution. A numerical example involving an offshore 3 MW twin-blade wind turbine subjected to wind gust is considered to illustrate the application of the proposed method.