Mechanical and Civil Engineering Seminar

Propagation of uncertainties in complex engineering dynamical systems is receiving increasing attention.  When uncertainties are taken into account, the equations of motion of dynamical systems can be expressed by differential equations with stochastic coefficients. The computational cost for the solution of such systems mainly depends on the number of degrees of freedom and number of random variables. Among various numerical methods developed for such systems, response surface based methods (e. g., polynomial chaos) show significant promise because it is more accurate compared to the classical perturbation based methods and computationally more efficient compared to the Monte Carlo simulation based methods. However, these approaches are inherently 'numerical' in nature and may not always give the physical intuition generally available for a deterministic problem. In this talk, single and multiple degrees of freedom stochastic systems will be considered using a new physics based approach. The main motivation is to use natural frequencies and vibration mode shapes of the underlying deterministic dynamic system to represent the stochastic response characteristics. In this way, it would be possible to understand stochastic dynamical systems in the light of conventional modal properties of a deterministic system, which are already well understood.