Papers »

Quadratic partial eigenvalue assignment for large-scale stochastic dynamic systems

Structural systems such as high-rise buildings, bridges, wind-turbines, aircrafts, etc., are subjected to various types of dynamic loads during their service periods. They undergo vibration with high amplitude (resonance phenomenon) when some of their damped natural frequencies are close to the dominant frequencies of the dynamic loads. If the design process fails to properly account for such dynamic effects, the structural systems may collapse (e.g., failure of the Tacoma Narrows bridge, Washington in 1940) or lose functionality (e.g., wobbling of the Millennium bridge, London in 2000). One of the most popular techniques to prevent such catastrophic consequences is active vibration control (AVC) that essentially shift the damped natural frequencies of the structural systems away from the dominant range of the loading spectrum. Significant uncertainties are typically present in structural systems and may arise due to fluctuation in experimental data, scale effect, choice of loading pattern, and also due to variations in structural configurations, topology, imperfect boundary conditions, defective interfaces/joints, etc. Failure to account for the effects of these uncertainties might have adverse effects leading to unstable closed-loop system (active vibration controlled systems) that will essentially defeat the very purpose of designing controlled systems to reduce the vibration level. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty is presented here to rigorously account for these variations resulting in economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is proposed for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the structural system. The proposed scheme is suitable not only for simple and connected failure domain but also for failure domain which is disjointed and complex in shape. Numerical examples are presented to illustrate the proposed methodology.

Author(s):

Kundan Goswami    
University at Buffalo, NY, USA
United States

Sonjoy Das    
University at Buffalo, NY, USA
United States

Biswa N. Datta    
Northern Illinois University, IL, USA
United States