A New Decomposition Method for Solving Stochastic Eigenvalue Problems in Computational Dynamics


Sponsor:                           U.S. National Science Foundation
Contract No.:                    CMMI-0653279
Duration:                            August 15, 2007 – July 31, 2011
Principal Investigator:    Professor Sharif Rahman
Graduate Students:         V. Yadav
Partner Organizations:   Rockwell Collins, Cedar Rapids, IA



The overall objective of this research project was to conduct fundamental research on computational methods for solving random eigenvalue problems in modeling and simulation of stochastic dynamic systems.  The proposed effort involved:  (1) development of a new decomposition for lower-dimensional approximations of general complex-valued eigensolutions of random eigenvalue problems (Task 1); (2) development of a novel polynomial dimensional decomposition method for probabilistic characteristics of eigensolutions (Task 2); and (3) error analyses of polynomial dimensional decomposition and polynomial chaos expansion and global sensitivity analysis (Task 3).  The new decomposition methods and computational tools developed in this project will aid in accurate and efficient probabilistic characterization of dynamic system responses, such as natural frequencies and modes shapes.  The statistics and rare-event probabilities (e.g., failure probability) predicted by these methods may potentially lead to new or improved designs in the presence of uncertainties due to insufficient information, limited understanding of underlying phenomena, and inherent randomness.  Therefore, the research results will be of significant benefit to several commercial and industrial applications, such as civil, automotive, and aerospace infrastructure.  Potential engineering applications include analysis and design of civil structures; noise-vibration-harshness, and crashworthiness of ground vehicle systems; and fatigue durability of aerospace structures.  For the microelectronics industry, applications in reliability of microelectronics and interconnects, reliability of micro-electro-mechanical systems for sensors and actuators are relevant.  In summary, any application discipline that can be simulated or analyzed using computer software/tools should benefit from this research.