Abstract: The developments of jet and rocket propulsion systems have introduced problems in mechanical and structural vibrations since the 1940's. The intensive pressure fields produced by these systems can only be analyzed statistically because of their irregular time histories. In parallel, many modern structural systems such as tall buildings, structures that house nuclear reactors, naval undersea and surface systems must be designed to withstand various natural and man-made intensive loadings that have to be treated as nonstationary random processes. The intensive random excitations include earthquake loadings, pressure waves of explosions, continuous atmospheric turbulences, and extreme ocean waves. Owing to the high intensities of these loadings, linear analytical techniques can not be employed in this class of mechanical and structural vibration problems. Thus, over the years much efforts have been exerted by many researchers on providing analytical techniques in dealing with the aforementioned class of problems.
It is interesting to point out that to-date no exact solution seems to be available to systems with nonlinearities involving velocity as well as displacement and under nonstationary random excitation. Of course, there are various approximate techniques presented in the literature. The main objective of this paper is, however, to present a method for determining exact responses of nonlinear systems under nonstationary random excitations. For demonstration of the simplicity as well as correctness of the method, the van der Pol-Duffing oscillator under a nonstationary random excitation that is treated as a time modulated zero mean Gaussian white noise process is included in this presentation. Selected computed results are provided and compared with those generated by the Monte Carlo simulation algorithm. It is concluded that for the first time a simple method is available to provide exact solutions of general nonlinear systems with nonlinearities involving velocity as well as displacement and under nonstationary random excitations.

Brief Biography of the Speaker:
Dr. To obtained his doctoral degree in sound and vibration studies from the University of Southampton in April 1980. He is currently a professor in the Department of Mechanical Engineering at the University of Nebraska (UNL). Prior to joining UNL he was a professor (1994-96) and an associate professor (1986-94) at the University of Western Ontario. He was an associate professor (1985-86) and an assistant professor (1982-85) at the University of Calgary. Between 1982 and 1992 he was a University Research Fellow of the Natural Sciences and Engineering Research Council, Canada. He was a Research Fellow at the Institute of Sound and Vibration Research (ISVR), University of Southampton during his doctoral degree studies. After his doctoral degree studies he worked briefly in the Wolfson Unit of the ISVR on machinery noise and vibration problems of drop hammers, and vibration diagnostics in helicopters of the Royal Navy before moving to the University of Calgary. His main academic interests are in nonlinear stochastic structural dynamics, nonlinear finite element analysis with particular reference to laminated composite plates and shells, nonlinear dynamics and control, and mechanics of carbon nano-tubes.