Under this Presidential Young Investigator Award (PYI), the following studies will be pursued: (1) Dynamic response of linear and nonlinear secondary systems, (2) Reliability of systems with uncertain parameters, (3) Identification and optimization of complex systems, and (4) Vibration reduction of dynamic systems These studies are aiming at improving the understanding of the dynamic behavior of complex structures with subsystem components and the seismic design of such structures. This project is initiated in FY 88 and will run for five years.