Accession Number : ADA309674
Title : Theoretical and Experimental Studies in Nonlinear Mechanical Systems.
Descriptive Note : Final rept.,
Corporate Author : ILLINOIS UNIV AT URBANA DEPT OF ELECTRICAL ENGINEERING
Personal Author(s) : Namachchivaya, N. S. ; Doyle, Monica M.
PDF Url : ADA309674
Report Date : 30 APR 1996
Pagination or Media Count : 141
Abstract : The stability and bifurcation behavior of mechanical systems parametrically excited by small periodic or stochastic perturbations is studied. The almost-sure stability is defined by the sign of the maximal Lyapunov exponent the exponential growth rate of solutions to a linear stochastic system. A perturbative approach is employed to construct an asymptotic expansion for the maximal Lyapunov exponent of a four dimensional gyroscopic dynamical system driven by a small intensity real noise. The perturbative technique developed is then applied to study the lateral vibration instability in rotating shafts subject to stochastic axial loads and stationary shafts in cross flow with randomly varying flow velocity. The local and global bifurcation behavior of nonlinear deterministic gyroscopic and conservative systems subject to periodic parametric excitation is also examined. Throughout this work it is assumed that the dissipation. imperfections and amplitudes of parametric excitations are small. In this way it is possible to treat these problems as weakly Hamiltonian systems. Most of the analysis presented here is based on the recent work of perturbed Hamiltonian systems. (P.T.O.)
Descriptors : *VIBRATION, *SHAFTS(MACHINE ELEMENTS), LINEAR SYSTEMS, EXPERIMENTAL DATA, STOCHASTIC PROCESSES, EXCITATION, THEORY, INTENSITY, RATES, NONLINEAR SYSTEMS, FLOW RATE, STATIONARY, ASYMPTOTIC SERIES, PERTURBATIONS, NOISE, EXPONENTIAL FUNCTIONS, ROTATION, BIFURCATION(MATHEMATICS), INSTABILITY, AXIAL LOADS, MECHANICAL COMPONENTS, ANGULAR MOTION, HAMILTONIAN FUNCTIONS, CROSS FLOW, LYAPUNOV FUNCTIONS, PARAMETRIC DEVICES.
Subject Categories : Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE