Accession Number : ADA310001
Title : Theoretical and Experimental Studies in Nonlinear Mechanical Systems Under Harmonic and Stochastic Excitation.
Descriptive Note : Final rept. Dec 93-Dec 96,
Corporate Author : ILLINOIS UNIV AT URBANA DEPT OF AERONAUTICAL AND ASTRONAUTICAL ENGINEERING
Personal Author(s) : Namachchivaya, Sri ; Doyle, Monica M.
PDF Url : ADA310001
Report Date : 01 MAY 1996
Pagination or Media Count : 142
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 : *MATHEMATICAL MODELS, *NONLINEAR SYSTEMS, *SYSTEMS ANALYSIS, ALGORITHMS, FOURIER TRANSFORMATION, STABILITY, VIBRATION, PARAMETRIC ANALYSIS, STOCHASTIC PROCESSES, EQUATIONS OF MOTION, TIME DEPENDENCE, EXCITATION, CHAOS, PROBABILITY DISTRIBUTION FUNCTIONS, EIGENVALUES, APPROXIMATION(MATHEMATICS), ASYMPTOTIC SERIES, PARTIAL DIFFERENTIAL EQUATIONS, PERTURBATIONS, SHAFTS(MACHINE ELEMENTS), NONLINEAR ANALYSIS, EXPONENTIAL FUNCTIONS, APPLIED MATHEMATICS, BIFURCATION(MATHEMATICS), AXIAL LOADS, HAMILTONIAN FUNCTIONS, LAGRANGIAN FUNCTIONS, PERIODIC VARIATIONS, CROSS FLOW, LYAPUNOV FUNCTIONS, FOUR DIMENSIONAL.
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE