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Non-linear vibration in a driveline which incorporates a Hooke's joint is presented in this paper. In particular, torsional vibration due to fluctuating angular velocity ratio across the joint is examined. Linearized equations are used for the prediction of critical speed ranges where parametric instabilities characterized by exponential build up of torsional response amplitudes occur. Predicted instabilities indicate the range of driveshaft speeds to be avoided during the design of a driveline which employs a Hooke's joint. Numerical simulations and bifurcation analysis performed on the full non-linear equations further demonstrate the existence of parametric, quasi-periodic and chaotic motion. Onset of chaotic motion was shown to be characterized by a quasi-periodic route.

In this paper, the exact partial differential equations governing the system modes of a general two-link flexible manipulator are derived by matching the boundary equations at the elbow. The resulting partial differential equation formulation is solved numerically to yield the exact eigenfrequencies corresponding to arbitrary elbow angles. The eigenfrequencies are shown to be a strong function of manipulator configuration, varying by up to 30% as the manipulator sweeps across its range of motion; this is subsequently shown to accurately predict the eigenfrequencies of an experimental two-link manipulator.

The tension in power transmitting chains is subject to periodic fluctuation. This is brought about by factors such as polygonal action, eccentricity of sprockets, etc. A study of the dynamic stability of such a chain is presented. Instabilities due to polygonal action are investigated. The analysis is carried out by treating the chain as a travelling uniform heavy string.

Flexural instabilities in moving bands under random tension fluctuation are investigated. The discretized equations of flexural motion represent a gyroscopic system with randomly varying stiffness. Explicit stability conditions based on the mean square amplitudes are established by employing a stochastic averaging procedure. The effect of mean band speed on the band stability is discussed. Copyright 1993, 1999 Academic Press

This paper describes a theoretical and experimental development of a laminated spatially distributed piezoelectric torsional vibration actuator for a clamped-free cantilever beam. The strain energy transferred from a piezoelectric film actuator to a substructure is derived as a function of actuator strain only and is then used to calculate the induced strain in a substructure loaded in uniaxial extension/compression, bending and torsion. This transferred energy can be maximized by optimizing the actuator/structure dimensions and material properties. An experimental cantilever beam was constructed to examine the first mode decay in torsion under the influence of the actuators. The theoretical and experimental decay histories of the first torsion mode decay indicate a reduction in decay time for the controlled beam of greater than 10 times that of the uncontrolled beam.

The torsional vibration of moving bands subject to harmonic tension fluctuation is investigated. A thin rectangular strip translating longitudinally with a constant speed and simply supported at its end is considered. The linearized equation of motion, when suitably discretized, represents a linear gyroscopic system with periodically varying stiffness. The stability of the trivial solution of this system of equations, for tension fluctuations of small amplitude, is examined using the method of averaging. Analytic conditions for stability of torsional motion are obtained explicitly and shown graphically in the frequency vs excitation parameter space.

Dynamic instabilities in a torsional system which incorporates a Hooke's joint are investigated by means of Lyapunov exponents. Linearized analytical models for the torsional system are established for the purpose of stability analysis. The resulting two-degree-of-freedom system is parametrically excited due to an inherent non-linear velocity ratio across the Hooke's joint. Instabilities which correspond to sub-harmonic as well as combination resonances have been identified by studying the sign of the top Lyapunov exponent. Instability conditions have been presented graphically in the excitation frequency-excitation amplitude-top Lyapunov exponent space. Predicted instability conditions are adequate for the design of two-degree-of-freedom Hooke's joint driven systems.