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The paper describes a theoretical study on the speed of torsional elastic waves propagating in a circular cylinder whose outer radius varies periodically as a harmonic function of the axial coordinate. An approximate solution for the phase speed was obtained by using the perturbation technique for sinusoidal modulation of a small amplitude. This shows that the wave speed in the cylinder with a corrugated outer surface is less than that in a smooth cylinder by the square of the amplitude of the surface perturbation. This theoretical prediction reasonably agrees with an experimental observation reported earlier. It is also shown that the wave speed reduction due to the surface corrugation becomes larger for a thinner cylinder and for a bigger density of corrugation.

Harmonic and transient torsional responses of a laminated circular disc (or a laminated circular cylinder), caused by torques applied on both ends of the disc, is investigated with use of a continuous analysis. By the analysis, the difficulty brought about by multitudinous reflections and transmissions, taking place at the interfaces of the laminated medium, can be bypassed. The continuous analysis is based on the recognition that stresses at periodic locations in a periodic structure must vary smoothly; therefore these discrete values as a whole approximately form a continuous function, which can be treated analytically. Via the analysis, it is concluded that the real, heterogeneous laminated disc can be modelled into a homogeneous, effective one. The corresponding effective solution provides accurate or exact values of displacements and stresses at the periodic locations of the laminated disc. The density of the effective disc is not a geometric-material constant; it depends on, among others, the frequency and other vibration parameters in the problem. Numerical results are given to validate the analysis.

This paper proposes a hybrid damping design to control torsional vibration of a shaft with a circular cross section through use of actively constrained layer (ACL) damping treatments proposed by Baz (1993) and Shen (1993, 1994a). The ACL damping treatment consists of a piezoelectric constraining layer and a viscoelastic shear layer wrapping around the shaft in the form of a helix. In addition, the angular displacement of the shaft is fed back to regulate the helical motion of the piezoelectric constraining layer. The equation of motion of this design is derived, and its stability and controllability are discussed. Finally, numerical examples show that this ACL design can reduce torsional vibration of a shaft. A sensitivity analysis shows that ACL is most effective in suppressing those modes with significant torsional vibration response. Stability, in general, is not a critical factor in designing ACL systems, because the piezoelectric strain of the constraining layer at the threshold of instability is too large to occur.

Dynamic stability analysis of a driveline which incorporates a Hooke's joint is presented in this paper. In particular, torsional instabilities due to fluctuating angular velocity ratio across the joint are examined. The method of averaging is used to establish the critical speed ranges by considering the linearized equations which govern the torsional motion of the system. Within these ranges, parametric instability characterized by exponential build up of response amplitudes of the torsional modes occur. Closed form conditions for onset of sub-harmonic as well as sum-type combination resonance have been established. The significance of the sum-type combination resonance in a typical diesel hydraulic locomotive driveline has been demonstrated. Difference-type combination resonance has been shown to be absent. The instability conditions indicate the range of driveshaft speeds to be avoided during the design of a driveline which employs a Hooke's joint.

Synchronous motors produce damaging oscillating torques during startup. If the system is not properly analyzed and designed, the torsional excitation can be very destructive. This paper presents a systematic approach to the dynamic analysis of synchronous motor driven rotating machinery. The p-version of the finite element method is used in the formulation of the equations of motion which provides a great deal of simplicity in the modeling process. The convergence is achieved by increasing the polynomial order of the basis functions of the geometric elements. The system damping matrix can be constructed from the element level or can be calculated by specifying the critical damping factors for a given number of modes of interest. A modified Newmark integration method is employed in the nonlinear transient response calculation. The nonlinearity of the flexible resilient couplings can be easily implemented into this direct numerical integration algorithm. The dynamic stiffness and damping of the resilient couplings are updated at each time step to ensure the dynamic equilibrium. Two examples have been employed to illustrate the validity of the proposed algorithm. The effectiveness, accuracy, and simplicity of the use of p-method on the torsional vibration of synchronous motor driven trains are demonstrated in this paper.

In this paper transient torsional vibrations of a steam turbogenerator rotor shaft system due to high speed reclosing of the electric network are investigated. The analysis is performed using torsional elastic wave theory applied to a continuous model in the form of a stepped shaft. Wave solutions of the equations of motion are used in order to determine dynamic torsional elastic moments and vibratory angular velocitie in cross-sections of the turbine shafts. The results are illustrated in the form of graphs.

A dynamic system consisting of a servomotor, elastic shaft and inertial load, which may represent a disk or a robot arm, is chosen as an elastic control system. Equations of the torsional vibratory system are coupled with the servomotor control system equations and the transfer function of the elastic control system relating output angle to the desired input angle is obtained including not only control parameters but also the structural natural frequency and the structural damping of the torsional vibratory system. The ratio of the structural natural frequency to the substructural natural frequency and the ratio of substructural natural frequency to the control system frequency are defined as nondimensional parameters. System behavior is analyzed with respect to these parameters. The fourth order elastic control system transfer function is also reduced to the second order one and formulas for elastic control system frequency and damping are developed with respect to these parameters. [S0739-3717(00)70104-8]