A circular cylinder was placed in a flowing fluid with its axis across the stream. The fluctuating lift and drag forces, and the steady drag force were measured. The results for the stationary cylinder were given in a previous paper (Bishop & Hassan 1964). Here, the results are described and summarized for a cylinder that is made to oscillate transversely in a direction perpendicular to the stream.
SummaryThis paper is the first of a series of three which are concerned with the subject of “ hysteretic damping.” This type of damping, in a simple system with one degree of freedom, is like the familiar “ viscous damping ” in that it implies a resisting force which is in phase with velocity; but it is unlike viscous damping in that the magnitude of the force is not proportional to the velocity but to the displacement. When a system has n degrees of freedom, hysteretic damping implies that damping forces exist which are proportional to relative displacement but which are in phase with relative velocity.From a physical standpoint, hysteretic damping may give a better representation of the facts when the damping arises from the internal friction of solid materials. On the side of theory, it raises considerations which it is the purpose of these three papers to elucidate. It may be said, at the outset, that the notion of hysteretic damping raises no great mathematical difficulty; on the contrary, a main reason for presenting the theory is that it appears to allow of a much simpler discussion (than does viscous damping) of the nature of steady damped oscillation of systems having n degrees of freedom.In the first paper, the purpose is discussed of mathematical theories of damping in vibration theory. It is concluded that the theory of “ hysteretic damping ” is a useful one since it provides an alternative to the fiction of “ viscous ” damping while retaining the mathematical linearity of equations of motion. The word “ hysteretic” is proposed for use in this sense instead of the previously used adjective, namely “ structural.” “ Complex damping ” is related to hysteretic damping in a way which is explained.The theory is given for forced oscillations of a system with one degree of freedom. It is shown that free vibration cannot be treated satisfactorily unless the definition of hysteretic damping is widened in some way to cover non-harmonic motion.
The motion of a flexible unbalanced rotating shaft is examined. The effects of balancing such a shaft (as a ‘rigid body’) in a conventional low-speed balancing machine are explained. The underlying theory of a general method of balancing flexible rotors, mode by mode, is then given. The paper contains a discussion of the effects of dead weight on the deflection of a rotating shaft.
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