Pravin G. Bhuta

A viscous ring damper for a freely precessing satellite

Abstract A viscous ring damper for removing the wobble motion of a spin-stabilized satellite is proposed and analyzed. The analysis is performed by studying the energy dissipation in an auxiliary problem of the motion of a viscous liquid in a tube whose boundaries perform harmonic motion. The energy dissipated per unit mass of the damper fluid is maximized in terms of a “wobble Reynolds number”. This maximization is experimentally verified. The decay of the cone angle of free precession is then obtained by the use of the “energy-sink-approximation”. The results of the theory are compared with those from a laboratory experiment.

Hydroelastic Solutions of the Sloshing of a Liquid in a Cylindrical Tank

The problem of sloshing (free surface oscillations) of a liquid in a cylindrical tank having rigid walls and a flexible bottom (a thin elastic plate) is studied for both the axisymmetric and asymmetric cases. The coupled boundary‐value problem of the liquid and the elastic bottom is solved for small motions. The frequency equations are obtained and the effect of the coupling investigated. It is shown that the frequency equations reduce properly to the various limiting cases. The orthogonality of the coupled mode shapes is investigated and a theorem concerning the coupled mode shapes is proved.

Symmetric Planar Vibrations of a Rotating Disk

The complete problem of coupled symmetric radial and torsional vibrations of a thin, rotating, circular disk has been solved, using undeformed coordinates. The formulation of the problem used here yields several interesting and previously unreported results for the static problem. Two types of instabilities occur: “static resonances” and classical instabilities, for which radial and torsional displacements everywhere in the disk can become unboundedly large. These resonances have been explained physically. The solutions of the frequency equation and the mode shapes are obtained. The effect of rotation is to lower the natural frequencies of the disk. When deformed coordinates are used, as is the case in the classical analysis of a rotating disk, the instabilities are concealed.

Vibrations of a Whirling Rayleigh Beam

In this paper the vibrations of a whirling Rayleigh beam are studied. The vibrations are allowed to take place in the plane of rotation as well as in a direction perpendicular to the plane of rotation. Use has been made of undeformed coordinates resulting in the prediction of certain instabilities that have not been previously reported. The solutions of the frequency equations for a fixed‐free beam and a simply supported beam are discussed.

Exact nonlinear solution of the bending of a constrained beam

ZusammenfassungFür einen beidseitig eingespannten schlanken Stab, dessen Enden sich auf einem Kreis verschieben können, wird die exakte Lösung entwickelt. Die Reaktionen sowie die elastische Linie lassen sich mit Hilfe von elliptischen Integralen erster und zweiter Gattung bestimmen. Ein numerisches Beispiel zeigt die Anwendung der behandelten Methode, die bei der Konstruktion gewisser drehbarer Einspannung von Interesse ist.