VIBRATIONS OF ROTATING THICK OR THIN RINGS

JEONG-LUH LIN, Purdue University

Abstract

Complete sets of equations of motion for general in-plane vibrations of rotating thick and thin rings on elastic foundations are derived. This thick ring theory takes account of the effects of extensibility, transverse shear, rotatory inertia and rotation as well as the effects of initial stresses due to pressure loads and centrifugal force. Frequency predictions are very close to the experimental data for both nonrotating thick rings and rotating thin rings. It is argued that inextensional assumptions in thick ring theories are improper because extensional coupling effects are as important as shearing effects, especially for the rotating ring. The correct quadratic displacement terms in the strain-displacement relations, necessary for the complete description of initial stress effects, are also discussed. The dynamic response of a rotating thick ring is obtained, subjected to either force or displacement excitation. The equations of motion are formulated in an inertial reference frame with structural damping of ring and foundation being considered. A receptance approach is utilized for obtaining the solutions. These receptances have the special property of not following reciprocity because of Coriolis effects. The dynamic responses to different force or displacement excitations are compared. In particular, a tangentially constrained displacement excitation is investigated. The effects which foundation stiffness, pressure loading and structural damping have on the development of standing waves are investigated. A criterion for critical speed equivalent to the characteristic equation for zero eigenvalues is obtained and an explicit expression for critical speeds in extensible thin ring is derived. Responses of force and displacement actions which cause standing waves are analyzed and compared by using receptance methods.

Degree

Ph.D.

Subject Area

Mechanical engineering

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