The Steady-State Response of a Rotating Damped Disk of Variable Thickness

Abstract

The stress distribution and steady-state response of a rotating damped annular disk of variable thickness are determined by means of the matrix method. The equation of equilibrium and the equations for the flexural vibration of the rotating disk are written as a respective coupled set of first-order differential equations by use of the matrices of the disk. The elements of the matrices are calculated by numerical integration of the equations, and the stress components and the driving-point impedance and force transmissibility of the disk are obtained by using these elements. The method is applied to free-clamped rotating disks with linearly, exponentially, and hyperbolically varying thickness driven by a harmonic force at the free outer edge, and the effects of the angular velocity and the variable thickness are studied.