Free and Forced Vibrations of a Spinning Viscoelastic Beam

The free and forced response of spinning, viscoelastic, Rayleigh shafts is studied. Viscoelasticity is included using the three parameter solid model. The closed form polynomial frequency equation and integral expressions for the response to a general forcing function are derived. A convenient decay parameter is described. Results are given for natural frequencies and decay rates as functions of shaft rotation speed, stiffness, and viscosity. It is found that shaft materials are possible which have desirable damping and natural frequency characteristics. A parameter case is discussed in which natural frequency and damping simultaneous increase, while stiffness is held constant. Also, the special case of forced response to a step load is derived and used to illustrate the combined effects of viscoelasticity and gyroscopic forces.