Charles J. Konzelman
Marinos C. Stylianou
Dept. of Mech. Eng., Univ. of Victoria, Victoria, BC V8W 3P6, Canada
Everyone has performed this experiment at one time or another: Take a ruler, hold it over the edge of a tabletop like a cantilever beam, pluck the end, and slowly retract the ruler into the tabletop. The frequency of the resulting vibration is observed to increase as the ruler is retracted into the tabletop. Although numerical simulations based on the linearized equation of motion for this intruding cantilever beam reveal that its total energy increases with the passage of time, the source of the energy is apparently unaccounted for. This study examines the transport of energy into (and out of) a cantilever beam which intrudes or extrudes from a rigid support with uniform axial velocity. By examining some second-order effects at the support and over the length of the beam, an attempt is made to define the mechanisms of energy transport into (and out of) the beam. This has potential application to the solution of transverse vibration control problems, if the velocity of axial intrusion/extrusion is a properly prescribed function of time.