Dynamic analysis of a tapered cantilever beam under a
travelling mass
X.W. Zhao, Z.D. Hu & G.H.M. van der Heijden
We study the vibration of a tapered cantilever (Euler-Bernoulli) beam carrying
a moving mass. The tapering is assumed to be parabolic. Using the Galerkin
method we find approximate solutions in an energy formulation that takes into
account dynamic mass-beam coupling due to inertial, Coriolis and centrifugal
effects. The approximate solutions are exanded in terms of the mode shapes of
the free tapered beam, which can be obtained analytically. We then study the
effect the tapering as well as the magnitude and velocity of the mass have on
the tip deflections of the beam. We consider two different initial conditions,
one where the mass starts moving from a statically deformed beam and one
where the beam is initially triggered to vibrate. We find that tip deflections
are more irregular for strongly tapered beams. Our results are of interest
for barreled launch systems where tip deflections may adversely affect
projectile motion.
keywords: tapered cantilever beam, exact mode shape, moving mass, tip
oscillations
Meccanica 50, 1419-1429 (2015)