Free Vibrational Frequencies of an Isotropic Elastic Cylinder
The vibrational frequencies of an isotropic elastic cylinder are found both from
exact and approximate solutions and compared with results of molecular
dynamics simulations.
The coefficient of restitution of an object boucing either off the floor or off of
another object has been studied extensively, both experimentally and theoretically. In
particular, the problem of a rigid thin rod hitting a hard floor has been studied experimentally
and theoretically
[Hurmuzlu 1998
pdf::].
Consider a right circular cylinder of radius R and height h. The cylinder is made of
isotropic elastic material of Young's modulus Y, density ρ and Poisson ratio ν. The mass of the
cylinder is m, where m = ρ π R2 h. There is no viscous
dissipation.
References
Y. Hurmuzlu, "An Energy Based Coefficient of Restitution for Planar
Impacts of Slender Bars with Massive External Surfaces"
ASME Journal of Applied Mechanics, Vol. 65, pp. 952-962 (1998).
pdf::
Daniel Murray
Associate Professor
Math, Stats & Physics Unit
University of British Columbia - Okanagan
Kelowna, BC, Canada
daniel "dot" murray "at" ubc "dot" ca