Influence of Gravity and Taper on the Vibration of a Standing Column (Advances in Applied Mathematics and Mechanics, 2012)
The stability and natural vibration of a standing tapered verticalcolumn under its own weight are studied. Exact stability criteria arefound for the pointy column and numerical stability boundaries aredetermined for the blunt tipped column. For vibrations we use anaccurate, efficient initial value numerical method for the firstthree frequencies. Four kinds of columns with linear taper areconsidered. Both the taper and the cross section shape of thecolumn have large influences on the vibration frequencies. It isfound that gravity decreases the frequency while the degree oftaper may increase or decrease frequency. Vibrations may occurin two different planes.