Exact solutions for vibration of a vertical heavy string with a tip mass

Abstract

This technical note considers the free vibration problem of a vertical heavy, inextensible string/chain with a tip mass. The top end is fully restrained from moving in the vertical direction but it is partially restrained in the lateral direction by an elastic spring. The exact frequency characteristic equation for the aforementioned vibration problem is derived and the first five vibration frequencies are presented for various tip mass to string mass ratios and spring constants. © 2010 The Institution of Engineers, Singapore.