Affiliation:
1. Departments of Mathematics and Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA
Abstract
The unique solution for the fully stressed hanging string with a bottom load is found. For a given length of string, the problem depends on two parameters, representing the ratio of string density to maximum stress, and the ratio of bottom mass to maximum stress. The cross-sectional area of the string decays exponentially downward. Vibration frequencies are found from the exact characteristic equation. Results from analytic perturbation formulas compare well with those of numerical solution.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Mechanical Engineering,Ocean Engineering,Aerospace Engineering,Building and Construction,Civil and Structural Engineering