Lateral vibration of a beam carrying a concentrated mass at the mid-point, including the effect of rotatory inertia

Abstract

A general solution has been obtained for the lateral vibrations of a simply supported beam with constant cross-section carrying a concentrated mass at the mid-point of span. The elementary beam theory including the rotatory inertia of the beam is utilized. The frequency equation involves the product of two terms, roots arising from one of these being associated with symmetric vibration modes and from the other, antisymetric modes. The effect of the rotatory inertia of the beam on the roots of the frequency equations and on the normal mode shapes is investigated. The roots of ~he frequency equations are determined for the first ten modes for wide ranges of values of the significant parameters. These numerical results are depicted in tables and graphs. A study is made of the limiting values of the frequency roots for extreme values of the parameters.