Eigenvalue Analysis for Transverse Vibration of Stepped Column with Lumped Mass at the Top by Finite Difference Approach

Abstract

Differential eigenvalue problem of stepped column with lumped mass at the top was analysed by finite difference method. Exact differential governing equation and boundary conditions were discretized with central differences applied upon grid points along the column. Boundary value problem was transformed in an appropriate and compact structure of algebraic equations written in matrix form, suitable for development of computer routines. For a comparison purpose, a finite element method analysis was conducted in ANSYS. Presented model gave natural frequencies that were in a very good agreement with the results obtained from finite element simulation.