Central finite difference approach tо free vibrations of double-tapered cantilever beam with elastic foundation and tip mass

Abstract

Free vibration problem of double-tapered cantilever beam with tip mass and elastically restrained root was solved efficiently and accurately by building a compact structure of algebraic equations, based on central finite difference method. Exact differential governing equation and boundary conditions were discretized by central finite differences applied upon grid points along the beam. Influence of support rigidity on mode shape function was discussed in term of discretized boundary equation. Boundary value problem was transformed in an appropriate matrix form, suitable for development of computational algorithms and solving with MATLAB routines. For a comparison purpose, a finite element method analysis was conducted in ANSYS. Testing cases were set up for numerous values of non-dimensional stiffness and mass parameters. Presented model yielded natural frequencies that were in a very good agreement with the results obtained from finite element simulation.