Dynamic Analysis of Nonuniform Beams on Elastic Foundations

ABSTRACT

An analytical solution for the free vibration of a nonuniform flexural beam resting on an elastic foundation is obtained. The characteristics of the beam are assumed variable over the beam length while the soil is considered of Winkler type. A power distribution model is used to simulate the variations in the beam geometry, beam material and soil stiffness over the beam length. The fourth order differential equation of beam vibration under appropriate boundary conditions is transformed to the Bessel equation by factorization. Mode shapes and damped natural frequencies of the beam are obtained for wide range of beam-foundation system characteristics. Numerical comparison demonstrates that the present model results for uniform case agree with those found in literature. The present model analytical solutions may be used to verify the accuracy of other numerical and approximate solutions.

Keywords:

Damped vibration, tapered beam, differential equation, variable coefficients, series solution, mode shapes and natural frequencies.