Timoshenko Beams on Linear Viscoelastic Foundations

Abstract

A method of solution for quasistatic bending problems of Timoshenko beams on linear viscoelastic foundations obeying Winkler's hypothesis is developed by using the eigenfunctions derived from free vibration problems of Timoshenko beams resting on no foundation and by using the correspondence principle between the viscoelastic problem and the associated elastic problem. Series solutions of the eigenfunctions are rapidly convergent and give accurate results by taking only the first several terms of the series. A successive iteration method for evaluating the eigenvalues is also presented. Numerical results for the variations of deflection and reactive force in space and time are illustrated for a Timoshenko beam with free ends on the viscoelastic foundations of the Kelvin, Maxwell, and Standard linear solid types. The effect of shear deformation on the flexure of beam is discussed.