Viscoelastic Buckling of Euler-Bernoulli and Timoshenko Beams under Time Variant General Loading Conditions

摘要

A comprehensive study on the linear viscoelastic buckling of Euler-Bernoulli (E-B) and Timoshenko beams is presented. The mathematical formulation for visco elastic E-B beam under combined time variant general axial and transverse loading and for the viscoelastic Timoshenko beam only subjected to time variant general axial loading is developed. Various boundary conditions are defined then clamped edge constraints are applied. The E-B and Timoshenko cantilever beams are investigated under general axial loading. Both differential and integral forms of the beam governing equations are derived, but only the differential equations are solved, using the finite difference numerical technique assuming Kelvin material model. A computer programme is implemented for computing the beam deflections and a technique is described for obtaining the critical buckling loads. Where possible the finite difference numerical results are compared with other available results. The correlations of the results are extremely well. The important contributing factors are the general nature of the loading and the technique for calculating the critical buckling loads.