On nonuniform Euler-Bernoulli and Timoshenko beams with jump discontinuities: application of distribution theory

In this article, bending of nonuniform Euler-Bernoulli and Timoshenko beams with jump discontinuities in the slope. deflection and mechanical properti es are studied. The governing equations are obtained in the space of genera lized functions, and the expression of its governing differential equations in terms of a single displacement function and a single rotation function is shown always to be possible. In contrast, for a nonuniform Euter-Bernoul li beam with jump discontinuities in slope and deflection and abrupt change s in flexural stiffness, the governing equation can be written in terms of a single displacement function only under certain conditions. It is observe d that for most discontinuous nonuniform Euler-Bernoulli beams we cannot wr ite the governing differential equation in terms of a single displacement f unction: usually, if there are n discontinuity points on a nonuniform Euler -Bernoulli beam, n + I displacement functions appear in the governing equil ibrium equation. (C) 2001 Elsevier Science Ltd. All rights reserved.