Solvability of the clamped Euler-Bernoulli beam equation

In this study, solvability of the initial boundary value problem for general form Euler-Bernoulli beam equation which includes also moving point-loads is investigated. The complete proof of an existence and uniqueness properties of the weak solution of the considered equation with Dirichlet type boundary conditions is derived. The method used here is based on Galerkin approximation which is the main tool for the weak solution theory of linear evolution equations as well as in derivation of a priori estimate for the approximate solutions. All steps of the proposed technique are explained in detail. (C) 2019 Elsevier Ltd. All rights reserved.