The reconstruction of a solely time-dependent load in a simply supported non-homogeneous Euler-Bernoulli beam

In this paper, the theoretical and numerical determination of a solely time-dependent load distribution is investigated for a simply supported non-homogeneous Euler-Bernoulli beam. The missing source is recovered from an additional local integral measurement. The existence and uniqueness of a solution to the corresponding variational problem is proved by employing Rothe's method. This method also reveals a time-discrete numerical scheme based on the backward Euler method to approximate the solution. Corresponding error estimates are proved and assessed by two numerical experiments. (C) 2019 Elsevier Inc. All rights reserved.