Parametric Approximation of Connected Euler-Bernoulli Beams with Variable Beam Lengths

Abstract In this contribution an approach for parametric approximations of flexible beam systems is presented that consist of several serially connected Euler-Bernoulli beams with structural damping whose lengths are considered as free parameters. This leads to the need to adapt the approximations to the current beam lengths online with tolerable computation efforts. It is shown how such approximations can be obtained by aid of the Petrov-Galerkin projection for infinite-dimensional systems, whereas the time-consuming part, namely the computation of some integrations, can be done offline, so that an adaptation of the approximation to changed beam lengths online requires only to solve some linear equations, besides scalar addition and multiplication operations. By aid of the Krylov subspace method it is possible to obtain approximations whose steady-state behavior coincides with that of the original system.