Identification of fixedness and loading of an end of the Euler–Bernoulli beam by the natural frequencies of its vibrations

Abstract

Under consideration is the uniform Euler–Bernoulli beam whose left end is fixed, and some load elastically fixed by two springs is concentrated at the right end. If the beam is hit then it begins vibrating. The aim of the article is to determine the parameters of fixedness (rigidity coefficients of springs) and loading (the mass andmoment of inertia of the load) of the right end of the beam by natural frequencies of its flexural vibrations. It is shown that the four unknown parameters of the boundary conditions at the right end of the beam are uniquely determined from the five natural frequencies of its flexural vibrations. Some counterexample is presented showing that four natural frequencies are insufficient for the unique identification of these four nonnegative parameters.