Identification of Mode-shapes and Eigen-frequencies of Bi-hinge Beam with Distributed Mass and Stiffness

Abstract

 In the present paper, an equivalent Three Degree of Freedom (DoF) system of a bi-hinge beam, which has infinity number of degree of freedoms because possesses distributed mass and stiffness along its length, is presented. Based on the vibration partial differential equation of the abovementioned bi-hinge beam, an equivalent, mathematically, three-degree of freedom system, where the equivalent mass matrix is analytically formulated with reference on specific mass locations. Using the Three DoF model, the first three fundamental mode-shapes of the real beam can be identified. Furthermore, taking account the 3x3 mass matrix, it is possible to estimate the possible beam damages using a known technique of identification mode-shapes via records of response accelerations. Moreover, the way of instrumentation with a local network by three accelerometers is shown. It is worth noting this technique can be applied on bridges consist of bays with two hinges at its end sections, supported on elastometallic bearings, where the sense of concentrated mass is fully absent from the beam.