Development of a novel hybrid reduction scheme for identification of an open crack model in a beam

Abstract

In a dynamic system, estimation of the system model parameters from the experimental force-response measurements is generally termed as the identification. The present paper proposes a general identification algorithm to estimate crack flexibility coefficients and the crack depth based on the force-response information. The algorithm uses the standard dynamic reduction scheme to eliminate some of the degrees of freedom (dofs) of the system. However, it has limitation in that it requires the measurement of the rotational dofs at least at the crack element nodes. The general identification algorithm is extended to overcome practical limitations of measuring accurately the rotational dofs. For eliminating the rotational dofs at crack element nodes, a novel hybrid reduction scheme has been outlined based on the physical assumption of the present problem. The Euler–Bernoulli beam is used in the finite element modelling. The transverse surface crack is considered to remain open. The crack has been modelled by a local flexibility matrix of 4 dofs freedom by using the linear fracture mechanics approach. A harmonic force of known amplitude and frequency is used to dynamically excite the beam. The present identification algorithms have been illustrated through numerical examples. The algorithms have been found to be robust against the measurement noise.