Forward and Inverse Dynamic Analysis of Multiple Span Cracked Beam

Abstract

The structural discontinuities like cracks, present in the structural/mechanical components, can potentially threaten the safe performance and may lead to failure of the component during the service. It is desirable to monitor the structural/mechanical member and detect the damage at the earliest possible stage to avoid catastrophic failures. The long and slender beam always needs intermediate supports. These intermediate supports affect modal parameters of the beam. The present study provides a generalized analytical formulation of uncracked and cracked multi - span beam. The supports of the multi-span beam are treated as torsional and/or linear springs to make formulation general. The cracks are assumed to be transverse and one-dimensional. The cracks are modelled as equivalent rotational spring. Using forward approach, the effect of number of cracks, number of intermediate supports, intermediate support locations, crack locations, crack depths and end support conditions on frequency and mode shapes is presented in details, for multi-span cracked beam. The crack, present in the multi-span beam, alters the frequencies of the beam. The change in frequencies, due to crack, is made the basis to identify crack location and depth in the multi-span beam. The frequency of the cracked and uncracked beam is measured using the Fast Fourier Transformation (FFT) analyzer (LMS make). The crack/s are developed using wire -cut electro discharge machining (WEDM). These measured natural frequencies are input to the code for prediction of crack location and crack severity. Alternatively, the measured frequencies are also coupled with the genetic algorithm, which predicts crack parameters of the multi-span beam after desired convergence criterion is achieved. The results of predicted crack parameters of both the methods are compared with actual crack parameters. The presented generalized analytical formulation is applied to the beam, made of time invariant, isotropic and homogeneous materials.