THEORETICAL & FEM ANALYSIS OF CRACKED CANTILEVER BEAM

THEORETICAL & FEM ANALYSIS OF CRACKED CANTILEVER BEAM

ABSTRACT:

Most of rotating machines used in process industries or in manufacturing plant need maintenance and repair. However, failure of just one of these machines can disturb an entire process with losses in terms of production, manpower, and equipment repair or replacement. Also failure of a single machine component in the process industries like petrochemicals or power stations can result into loss of millions of rupees per down time hour. These facts together with higher costs for new equipments have placed increased demand on plant maintenance to keep existing equipment operating efficiently with higher availability.
A number of non-destructive crack detection techniques have been developed, such as ultrasonic testing, X-ray technique, magnetic particle method etc. Every method has some advantages and disadvantages. In recent years, ultrasonic testing has gained greater attention for monitoring the cracks in structures and machine components. Most of these methods are very laborious and time consuming, in case of larger components like bridges, long pipe lines, railway tracks etc. These inconveniences can be avoided by use of vibration monitoring technique such as modal analysis. Therefore the development of vibration monitoring techniques has received increasing attention in recent years.
Damage in structure alters its dynamic characteristics. The change is characterized by change in modal parameters i.e. modal frequencies, modal damping values and mode shapes associated with each modal frequencies. Changes also occur in some of the structural parameters like mass, damping, stiffness and flexibility matrices of structure. Thus vibration technique can be suitably used as a non-destructive test for crack detection of component to be tested.
In this paper, theoretical and actual analysis of vibrating cantilever beam with crack is carried out. This method is used to address the inverse problem of assessing the crack location and crack size in various beam structures. The method is based on measurement of natural frequencies, which are global parameters and can be easily measured from any point on the structure.
In theoretical analysis the crack is simulated by an equivalent spring, connecting the two segments of the beam. Analysis of this approximate model results in an algebraic equation, which relates the natural frequencies of the beam, and crack location. Also the relationship between the natural frequencies, crack location and crack size has also been developed. For identification of crack location and crack size, it was shown that data on the variation of the first natural frequencies is sufficient. The computation of natural frequencies of uncracked and cracked beam is facilitated by ANSYS FEM package. This database is to be utilized in analytical method to address the inverse problem to identify the crack location and crack size.

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