In this paper, theoretical and experimental analysis of a vibrating, simply supported beam with a 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 of global parameter 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 algebraic equations, which relate 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 the crack location and crack size, it was shown that data on the variation of the first two natural frequencies is sufficient. The computation of natural frequencies of an uncracked and cracked beam is facilitated by a finite element method package. This database is to be utilized in an analytical method to address the inverse problem to identify the crack location and crack size. Experiments have also been performed on a simply supported beam. The experimental analysis is done to verify the practical applicability of the theoretical method developed. A good agreement between the predicted and actual crack location and crack size is obtained. The results obtained by theoretical and experimental methods are compared graphically.

Damage in structure alters its dynamic characteristics. The change is characterized by change in modal parameters i.e., modal frequencies. Mostly modal frequencies are used for monitoring the crack because modal frequencies are properties of the whole component. Thus vibration technique can be suitably used as a nondestructive test for testing crack detection of component. In this article efforts are made to develop a suitable method that can serve as a basis for detection of crack location and crack size from measured axial vibration data. This method is used to address the inverse problem of assessing the crack location and crack size in various beam structure. The method is based on measurement of axial natural frequencies, which are global parameter and can be easily measured from any point on the structure. In theoretical analysis the crack is simulated by an equivalent axial spring, connecting the two segments of the beam. Analysis of this approximate model results in 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 two natural frequencies is sufficient. The experimental analysis is done to verify the practical applicability of the theoretical method developed.

Nowadays, sophisticated structures and machinery parts are constructed by using metallic beams. Beams are widely used as structural element in civil, mechanical, naval, and aeronautical engineering. In structures and machinery, one undesirable phenomenon is crack initiation in which the impact cannot be seen overnight. Cracks develop gradually through time that lead finally to catastrophic failure. Therefore, crack should be monitored regularly with more care. This will lead to more effective preventive measure and ensure continuous operation of the structure and machine. Damage in structure alters its dynamic characteristics. The change is characterized by change in modal parameters, that is, modal frequencies. Thus, vibration technique can be suitably used as a nondestructive test for crack detection of component to be tested. Mostly modal frequencies are used for monitoring the crack because modal frequencies are properties of the whole structure component. In this paper, efforts are made to develop suitable methods that can serve as the basis to detection of crack location and crack size from measured axial vibration data. This method is used to address the inverse problem of assessing the crack location and crack size in various beam structure. The method is based on measurement of axial natural frequencies, which are global parameter and can be easily measured from any point on the structure and also indeed, the advantage in modeling complexity. In theoretical analysis, the relationship between the natural frequencies, crack location, and crack size has been developed. For identification of crack location and crack size, it was shown that data on the variation of the first two natural frequencies is sufficient. The experimental analysis is done to verify the practical applicability of the theoretical method developed.

Vibration absorbers are frequently used to control and minimize excess vibration in structural systems. Dynamic vibration absorbers are used to reduce undesirable vibration in many applications such as pumps, gas turbines, engines, bridges, electrical generators, etc. To reduce the vibration of the system, the frequency of the absorber should be equal to the excitation frequency. The aim of this paper is to investigate the use of a variable stiffness type magnetic vibration absorber to control the vibration of beam structure. This study will aim to develop variable stiffness of a magnetic vibration absorber to adapt to the change in a vibratory system; its stiffness can be varied by changing the distance between magnets. The absorber system is mounted on a cantilever beam acting as primary system. The objective is to suppress the vibration of the primary system subjected to a harmonic excitation whose frequencies vary. This can be achieved by varying the stiffness by changing the distance between the magnets. The advantage of a magnetic vibration absorber is that it can be easily tuned to the excitation frequency, so it can be used to reduce the vibration of a system subjected to variable excitation frequency.

Most of the 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 process industries like petrochemicals or power stations can result in the loss of millions of rupees per down time hour. These facts together with higher costs for new equipment 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 the case of larger components like bridges, long pipe lines, railway tracks etc. These inconveniences can be avoided by the use of vibration monitoring technique such as model 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 a change in model parameters i.e. model frequencies, model damping values and mode shapes associated with each model frequencies. Changes also occur in some of the structural parameters like mass, damping, stiffness and flexibility matrices of structure. Thus a vibration technique can be suitably used as a nondestructive test for crack detection of components to be tested. In this paper, theoretical and experimental analysis of a vibrating cantilever beam with a crack is carried out. This method is used to address the inverse problem of assessing the crack location and crack size in various beam structure. The method is based on measurement of natural frequencies, which are global parameter 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 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 two natural frequencies are sufficient. The computation of natural frequencies of uncracked and cracked beam is facilitated by a finite element method package. This database is to be utilized in an analytical method to address the inverse problem to identify the crack location and crack size.