Abstract: Specimens are prepared for performing experiment. Four Aluminium specimen having dimensions 450 mm x 40 mm x 10 mm is prepared. Then out of four specimens one specimen is kept notch free. On second one specimen a notch on entire width and longitudinal distance of 90 mm from free end is prepared. Similarly third and fourth specimen have notch on 120 mm and 150 mm from free end respectively. We have to observed the impact of crack on cantilever beam of length 390 mm, 340 mm and 290 mm, and We also determined the effect of position of artificially generated notch (90 mm, 120 mm and 150 mm from free end). During the experiment our main motive is to measure the velocity of vibration (V) at different longitudinal distance from free end of the cantilever beam ranging from 50 mm to 250 mm at an interval of 50 mm. Frequency of vibration is kept constant during the process. After one complete reading, process is repeated for different required frequency. Since we have to find the crack Development rate on the observed velocity of vibration that’s why we have to develop a relation between velocities of vibration with crack Development rate.Here relation is found out by using Buckingham Pie Theorem. The variables considered for the analysis is, velocity of vibration (V), force per cross sectional area (W), distance of crack from fixed end (B), frequency of the force per fixing length (F), distance of accelerometer from free end (D) and Crack Development per unit time (G).As mentioned above, total number of variables considered for present investigation is, ‘6’. Three out of 6 variables are considered as fundamental variables and a functional relationship is established as Φ (V, W, D, F, B, G) = 0. The derived groups are, V/(D².F), B/D and G/(D².F). The relationship obtained using Buckingham Pi Theorem as, G/(D².F) = f (B/D, V/D².F).Crack Development rate for cantilever specimen at different length 390 mm, 340 mm, 290 mm are calculated at frequency of 60 Hz, 80 Hz, 100 Hz, 120 Hz. Also at each frequency Crack Development rate is measured at an Accelerometer distance of 50 mm, 100 mm, 150 mm, 200 mm and 250 mm from free end.
Keywords: Cantilever Beam, Crack Growth Rate, Crack Location, Fixing Length effect, Frequency of Vibration.
Title: Study and Determination of Crack Development on Aluminium Cantilever Beam by the Help of Pre-Existing Crack Using Buckingham Pie Theorem
Author: Mr. Ashwani Ranjan, Mr. Yogesh Sharma
International Journal of Civil and Structural Engineering Research
ISSN 2348-7607 (Online)
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