Abstract
Elastic material properties critically affect the vibration behavior of structures. The value of natural frequencies changes due to change in the plate constants/plate stiffness which is a function of elastic modulus. At each natural frequency, the plate has a unique mode shape of vibration which can be easily differentiated from mode shapes at other natural frequencies. In this paper, a technique for the evaluation of the elastic modulus is proposed which is based on the vibration analysis of the plate using digital speckle pattern interferometry (DSPI) and Rayleigh method. Large numbers of experiments were conducted on square aluminium plate for the boundary condition; one edge is fixed and other edges free. The experimental result reveals that a single observation of frequency at first torsional mode is sufficient to evaluate the elastic modulus for all practical purposes. The evaluated experimental error was found to be less than 1%. Ease in sample preparation, simplicity in evaluation, non destructive nature of the DSPI and speed of DSPI has good prospect to evaluate elastic modulus of a material.
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References
ASTM Standard E132-97, Standard test method for Young’s modulus, tangent modulus and chord modulus. In: Annual Book of ASTM Standards. Am. Soc. Test Mater 03.01, pp. 244–250 (2002)
Gascón, F., Salazar, F.: A procedure for calculating through laser speckle interfer-ometry the elastic constants of isotropic materials. Opt. Commun. 123(4-6), 734–742 (1996)
Kang, X., Tay, C.J., Quan, C.: Evaluation of Young’s modulus of a vibrating beam by optical method. Opt. Eng. 42(10), 3053–3058 (2003)
Seebacher, S., Osten, W., Baumbach, T., Jüptner, W.: The determination of material parameters of microcomponents using digital holography. Opt. Laser Eng. 36(2), 103–126 (2001)
Viotti, M.R., Kaufmann, G.H., Galizzi, G.E.: Measurement of elastic moduli using spherical indentation and digital speckle pattern interferometrywith automated data processing. Opt. Laser Eng. 44(6), 495–508 (2006)
Kang, K., Kim, K., Lee, H.: Evaluation of elastic modulus of cantilever beam by TA-ESPI. Opt. Laser Technol. 39(3), 449–452 (2007)
Moore, A.J., Jones, J.D.C., Valera, J.D.R.: Dynamic measurements. In: Rastogi, P.K. (ed.) Digital speckle pattern interferometry and related techniques, pp. 225–288. Wiley, Chichester (2001)
Wang, W.C., Hwang, C.H., Lin, S.Y.: Vibration measurement by the time-averaged electronic speckle pattern interferometry. Appl. Opt. 35, 4502–4509 (1996)
Huang, C.H.: Experimental measurements by an optical method of resonance frequencies and mode shapes for square plates with rounded corners and chamfers. J. Sound Vib. 253(3), 571–583 (2002)
Shakher, C., Kumar, R.: System and method for real time monitoring of vibrations and large deformation in diffused material using sequential subtraction and image en-hancement. Indian Patent office application no.: 925/DEL/2002. September 12 (2002)
Kumar, R., Shakher, C.: Application of digital speckle pattern interferometry and wavelet transform in measurement of transverse vibrations in square plate. Opt. Laser Eng. 42(5), 585–602 (2004)
Kumar, R., Singh, I.P., Shakher, C.: Measurement of out-of-plane static and dy-namic deformations by processing digital speckle pattern interferometry fringes using wavelet transform. Opt. Laser Eng. 41(1), 81–93 (2004)
Mirza, S., Singh, P., Kumar, R., Vyas, A.L., Shakher, C.: Measurement of transverse vibrations/ visualization of mode shapes in square plate by using digital speckle pat-tern interferometry and wavelet transform. Opt. Laser Eng. 44(1), 41–55 (2006)
Stokey, W.F.: Vibrations of systems having distributed mass and elasticity. In: Harris, C.M. (ed.) Shock and vibration handbook, pp. 7.1–7.37. McGraw-Hill Book Comp., New York (1961)
Young, D.: Vibration of rectangular plates by the Ritz method. J. Appl. Mech. 17, 448–453 (1950)
Leissa, A.W.: The free vibration of rectangular plates. J. Sound Vib. 31(2), 257–293 (1973)
Lu, B., Yang, X., Abendroth, H., Eggers, H.: Time-average subtraction method in electronic speckle pattern interferometry. Opt. Commun. 70(3), 177–180 (1989)
Lu, B., Hu, Z., Abendroth, H., Eggers, H., Ziolkowski, E.: Improvement of time-average subtraction technique applied to vibration analysis with TV-holography. Opt. Commun. 78(3-4), 217–221 (1990)
Moore, A.J., Jones, J.D.C., Valera, J.D.R.: Dynamic measurements. In: Rastogi, P.K. (ed.) A Book on Digital Speckle Pattern Interferometry and Related Techniques, pp. 225–288. John Wiley & Sons Ltd., England (2001)
IMAQTM Vision for G Reference Manual. National Instrum Corp., Austin (1997)
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Shakher, C., Kumar, R. (2011). Application of Digital Speckle Pattern Interferometry (DSPI) in Determination of Elastic Modulus Using Plate Vibration. In: Kounadis, A.N., Gdoutos, E.E. (eds) Recent Advances in Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0557-9_17
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DOI: https://doi.org/10.1007/978-94-007-0557-9_17
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-0556-2
Online ISBN: 978-94-007-0557-9
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