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Modal Analysis of Uniform Short Cantilever Beam using Theoretical and Experimental Approaches


Affiliations
1 Mechanical Engineering Department, University College of Engineering, JNTUK, Kakinada, India
     

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In this investigation, experimental, theoretical models like Timoshenko Beam Theory (TBT), Euler-Bernoulli Beam Theory (EBT), and simulation software ANSYS R14.5 are used for executing the free transverse vibration analysis of a short cantilever beam for estimating the fundamental natural frequencies for different lengths of uniform short cantilever beam. The cross-section of the cantilever beam is rectangular and the material used for analysis is Mild Steel. The obtained results from experimental, both analytical theories, and simulation software ANSYS R14.5 are compared. Although the results obtained from both analytical models are closer to each other, results from Timoshenko beam model are nearer to those of results from ANSYS R14.5 and then to the experimental results than those obtained from the Euler-Bernoulli beam model. Also, for an arbitrary length of cantilever beam natural frequencies for the first four modes are obtained from ANSYS R14.5, TBT, and EBT models and are compared. Here also TBT model, ANSYS R14.5 results are nearer to each other than the results from EBT model. Hence, Timoshenko beam model is accurate theoretical model in analyzing the short cantilever beams for their modal analysis.

Keywords

Short Uniform Rectangular Cantilever Beam, Mild steel, Experimental Modal Analysis using FRF, Timoshenko Beam Theory, Euler-Bernoulli Beam Theory, ANSYS R14.5.
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  • Timoshenko, SP: On the correction for shear of the differential equation for transverse Vibration of prismatic bars, 'Philos. Mag.', vol. 41, 1921, 744-746.

  • Timoshenko, SP: On the transverse vibrations of bars of Uniform cross section, 'Philos. Mag.', vol. 43, 1922, 125-131.

  • Stephen P, Timoshenko: Vibration Problems in Engineering, 2nd Ed., Princeton, N. J. D. Van Nostrand Co., Inc., 1938.

  • Cowper, GR: The shear coefficient in Timoshenko’s beam theory, 'ASME, Journal of Applied Mechanics', vol. 33, 1966, 335-340.

  • Kaneko, T: On Timoshenko correction for shear in vibrating beams, 'J. Phys. D', vol. 8, 1975,1927-1936.

  • Hutchinson, JR; Zilmer, SD: On the transverse vibrations of beams of Rectangular crosssection,” ASME J. Appl. Mech., 53, 1986, 39-44.

  • Rao, SS: Mechanical Vibrations, 4th Ed., 'Pearson Education, Inc.', 2004.

  • Jong-Shyong, Wu: Analytical and Numerical Methods for Vibration Analysis, First Ed., John Wiley & Sons Singapore Pvt. Ltd., 2013.

  • ANSYS R14.5.

  • MATLAB R2013a


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  • Modal Analysis of Uniform Short Cantilever Beam using Theoretical and Experimental Approaches

Abstract Views: 454  |  PDF Views: 0

Authors

Yemineni Siva Sankara Rao
Mechanical Engineering Department, University College of Engineering, JNTUK, Kakinada, India
Kutchibotla Mallikarjuna Rao
Mechanical Engineering Department, University College of Engineering, JNTUK, Kakinada, India

Abstract


In this investigation, experimental, theoretical models like Timoshenko Beam Theory (TBT), Euler-Bernoulli Beam Theory (EBT), and simulation software ANSYS R14.5 are used for executing the free transverse vibration analysis of a short cantilever beam for estimating the fundamental natural frequencies for different lengths of uniform short cantilever beam. The cross-section of the cantilever beam is rectangular and the material used for analysis is Mild Steel. The obtained results from experimental, both analytical theories, and simulation software ANSYS R14.5 are compared. Although the results obtained from both analytical models are closer to each other, results from Timoshenko beam model are nearer to those of results from ANSYS R14.5 and then to the experimental results than those obtained from the Euler-Bernoulli beam model. Also, for an arbitrary length of cantilever beam natural frequencies for the first four modes are obtained from ANSYS R14.5, TBT, and EBT models and are compared. Here also TBT model, ANSYS R14.5 results are nearer to each other than the results from EBT model. Hence, Timoshenko beam model is accurate theoretical model in analyzing the short cantilever beams for their modal analysis.

Keywords


Short Uniform Rectangular Cantilever Beam, Mild steel, Experimental Modal Analysis using FRF, Timoshenko Beam Theory, Euler-Bernoulli Beam Theory, ANSYS R14.5.

References