V. A. Chirikov, D. M. Dimitrov, K. P. Kostov

UNIVERSAL EXPERIMENTAL RELATION FOR NATURAL FRIQUENCIES OF TRANSVERSAL VIBRATION OF STUBBY FREE-FREE BEAMS

On the basis of set of experimental tests a universal experimental relation for determination of natural transversal frequencies of short bulky bars with free ends is established. It is shown that the relation totally corresponds to approximate solution of the notorious differential equation obtained by Timoshenko for transversal vibration of stubby beams. The relation gives an opportunity for brief calculation of the transversal natural frequencies of stubby beams by avoiding complex and hard algorithms of vibration analysis. The achieved relation can be successfully used for control purposes of robot arms articulation, etc. An option of new differential equation for stubby both ends pinned beams transversal vibration is discussed.

References:

1. Timoshenko S.P. On the Correction for Shear of the Differential Equation for Transverse Vibration of Prismatic Bars. Philosophical Magazine, 1921, vol.6, no. 41, pp. 744–746.
2. Timoshenko S.P. Kolebaniya v inzhenernom dele [Vibration Problems in Engineering]. Moscow, Nauka Publ., 1967, 444 p. (In Russian).
3. Chirikov V.A. On the Range of Rotary Inertia and Shear Effects for Beams. In: Applied Mechanics in the Americas, PACAM VII. Temuco, Chile, 2002, vol. 9, pp. 9–12.
4. Chirikov Victor A., Koichi Ozaki. Experimental Formula for Transverse Vibrations of Stubby Free–Free Beams. In: International Conference “Tehnonav 2004”. Constantsa, Romania, 2004, pp. 25–28. ISSN 1223-7221.
5. Chirikov V.A. Uravneniya poperechnykh kolebaniy korotkikh balok [Equations for Transversal Vibrations of Stubby Beams]. Dep. in VINITI 06.12.2005, no. 1595–В2005. (In Russian).
6. Dimitrov D.M. Application of dynamic methods for the determination of elastic constants of materials produced by powder metallurgy. Nauchni Izvestiya na NTSM, June 2013, vol. ХХI, iss. 2(139), pp. 433–435. ISSN 1310-3946. (In Bulgarian).
7. Kostov K. Determination of natural frequencies of beams with distributed parameters for free vibration. In: Yubileina studentska nauchna sessiya na TU-Varna, 04.04.2012. (In Bulgarian).
8. ASTM E1876-09 Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Impulse Excitation of Vibration. Book of Standards Volume: 03.01. ASTM, USA, 2012.

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