Sommario
In un precedente lavoro le equazioni di equilibrio dinamico di un'asta svergolata soggetta a vibrazioni libere lungo il proprio asse erano state risolte in forma chiusa per tre sole condizioni di vincolo al contorno particolarmente semplici (estremità torsionalmente ed assialmente libere o incastrate). Nel presente lavoro vengono determinate le formule finali relative alle altre sette condizioni di vincolo che si ottengono imponendo in almeno una delle estremità dell'asta la rotazione libera e lo spostamento assiale impedito o viceversa. Viene anche svolto un esempio di calcolo numerico determinando in uno dei casi considerati il modo di variare delle prime pulsazioni proprie al crescere dello svergolamento dell'asta.
Summary
In a previous paper concerning the determination of angular frequencies of a twisted straigth bar of constant section, only three simple constraint conditions at the ends had been considered (free end, constrained end). In the present paper the other seven possible (asymmetric) constraint conditions are considered and the corresponding frequency equations are found. A final numerical example with several increasing twisting degrees shows the different influence of this increase upon the frequencies having axial or torsional origin.
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References
Curti G., Risitano A.,Coupled free, torsional and axial vibration of pre-twisted bars, Meccanica, Journal of the Italian Association of Theoretical and Applied Mechanics, Sept. 1979.
Garland Clyne F.,The normal modes of vibrations of beams having noncollinear elastic and mass axes, Journal of Applied Mechanics, Sept. 1940.
Dawson B.,Coupled bending-bending vibrations of pre-twisted cantilever blading treated by the Rayleigh-Ritz energy method, Journal of Mech. Engineering Science, Vol. 10, n. 5, 1968.
Dawson B., Carnegie, W.,Modal curves of pre-twisted beams of rectangular cross-section, Journal of Mech. Engineering Science, Vol. 11, n. 1, 1969.
Kar R.C., Hauger W.,Stability of a pre-twisted tapered cantilever beam subjected to dissipative and follower forces, Journal of Sound and Vibration (1982) 81 (4), 565–573.
Carnegie W.,Vibrations of pre-twisted cantilever blading, Proc. Instn. Mech. Engrs., Vol. 173, n. 12, 1959.
Carnegie W.,Vibrations of pre-twisted cantilever blading: an addition effect due to the torsion, Proc. Instn. Mech. Engrs., Vol. 176, n. 13, 1962.
Rao J.S.,Torsional vibration of pret-wisted cantilever beams, Journal of the Institution of Engineers (India), Vol. 52, n. 9, May 1972.
Rao J.S., Carnegie W.,Torsional vibration of pre-twisted tapered cantilever beams treated by collocation method, Indian Journal of Pure & Applied Physics, Vol. 1, June 1972.
Rao J.S.,Vibrations of pre-twisted tapered cantilever beams in torsion, Archiwum Budowy Maszyn Tom. XVIII, 1971, Zeszyt 3.
Rao J.S., Belgaumkar B.M., Carnegie W.,Torsional vibration of a cantilever beam of rectangular cross-section with uniform taper, Bull. Mech. Engng. Educ. Vol. 9, pp. 61–67, Pergamon-Press, 1970.
Rao J.S., Carnegie W.,Solution of the equations of motion of coupled bending torsion vibrations of turbine blades by the method of Ritz-Galerkin, Int. J. Mech. Science, Pergamon-Press 1970, Vol. 12, pp. 875–882.
Rao J.S., “Coupled bending torsion vibrations of cantilever beams, Journal of the Aeronautical Society of India, February 1972, Vol. 24, n. 1, pp. 265–268.
Di Prima R.C.,Coupled torsional and longitudinal vibrations of a thin bar, Journal of Applied Mech., Dec. 1959, pp. 510–512.
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Curti, G., Risitano, A. Longitudinal vibrations of pre-twisted bars with “asymmetric” boundary conditions. Meccanica 20, 160–163 (1985). https://doi.org/10.1007/BF02337635
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DOI: https://doi.org/10.1007/BF02337635