Summary
The present paper deals with the problem of three-dimensional forced harmonic motions of a cantilever planar-curved bar being considered as a discrete system of-n-points of mass. At these points the mass of the bar is supposed as being lumped under the form of small rectangular parallelepipeds, so that the influences of shearing forces and rotatory inertias to be taken into account. In the beginning, the generalized flexibility matrix of the system is formulated; then, based on this matrix, two independent vectorial differential equations of forced harmonic vibrations of the bar are constructed and their exact solutions are derived. Finally, as an application of the method the generalized flexibility matrix of a cantilever circular bar is formulated and the natural frequencies of the system are calculated when a small cubic body being attached at its free end is vibrating vertically to the plane of the bar.
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References
Timoshenko, S., Young, D. H., Weaver, W.: Vibration problems in engineering, 4th ed. New York-London: Wiley 1974.
Nowacki, W.: Dynamics in elastic structures. London: Chapman and Hall 1963.
Koloušek, V.: Dynamics in engineering structures. London: Butterworths 1973.
Biggs, J. M.: Introduction to structural dynamics. New York: McGraw-Hill 1964.
Glough, R. A.: Dynamics of structures. New York: McGraw-Hill 1975.
Anderson, R. A.: Flexural vibration of uniform beams according to the Timoshenko theory. J. of Appl. Mech., ASME20, 504–510 (1953).
Edmer, A., Billington, D.: Steady-state vibration of damped Timoshenko beams. J. of the Struct. Div. ASCE94, 737–760 (1968).
Gladwell, G. M. L.: The approximation of uniform beams in transverse vibration by sets of masses elastically connected. Proccedings, 4th U.S. Nat. Congress of Appl. Mech.1, 169–176 (1962).
Herrmann, G.: Forced motions of Timoshenko beams, J. of Appl. Mech. ASME22, 53–56 (1955).
Volterra, E.: Vibrations of circular elastic rings. Israel J. of Techn.5, 225–233 (1967).
Culver, G. C.: Natural frequencies of horizontally curved beams. J. of the Struct. Div. ASCE93, 189–203 (1967).
Ball, R. E.: Dynamic analysis of rings by finite difference. J. of the Engin. Mech. Div. ASCE93, 1–10 (1967).
Pereira, C. A. L.: Free vibration of circular arches. Thesis presented to Rice University, at Houston, Texas, in 1968, in partial fulfillement of the requirements for the degree of Master of Science.
Rao, S. S.: Effects of transverse shear and rotatory inertia on the coupled twistbending vibrations of circular rings. J. of Sound and Vibration16, 551–566 (1971).
Wung, S. J.: Vibration of hinged circular arches. Thesis presented to Rice University, at Houston, Texas, in 1967, in partial fulfillement of the requirements for the degree of Master of Science.
Panayotounakos, D. E., Theocaris, P. S.: The dynamically loaded circular beam on an elastic foundation. J. of Appl. Mech. ASME47, 139–144 (1981).
Theocaris, P. S., Panayotounakos, D. E.: The differential equations of skew-curved bars due to harmonic motions. J. of Sound and Vibration. (Accepted for publication.)
Young, M. C.: Flexibility influence functions for curved beams. J. of the Struct. Div. ASCE95, 1407–1429 (1969).
Panayotounakos, D. E., Theocaris, P. S.: Flexibility matrix for skew-curved beams. Inter. J. of Sol. and Struct.15, 783–794 (1979).
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Panayotounakos, D.E. Forced motions of cantilever planar-curved bars considered as discrete systems by the flexibility method. Acta Mechanica 50, 105–118 (1983). https://doi.org/10.1007/BF01170444
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DOI: https://doi.org/10.1007/BF01170444