Complete non-series solutions for steady-state vibrations of uniform-section beams with all possible combinations of various supports are given, using a generalization of the Macaulay notation commonly used for evaluating static beam deflections. The presence of flexible restraints and elastic hinges is considered within the same framework. The application of the method is shown by some specific calculations.
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References
1.
BishopR. E. D.1955Proc. Instn mech. Engrs, Lond.vol. 169, p. 1031, ‘The Analysis of Vibrating Systems which Embody Beams in Flexure’.
2.
DuncanW. J.1943Phil Mag., vol. 34, p. 49, ‘Free and Forced Oscillations of Continuous Beams: Treatment by the Admittance Method’.
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BishopR. E. D.JohnsonD. C.1956‘Vibration Analysis Tables’ (Cambridge University Press).
