Vibrations of Timoshenko Beams and Frameworks

by Franklin Y. Cheng, (A.M.ASCE), Assoc. Prof. of Civ. Engrg.; Univ. of Missouri-Rolla, Rolla, MO,

Serial Information: Journal of the Structural Division, 1970, Vol. 96, Issue 3, Pg. 551-571

Document Type: Journal Paper


A general matrix formulation suitable for a use of the digital computer is presented for dynamic analysis of frameworks composed of prismatic members. The dynamic stiffness coefficients are derived in the form of nondimensional parameters corresponding to the effects of rotatory inertia, shear deformation, and of bending deformation. The individual parameter may be dropped when the appropriate effect is not considered; hence, the stiffness coefficients can be applied to a problem with various considerations of Timoshenko theory, Rayleigh theory, bending and shear, and of Bernoulli-Euler theory. Input data for the computer include the configurations of the framework and the elastic properties of constituent members. The method may be applied to irregular frameworks composed of sloping members with and without sidesway. Numerical examples presented indicate that the effect of rotatory inertia and of shear deformation on the frequencies of frameworks without sidesway is more significant than that of swayed structures.

Subject Headings: Shear deformation | Frames | Vibration | Beams | Stiffening | Parameters (statistics) | Rotation | Inertia

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