The correspondence principle has been applied to derive the differential equations of viscoelastic Timoshenko beams with external viscous damping. These equations are solved by Laplace transform and boundary conditions are applied to obtain complex frequency equations and mode shapes for beams of any combination of end conditions. For beams without external damping, the correspondence principle can be applied directly to the available solutions of elastic Timoshenko beams. Numerical illustration is given.
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Free Vibrations of Viscoelastic Timoshenko Beams
T. C. Huang,
T. C. Huang
Department of Engineering Mechanics, University of Wisconsin, Madison, Wisc.
C. C. Huang
Littleton Research Engineering Corp., Littleton, Mass.
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Huang, T. C., and Huang, C. C. (June 1, 1971). "Free Vibrations of Viscoelastic Timoshenko Beams." ASME. J. Appl. Mech. June 1971; 38(2): 515–521. https://doi.org/10.1115/1.3408805
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