Vibrations of a Three-Layer Beam with a Viscoelastic Middle Layer

Citation

Van Dillen, David Edwin (1972) Vibrations of a Three-Layer Beam with a Viscoelastic Middle Layer. Engineer's thesis, California Institute of Technology. doi:10.7907/P2BD-K350. https://resolver.caltech.edu/CaltechTHESIS:08262010-162507540

Abstract

The equations governing a three-layer beam in which the middle layer is viscoelastic were derived by means of a variational principle. These equations were solved subject to arbitrary time dependent boundary conditions of both the simply-supported and cantilever type. In the simply-supported case, an eigenfunction expansion was constructed after the governing equations had been transformed through operation by a differential operator. In the cantilever case, the solution was obtained by Fourier transform with respect to time, and inversion by residue theory. An analysis of the theoretical response of the cantilever beam to steady state sinusoidal loading was carried out, and an experiment was conducted for comparison.

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