Forced Lateral Vibration of a Uniform Cantilever Beam With Internal and External Damping

Abstract

The steady-state response problem of a uniform beam with a sinusoidal shaking force at the base is studied for the case where the beam material is the general linear substance represented by a model having an additional spring element in parallel with the Maxwell elements. In the analysis, the stress-strain relationship is applied only to the longitudinal strain of the beam, leaving the shear stress-strain relation to be that of a perfectly elastic material. The exact solution with a numerical example is given for one case where the shear and rotatory inertia effects are neglected. This result is compared with the solution obtained by a tabular method. The results of both methods are in excellent agreement.