The Damping of Beam Vibration by Rotational Damping at the Supports

摘要

If the edges of a plate are embedded in a visco-elastic material, flexural vibration of the plate is damped by virtue of the damping forces and couples exerted at its boundaries. This paper analyses and assesses the effectiveness of this form of artificial damping when applied to a uniform beam and compares it with the effectiveness of homogeneous damping layers applied throughout the length of the beam. The theory is developed for the linear flexural response of the uniform beam to uniform harmonic loading. Transverse displacements of the beam are prevented altogether while rotation is opposed by the linear elastic and damping couples from the embedding material. Explicit expressions are derived for the amplitudes of curvature at the centre of the beam and from these it is shown that there exist optimum values of the end constraint damping properties which will minimize the beam resonant response. Methods of estimating these optimum values are discussed. It is shown that different optimum values are required to give the maximum effective flexural loss factors of the beam. This greatest value may be of the order of 0.33. Comparison with the effectiveness of homogeneous layers shows that the edge-constraint damping mechanism is more effective than thin homogeneous layers, but much less effective than thick layers. (Author)