No abstract

Theoretical damping values have been determined for three-and five-layer beams having representative cross sections. Trends are obtained that show damping effects produced by changes in cross-sectional geometry of the beam and properties of the damping material. The results are a series of characteristic curves displaying an increase in damping with increased frequency for the low frequency range, a peaking of the curves in the midfrequency range and a decrease in damping for the high frequencies. In addition, they show that increased viscoelastic material thickness and increased shear storage modulus shift the damping curve toward the low frequencies, while an increased thickness of the elastic layers, considered herein, appear to have no appreciable effect on composite damping behavior. For equal over-all beam thickness and equal viscoelasticmaterial thicknesses, the three-layer beam provided higher damping at the low frequencies whereas the five-layer beam yielded better damping at the peak, and at higher frequencies. Approximate analytical expressions are derived that verify the low-and high-frequency characteristics and predict the peak damping frequency and composite loss factor. * The opinions and assertions made herein are those of the authors and are not to be construed as official or reflecting the views of the U.S. Department of the Navy or the naval service at large.

The composite loss factors for beams having alternate laminae of elastic and viscoelastic materials have been computed for variations of frequency for 3- and 5-layer beams using the results obtained by Kerwin [E. M. Kerwin, D. Ross, and E. E. Ungar, “Damping of Plates in Flexural Vibrations by Means of Viscoelastic Laminae,” in Structural Damping (Am. Soc. Mech. Eng., New York, 1959)]. To properly design structures with laminated materials, in order to withstand and attenuate vibratory energy, it is desired to know the composite loss factor of the beam for different cross sections and materials. The results of this investigation obtained through the use of high-speed computers as a series of curves displaying the variations of composite loss factors as a function of frequency for different cross sections and materials. The cross-sectional configurations and materials were selected so that trends in composite loss factor could be obtained for such considerations as changes in thickness and/or physical properties of the elastic and/or viscoelastic material. These results may serve as a guide to the proper vibratory design of laminated materials.

The use of laminated elastic-viscoelastic beams as a means for obtaining vibration damping, together with reasonable structural stiffness, has been the object of extensive theoretical and experimental investigations. The particular theoretical and experimental work considered herein is the effect of end constraints on the composite loss factor of vibrating laminated beams. According to theoretical findings, the damping of laminated beams is independent of boundary conditions and depends solely on the geometry of the beam's cross section and properties of the damping material [R. A. DiTaranto, “Theory of Vibratory Bending of Laminated Beams,” (to be published)]. To check the theory, 3- and 5-layer laminated beams were investigated for ends constrained in several different manners: namely, free-free with and without bolted ends, and both ends clamped. For both the 3- and 5-layer beams, satisfactory agreement was obtained with theory, indicating the variation of composite loss factor with frequency of vibration to be independent of end conditions.