A comparison of some equations for the flexural vibration of damped sandwich beams

This paper compares the theories of flexural vibration of damped, three-layer sandwich beams as presented by Yan and Dowell, and by DiTaranto and Mead and Markus. Depending on the assumptions made about the internal shear stress distribution, the differential equation of transverse flexural displacement is either of fourth or sixth order. The inclusion of the effects of face-plate shear deformation and longitudinal inertia in the analysis yields a sixth order differential equation if the beam section is symmetric, and an eighth order equation if the section is unsymmetric. Flexural wave speeds and loss factors computed from the theories are presented and compared. The DiTaranto and Mead and Markus equations yield reliable values provided the flexural wavelength is greater than about four face-plate thicknesses. The Yan and Dowell equations yield reliable values only at much greater wavelengths or when the central layer in the sandwich is very thick.