Abstract
The exact equations of dynamic viscoelasticity are used to determine the resonance damping for a vibrating plate, which is assumed as isotropic and homogeneous. To determine the validity of thin-plate theory, the same problem is investigated by means of the classical thin-plate equation that does not include shear deformation or rotatory inertia terms. The comparison between the thin-plate theory and the exact theory is carried out for two types of materials that correspond to real and complex values of the bulk modulus. In each case, the shear modulus is μ(1+ig), and values of g to 0.1 were used in the calculations. The two theories are in excellent agreement in a range of wavelengths as low as 10 times the thickness. It is found that thin-plate theory evaluates the damping more accurately than the static rigidity. [This work was performed at the Adelphi Research Center, Garden City, New York, under a contract with the Aeronautical Systems Division of Wright-Patterson Air Force Base, Ohio, AF 33(616)-8274, with M. A. Biot as Scientific Director.]
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