A CORRESPONDENCE PRINCIPLE FOR FREE VIBRATIONS OF A VISCOELASTIC SOLID.
BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS
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A correspondence principle was established for free vibrations in the classical linearized theory of viscoelasticity. It was shown that for motions which are either irrotational or solenoidal there is always an associated elastic problem with the following properties 1 every mode shape for the viscoelastic problem is also a mode shape for the elastic problem and 2 the viscoelastic frequencies can, in principle, be calculated from a knowledge of the elastic spectrum and the relevant relaxation function. It was also shown that, in general, for motions which are neither irrotational nor solenoidal, this correspondence exists only for a restricted class of viscoelastic materials. Author