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Dynamics of Elastic Foundations and Constrained Bars
WATERVLIET ARSENAL NY
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A variational principle is used to derive the equations of motion of a slender bar that has one lateral face clamped or welded onto a rigid surface. Correction factors for the transverse shear and normal strains are incorporated into the expression for the strain energy of the system. These factors are evaluated by requiring the lowest depth-shear and depth-stretch frequencies, as derived from the new approximate theory, to agree with the corresponding frequencies obtained from the full theory of generalized plane stress. The frequency equation for a simple supported constrained bar is derived, and plots of the variations of the natural frequencies of the transverse and longitudinal modes versus the length to depth ratio of the bar are presented.
APPROVED FOR PUBLIC RELEASE