FORCED MOTIONS OF ELASTIC RODS
COLUMBIA UNIV NEW YORK DEPT OF CIVIL ENGINEERING AND ENGINEERING MECHANICS
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A formal solution is presented of the equations of motion, the stress-strain relationships, and the boundary conditions in Mindlin and Herrmanns 1-dimensional theory of vibrations of rods incorporating the effects of radial inertia and shear deformation Proc. US Nat. Cong. Appl. Mech., Chicago, 1951. Lagranges equations of motion are used to develop solutions for a rod of finite length and any admissible combination of time-dependent boundary displacements and arbitrary initial conditions.