A theory of vibrations of ship beams

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A theory of vibrations of ship beams

Doekmeci, M.C.

An isothermal, deterministic, large deflection theory for vibrations of ship beams is developed. The stearting point for derivation is the three-dimensional equations of elastodynamics in terms of a reference state. First, one-dimensional governing equations of successively higher orders of approximation of the theory are systematically and consistently derived by use of a recent variational principle together with a series expansions for kinematic variables. Then, certain special cases of interest are pointed out, and in particular, the linearized version of the dynamical theory is presented. Also, a theorem of uniqueness is established in solutions of the linearized governing equations of ship beams. Further, the influence of hydrodynamic pressure on ship beams immersed in an ideal fluid is studied. The results incorporate the effects of warping, shear deformations, rotatory inertia and of temperature as deemed necessary in any particular case for ship beams made of anisotropic, non-polar elastic material.(Wassmann)