Abstract
In this paper, based on the theory of refined dynamic equations of thick plates bending, applied the differential operator algebra and decomposition of operator spectra, the refined dynamic equation of the beam flexural motion is first obtained by using proper gauge conditions and satisfying the boundary conditions. The refined equation of beams is a fourth-order equation, which governs the generalized displacement functions <italic>W</italic>, <italic>F</italic> and <italic>f</italic>. The dispersion relations, which are from the given beam theory, Euler-Bernoulli beam and Timoshenko beam, respectively, are compared. The refined equations of thick beams and applicable condition are investigated and discussed. Since derivation of the refined dynamic equation is conducted without any assumptions, so the proposed equation of thick beam bending is exact, that can be used to analyze vibration of thick beams at the high frequency and to evaluate the applicable condition of the engineering beam theory.
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