BOUNDARY CONDITIONS AND VIBRATION OF SLENDER BEAMS

Abstract eng:
The list of all possible boundary conditions corresponding to particular differential operator is much greater than usually presented in open literature. Gallery of various types of boundary conditions is presented for coupled bending-torsional vibration of a bar in compression and torsion. General condition to decide the selfadjointness is derived. Referenced cases are classified into selfadjoint or nonselfadjoint boundary conditions. Class of problems is distinguished, for which their selfadjointness guarantees the validity of the Euler method of stability analysis. For nonselfadjoint boundary conditions the stability analysis has to be carried out as dynamical problem even when the bar under consideration is loaded only statically.

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