OSCILLATION OF CUSPED EULER-BERNOULLI BEAMS AND KIRCHHOFF-LOVE PLATES

Abstract

In this paper, mathematical problems of cusped Euler-Bernoulli beams and Kirchhoff-Love plates are considered. Changes in the beam crosssection area and the plate thickness are, in general, of non-power type. The criteria of admissibility of the classical bending boundary conditions [clamped end (edge), sliding clamped end (edge), and supported end (edge)] at the cusped end of the beam and on the cusped edge of the plate have been established. The cusped end of the beam and the cusped edge of the plate can always be free independent of thecharacter of the sharpening. A sufficient conditions for the solvability of the vibration frequency have been established. The appropriate weighted Sobolev spaces have been constructed. The well-posedness of the admissible problems has been proved by means of the Lax-Milgram theorem.