SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2006 / Cilt: 35 - Sayı: 1

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

ALois KUFNER
George V. JAIANI
Pages
7–53
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The well-posedness of the admissible problems has been proved by means of the Lax-Milgram theorem.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, mathematical problems of cusped Euler-Bernoulli beams and Kirchhoff-Love plates are considered.
📊
Key Findings & Data:Changes in the beam crosssection area and the plate thickness are, in general, of non-power type.
💡
Conclusion & Impact:The well-posedness of the admissible problems has been proved by means of the Lax-Milgram theorem.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Cusped elastic plate · Cusped elastic beams · Vibration

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.

🔖

Cite This Article

KUFNER, A., JAIANI, G. V. (2022). OSCILLATION OF CUSPED EULER-BERNOULLI BEAMS AND KIRCHHOFF-LOVE PLATES. Hacettepe Journal of Mathematics and Statistics, Cilt: 35 - Sayı: 1, 7–53. https://ajindex.com/articles/530767

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (15)

  1. Bitsadze, A. V. Mixed-Type Equations ((in Russian) Moscow, 1959 ). Donnel, L. H. Beams, Plates, and Shells (McGraw-Hill Book Company, 1976).
  2. Jaiani, G. V. On the deflections of thin wedge-shapped shells, Bulletin of the Academy of Sciences of the Georgian Republic 65 (3) (in Russian), 543–546, 1972.
  3. Jaiani, G. V. Elastic bodies with non-smooth boundaries-cusped plates and shells, ZAMM 76Suppl. 2, 117–120, 1996.
  4. Jaiani, G. V. Initial and Boundary Value Problems for Singular Differential Equations and Applications to the Theory of Cusped Bars and Plates, ISAAC Serials Vol. 6, Eds.: H. Begehr, O. Celebi, W. Tutschke, Kluwer, Dordrecht, 113–149, 1999.
  5. Jaiani, G. V. On a mathematical model of bars with variable rectangular cross-sections, ZAMM-Zeitschrift fuer Angewandte Mathematik und Mechanik 81 (3), 147–173, 2001.
  6. Jaiani, G. V. Bending of an orthotropic cusped plate, Applied Mathematics and Informa- tioncs 4 (1), 29–65, 1999.
  7. Keldysh, M. V. On Some Cases of Degeneration of an Equation of Elliptic Type on the Domain Boundary, DAN SSSR 77 (2), 181–183, 1951.
  8. Kharibegashvili, S. S. and Jaiani, G. V. Dynamical Problems in the (0,0) and (1,0) Approx- imations of a Mathematical Model of Cusped Bars, Proceedings of the International Graz Workshop, Functional-Analytic and Complex Methods, Interactions, and Applications to Partial Differential Equations, World Scientific, 188–248, 2001.
  9. Khvoles, A. R. The general representation for solutions of equilibrium equations of prismatic shell with variable thickness, Seminar of the Institute of Applied Mathematics of Tbilisi State University, Annot. of Reports 5 (in Russian), 19–21, 1971.
  10. Kiguradze, I. T. and Shekhter, B. L. Singular Boundary Value Problems for Ordinary Dif- ferential Equations of the Second Order (Itogi Nauki i Tekhniki, Ser. Sovrem. Probl. Mat., Nov. Dost., 30 (in Russian), (Moscow, 1987).
  11. Kufner, A. Weighted Sobolev Spaces (John Wiley & Sons, 1985).
  12. Kufner, A. and Opic, B. How to define reasonably weighted sobolev spaces, Commentations Mathematicae Universitatis Carolinae 25 (3), 537–554, 1984.
  13. Mikhlin, S. G. Variational Methods in Mathematical Physics ((in Russian) Nauka, Moscow, 1970).
  14. Naguleswaran, S. The vibration of a “complete” Euler-Bernoulli beam of constant depth and breadth proportional to axial coordinate raised to a positive exponent. J. Sound Vib. 187(2), 311–327, 1995.
  15. Nikolskii, S. M. Approximation of Functions of Several Variables and Embedding theorems ((in Russian) Moscow, 1977). Nikolsk