Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-31T19:45:22.937Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on the Free Vibrations of Cantilever Plates with Swept-Back Leading Edge*

Published online by Cambridge University Press:  04 July 2016

A. Kornecki  and
G. Maimon
A. Kornecki
Affiliation:
Technion Israel Institute of Technology, on leave to Courant Institute of Mathematical Sciences, New York University
G. Maimon
Affiliation:
Technion Israel Institute of Technology, on leave to Courant Institute of Mathematical Sciences, New York University
Get access Rights & Permissions [Opens in a new window]

Extract

Free vibrations of triangular and trapezoidal plates have been analysed recently theoretically and experimentally by many authors. Some of them applied the Rayleigh-Ritz procedure, while others proposed to use the Kantorovich-Vlasov method, reducing the problem to solution of an ordinary differential equation.

In this note, the method developed in ref. 7 on the basis of Reissner’s modified variational theory is extended to include trapezoidal cantilever plates (Fig. 1).

Comparison of theory and experiment shows that, retaining four terms in the deflection function, one obtains three natural frequencies to a high degree of accuracy.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 70 , Issue 665 , May 1966 , pp. 604 - 605
Copyright
Copyright © Royal Aeronautical Society 1966

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

This note forms a part of G. Maimon’s M.Sc. Thesis at the Aeronautical Engineering Department of the Technion, Israel Institute of Technology.

References

1. Gustafson, G. N. et al The effect of tip removal on the natural vibrations of uniform cantilever triangular plates. Journal of Aer. Science, 1954. Vol. 21, p. 621–627.Google Scholar
2. Heiba, A. E. Vibration characteristics of a cantilever plate with swept-back leading edge. College of Aeronaut. Rep. No. 82, 1954.Google Scholar
3. Kawai, T. et al On the natural vibration of plate like wing. Proceedings of the XIIth Japan National Congress of Applied Mechanics, 1962, p. 225–229.Google Scholar
4. Marchenko, G. S. Investigation in vibrations of skew triangular and trapezoidal plates (in Russian), Aviatsionnaja Tekhnika, 1965, Vol. 8, p. 115–119.Google Scholar
5. Nagaradja, J. V. Effect of tip removal upon the frequencies of natural vibrations of triangular plates. Journal of Sc. Industr. Research, 1961, Vol. 20B, p. 479–482.Google Scholar
6. Ryabinskii, N. L. Calculation of cantilever plates by the variational method of V. Z. Vlasov (in Russian), Aviatsionnaja Tekhnika, 1963, Vol. 6, p. 58–66.Google Scholar
7. Plass, H. J. et al. Application of Reissner’s variational principle to cantilever plate deflection and vibration problems. Journal of Applied Mechanics, 1962, Vol. 29, p. 127–135.Google Scholar
8. Kantorovich, L. V. On a method of approximate solution of partial differential equations (in Russian), Transactions (Doklady) of The Acad, of Sc. of USSR, 1934, Vol. 2, p. 532–536.Google Scholar
9. Reissner, E. On a variational theorem in elasticity. Journal of Math, and Physics, 1950, Vol. 29, p. 90–95.Google Scholar
10. Vlasov, V. Z. Approximate theory of prismatic folded structures and plates (in Russian). Collected papers: Investigations in the Dynamics of Structures. Edited by: Rabinowitz, I. M., Moscow 1947, p. 5–74.Google Scholar