Skip to main content
SpringerLink
Log in

Nonlinear vibrations of elastic circular plates exhibiting rectilinear orthotropy

  • Original Papers
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Zusammenfassung

Es werden mittels einer Verallgemeinerung der von-Kármánschen Gleichungen auf den dynamischen und orthotropen Fall die nichtlinearen Schwingungen elastisch orthotroper Kreisplatten untersucht. Die Bewegungsgleichung wird mittels des Galerkin-Verfahrens von den Ortsvariablen befreit. Als Beispiel wird Einspannung des Randes unter Erhaltung der radialen Verschieblichkeit angenommen, und es wird unter diesen Randbedingungen der Einfluss der Anisotropie und der relativen Amplitude auf die Eigenschwingungen sowie den Spannungszustand studiert. Als Sonderfall wird der nichtlineare Gleichgewichtszustand diskutiert.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. J. Nowinski,Nonlinear Transverse Vibrations of Circular Elastic Plates Built-In at the Boundary, Proc. Fourth U.S. Nat. Congr. Appl. Mech., Berkeley 1962 (forthcoming).

  2. E. F. Burmistrov,Nonlinear Transverse Vibrations of Orthotropic Shells of Revolution (in Russian), Insh. Sbornik26 (1958), 5–20.

    Google Scholar 

  3. S. G. Lekhnitski,Anisotropic Plates (in Russian) (1957), 375.

  4. J. Nowinski,Application of Some Familiar Approximate Methods to Problems Concerning Orthotropic Plates with Large Deflections (in Polish), Rozpr. Inz.9 (1957), 331.

    Google Scholar 

  5. M. Hirsch,Integraltafeln (Duncker and Humblot, Berlin 1810).

    Google Scholar 

  6. S. P. Timoshenko,Vibration Problems in Engineering (Van Nostrand Co., 1937), 449.

  7. A. S. Volmir,Flexible Plates and Shells (in Russian) (1956), 188.

  8. N. W. McLachlan,Ordinary Non-Linear Differential Equations (Clarendon Press, 1958).

  9. E. I. Grigoliuk,Nonlinear Vibrations and Stability of Shallow Shells and Rods (in Russian), Izv. Ak. Nauk SSR, Otd. T.N., No.3 (1955), 33.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dpt. of Mechanical Engineering, University of Delaware, Newark, Delaware, U.S.A.

    Jerzy L. Nowinski

Authors
  1. Jerzy L. Nowinski
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The preparation of this paper has been sponsored in part by the National Defense Education Act.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nowinski, J.L. Nonlinear vibrations of elastic circular plates exhibiting rectilinear orthotropy. Journal of Applied Mathematics and Physics (ZAMP) 14, 112–124 (1963). https://doi.org/10.1007/BF01589264

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01589264

Keywords

Search

Navigation