Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Deformation and Vibration of an Oblique Elliptic Torus

Version 1 : Received: 10 March 2021 / Approved: 11 March 2021 / Online: 11 March 2021 (08:39:27 CET)

How to cite: Sun, B. Deformation and Vibration of an Oblique Elliptic Torus. Preprints 2021, 2021030300 (doi: 10.20944/preprints202103.0300.v1). Sun, B. Deformation and Vibration of an Oblique Elliptic Torus. Preprints 2021, 2021030300 (doi: 10.20944/preprints202103.0300.v1).

Abstract

The formulation used by the most of studies on an elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of the torus, application of those formulations has encountered great difficulty. It is highly demanded to have a displacement-type formulation for the torus. In this paper, I will simulate some typical problems and free vibration of the torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. My investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than outer torus due to the property of their Gaussian curvature. Regarding the free vibration of the torus, our analysis indicates that both initial in u and w direction must be included otherwise will cause big errors in eigenfrequency.

Subject Areas

elliptic torus; oblique; deformation; vibration; Gauss curvature; Maple

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.