The University of Southampton
University of Southampton Institutional Repository

The generalized Vincent circle in vibration suppression

The generalized Vincent circle in vibration suppression
The generalized Vincent circle in vibration suppression
In 1972 A. H. Vincent, the then Chief Dynamicist at Westland Helicopters, discovered that when a structure excited at point p with a constant frequency is modified, for example by the addition of a spring between two points r and s, then the response at another point q traces a circle when plotted in the complex plane as the spring stiffness is varied from minus infinity to plus infinity. This discovery, although apparently little known today, has many useful applications some of which are described in papers by various authors appearing in the 1970s and early 1980s. Vincent's discovery is in fact a particular example of the bilinear transformation due to August Ferdinand Moebius (1790–1868). In this paper, the Vincent circle method is generalized for the case of any straight-line modification in the complex plane, typically z=k+i?c–?2m, where c=?(k-?2m)+?. A new method for the visualization of Vincent circle results, including the case of multiple modifications is also presented.
0022-460X
661-675
Ghandchi Tehrani, Maryam
c2251e5b-a029-46e2-b585-422120a7bc44
Wang, Weizhuo
c1016898-10c0-430f-bf78-db8371c31541
Mares, Cristinel
d0015cd9-3c54-40f1-9018-8f83af17c4dc
Mottershead, John E.
5d20857f-6fb2-4d26-974b-3a0f1f3b36ff
Ghandchi Tehrani, Maryam
c2251e5b-a029-46e2-b585-422120a7bc44
Wang, Weizhuo
c1016898-10c0-430f-bf78-db8371c31541
Mares, Cristinel
d0015cd9-3c54-40f1-9018-8f83af17c4dc
Mottershead, John E.
5d20857f-6fb2-4d26-974b-3a0f1f3b36ff

Ghandchi Tehrani, Maryam, Wang, Weizhuo, Mares, Cristinel and Mottershead, John E. (2006) The generalized Vincent circle in vibration suppression. Journal of Sound and Vibration, 292 (3-5), 661-675. (doi:10.1016/j.jsv.2005.08.024).

Record type: Article

Abstract

In 1972 A. H. Vincent, the then Chief Dynamicist at Westland Helicopters, discovered that when a structure excited at point p with a constant frequency is modified, for example by the addition of a spring between two points r and s, then the response at another point q traces a circle when plotted in the complex plane as the spring stiffness is varied from minus infinity to plus infinity. This discovery, although apparently little known today, has many useful applications some of which are described in papers by various authors appearing in the 1970s and early 1980s. Vincent's discovery is in fact a particular example of the bilinear transformation due to August Ferdinand Moebius (1790–1868). In this paper, the Vincent circle method is generalized for the case of any straight-line modification in the complex plane, typically z=k+i?c–?2m, where c=?(k-?2m)+?. A new method for the visualization of Vincent circle results, including the case of multiple modifications is also presented.

Full text not available from this repository.

More information

Published date: 9 May 2006

Identifiers

Local EPrints ID: 188551
URI: https://eprints.soton.ac.uk/id/eprint/188551
ISSN: 0022-460X
PURE UUID: c0d9a768-89bf-4821-99f0-43c701b363f9

Catalogue record

Date deposited: 31 May 2011 14:10
Last modified: 18 Jul 2017 11:42

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×