Instability of an oscillator moving along a thin ring on a viscoelastic foundation

Tao Lu; Andrei Metrikine

doi:10.1016/j.proeng.2017.09.323

Instability of an oscillator moving along a thin ring on a viscoelastic foundation

Tao Lu, Andrei Metrikine

Research output: Contribution to journal › Conference article › Scientific › peer-review

2 Citations (Scopus)

52 Downloads (Pure)

Abstract

The stability of an oscillator uniformly moving along a thin ring that is connected to an immovable axis by a distributed viscoelastic foundation has been studied. The dynamic reaction of the ring to the oscillator is represented by a frequency and velocity dependent equivalent stiffness. The characteristic equation for the vibration of the oscillator is obtained. It is shown that this equation can have roots with a positive real part, which imply the exponential increase of the amplitude of the oscillator’s vibration in time, i.e. instability. The critical velocity after which instability can occur is determined. With the help of the D-decomposition method, the instability domains are found in the space of the system parameters. Parametric study of the stability domains is carried out.

Original language	English
Pages (from-to)	2555-2560
Number of pages	6
Journal	Procedia Engineering
Volume	199
DOIs	https://doi.org/10.1016/j.proeng.2017.09.323
Publication status	Published - 2017
Event	10th international conference on recent advances in structural dynamics - Faculty of Civil and Industrial Engineering of Sapienza University of Rome, Roma, Italy Duration: 12 Jul 2010 → 14 Jul 2010 Conference number: 10 https://www.eurodyn2017.it/

Keywords

Thin ring
viscoelastic foundation
moving oscillator
instability

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10.1016/j.proeng.2017.09.323

1-s2.0-S1877705817338080-mainFinal published version, 557 KBLicence: CC BY-NC-ND

Cite this

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title = "Instability of an oscillator moving along a thin ring on a viscoelastic foundation",

abstract = "The stability of an oscillator uniformly moving along a thin ring that is connected to an immovable axis by a distributed viscoelastic foundation has been studied. The dynamic reaction of the ring to the oscillator is represented by a frequency and velocity dependent equivalent stiffness. The characteristic equation for the vibration of the oscillator is obtained. It is shown that this equation can have roots with a positive real part, which imply the exponential increase of the amplitude of the oscillator{\textquoteright}s vibration in time, i.e. instability. The critical velocity after which instability can occur is determined. With the help of the D-decomposition method, the instability domains are found in the space of the system parameters. Parametric study of the stability domains is carried out.",

keywords = "Thin ring, viscoelastic foundation, moving oscillator, instability",

author = "Tao Lu and Andrei Metrikine",

year = "2017",

doi = "10.1016/j.proeng.2017.09.323",

language = "English",

volume = "199",

pages = "2555--2560",

journal = "Procedia Engineering",

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note = "10th international conference on recent advances in structural dynamics, EURODYN 2017 ; Conference date: 12-07-2010 Through 14-07-2010",

url = "https://www.eurodyn2017.it/",

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TY - JOUR

T1 - Instability of an oscillator moving along a thin ring on a viscoelastic foundation

AU - Lu, Tao

AU - Metrikine, Andrei

N1 - Conference code: 10

PY - 2017

Y1 - 2017

N2 - The stability of an oscillator uniformly moving along a thin ring that is connected to an immovable axis by a distributed viscoelastic foundation has been studied. The dynamic reaction of the ring to the oscillator is represented by a frequency and velocity dependent equivalent stiffness. The characteristic equation for the vibration of the oscillator is obtained. It is shown that this equation can have roots with a positive real part, which imply the exponential increase of the amplitude of the oscillator’s vibration in time, i.e. instability. The critical velocity after which instability can occur is determined. With the help of the D-decomposition method, the instability domains are found in the space of the system parameters. Parametric study of the stability domains is carried out.

AB - The stability of an oscillator uniformly moving along a thin ring that is connected to an immovable axis by a distributed viscoelastic foundation has been studied. The dynamic reaction of the ring to the oscillator is represented by a frequency and velocity dependent equivalent stiffness. The characteristic equation for the vibration of the oscillator is obtained. It is shown that this equation can have roots with a positive real part, which imply the exponential increase of the amplitude of the oscillator’s vibration in time, i.e. instability. The critical velocity after which instability can occur is determined. With the help of the D-decomposition method, the instability domains are found in the space of the system parameters. Parametric study of the stability domains is carried out.

KW - Thin ring

KW - viscoelastic foundation

KW - moving oscillator

KW - instability

UR - http://resolver.tudelft.nl/uuid:e5aca022-a283-4ff8-a2b9-f12abc07c0b7

U2 - 10.1016/j.proeng.2017.09.323

DO - 10.1016/j.proeng.2017.09.323

M3 - Conference article

SN - 1877-7058

VL - 199

SP - 2555

EP - 2560

JO - Procedia Engineering

JF - Procedia Engineering

T2 - 10th international conference on recent advances in structural dynamics

Y2 - 12 July 2010 through 14 July 2010

ER -

Instability of an oscillator moving along a thin ring on a viscoelastic foundation

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