Mathematical Analysis of Stability of a Spinning Disk Under Rotating, Arbitrarily Large Damping Forces

Author:

Huang F. Y.1,Mote C. D.1

Affiliation:

1. Department of Mechanical Engineering, University of California, Berkeley, Berkeley, CA 94720

Abstract

Stability of a rotating disk under rotating, arbitrarily large damping forces is investigated analytically. Points possibly residing on the stability boundary are located exactly in parameter space based on the criterion that at least one nontrivial periodic solution is necessary at every boundary point. A perturbation technique and the Galerkin method are used to predict whether these points of periodic solution reside on the stability boundary, and to identify the stable region in parameter space. A nontrivial periodic solution is shown to exist only when the damping does not generate forces with respect to that solution. Instability occurs when the wave speed of a mode in the uncoupled disk, when observed on the disk, is exceeded by the rotation speed of the damping force relative to the disk. The instability is independent of the magnitude of the force and the type of positive-definite damping operator in the applied region. For a single dashpot, nontrivial periodic solutions exist at the points where the uncoupled disk has repeated eigenfrequencies on a frame rotating with the dashpot and the dashpot neither damps nor energizes these modes substantially around these points.

Publisher

ASME International

Subject

General Engineering

Cited by 23 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3