A new approach to compute natural frequencies and mode shapes of non-uniform continuous bar, circular shaft and beam vibration

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

The wave equation governing longitudinal vibration of a bar and torsional vibration of a circular shaft, and the Euler-Bernoulli equation governing transverse vibration of a beam were developed in the eighteenth century. Natural frequencies and mode shapes are easily obtained for uniform or constant spatial parameters (cross sectional area, material property and mass distribution). But, real engineering structures seldom have constant parameters. For non-uniform continuous structure, a large number of papers have been written for more than 100 years since the publication of Kirchhoff’s memoir in 1882. There are analytical solutions only in few cases, and there are approximate numerical methods to deal with other (almost all) cases, most notably Stodola, Holzer and Myklestad methods in addition to Rayleigh-Ritz and finite element methods. This paper presents a novel approach to compute natural frequencies and mode shapes for arbitrary variations of spatial parameters on the basis of linear time-varying system theory. The advantage of this approach is that now it can be claimed that “almost” closed-form solutions are available to find natural frequencies and mode shapes of any non-uniform, linear and one-dimensional continuous structure.

Original languageEnglish (US)
Title of host publication31st Conference on Mechanical Vibration and Noise
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791859285
DOIs
StatePublished - Jan 1 2019
EventASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2019 - Anaheim, United States
Duration: Aug 18 2019Aug 21 2019

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume8

Conference

ConferenceASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2019
CountryUnited States
CityAnaheim
Period8/18/198/21/19

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation

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