Computing natural frequencies and mode shapes of an axially moving non-uniform beam

Alok Sinha

doi:10.1115/DETC2020-22073

Computing natural frequencies and mode shapes of an axially moving non-uniform beam

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The partial differential equation of motion of an axially moving beam with spatially varying geometric, mass and material properties has been derived. Using the theory of linear time-varying systems, a general algorithm has been developed to compute natural frequencies, mode shapes, and the critical speed for stability. Numerical results from the new method are presented for beams with spatially varying rectangular cross sections with sinusoidal variation in thickness and sine-squared variation in width. They are also compared to those from the Galerkin method. It has been found that critical speed of the beam can be significantly reduced by non-uniformity in a beam's cross section.

Original language	English (US)
Title of host publication	32nd Conference on Mechanical Vibration and Noise (VIB)
Publisher	American Society of Mechanical Engineers (ASME)
ISBN (Electronic)	9780791883969
DOIs	https://doi.org/10.1115/DETC2020-22073
State	Published - 2020
Event	ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020 - Virtual, Online Duration: Aug 17 2020 → Aug 19 2020

Publication series

Name	Proceedings of the ASME Design Engineering Technical Conference
Volume	7

Conference

Conference	ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020
City	Virtual, Online
Period	8/17/20 → 8/19/20

All Science Journal Classification (ASJC) codes

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

Access to Document

10.1115/DETC2020-22073

Cite this

@inproceedings{6f82feed6cb6475eb946fe8ed3567e99,

title = "Computing natural frequencies and mode shapes of an axially moving non-uniform beam",

abstract = "The partial differential equation of motion of an axially moving beam with spatially varying geometric, mass and material properties has been derived. Using the theory of linear time-varying systems, a general algorithm has been developed to compute natural frequencies, mode shapes, and the critical speed for stability. Numerical results from the new method are presented for beams with spatially varying rectangular cross sections with sinusoidal variation in thickness and sine-squared variation in width. They are also compared to those from the Galerkin method. It has been found that critical speed of the beam can be significantly reduced by non-uniformity in a beam's cross section.",

author = "Alok Sinha",

note = "Publisher Copyright: Copyright {\textcopyright} 2020 ASME. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020 ; Conference date: 17-08-2020 Through 19-08-2020",

year = "2020",

doi = "10.1115/DETC2020-22073",

language = "English (US)",

series = "Proceedings of the ASME Design Engineering Technical Conference",

publisher = "American Society of Mechanical Engineers (ASME)",

booktitle = "32nd Conference on Mechanical Vibration and Noise (VIB)",

}

Sinha, A 2020, Computing natural frequencies and mode shapes of an axially moving non-uniform beam. in 32nd Conference on Mechanical Vibration and Noise (VIB)., V007T07A033, Proceedings of the ASME Design Engineering Technical Conference, vol. 7, American Society of Mechanical Engineers (ASME), ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020, Virtual, Online, 8/17/20. https://doi.org/10.1115/DETC2020-22073

Computing natural frequencies and mode shapes of an axially moving non-uniform beam. / Sinha, Alok.
32nd Conference on Mechanical Vibration and Noise (VIB). American Society of Mechanical Engineers (ASME), 2020. V007T07A033 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 7).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Computing natural frequencies and mode shapes of an axially moving non-uniform beam

AU - Sinha, Alok

PY - 2020

Y1 - 2020

N2 - The partial differential equation of motion of an axially moving beam with spatially varying geometric, mass and material properties has been derived. Using the theory of linear time-varying systems, a general algorithm has been developed to compute natural frequencies, mode shapes, and the critical speed for stability. Numerical results from the new method are presented for beams with spatially varying rectangular cross sections with sinusoidal variation in thickness and sine-squared variation in width. They are also compared to those from the Galerkin method. It has been found that critical speed of the beam can be significantly reduced by non-uniformity in a beam's cross section.

AB - The partial differential equation of motion of an axially moving beam with spatially varying geometric, mass and material properties has been derived. Using the theory of linear time-varying systems, a general algorithm has been developed to compute natural frequencies, mode shapes, and the critical speed for stability. Numerical results from the new method are presented for beams with spatially varying rectangular cross sections with sinusoidal variation in thickness and sine-squared variation in width. They are also compared to those from the Galerkin method. It has been found that critical speed of the beam can be significantly reduced by non-uniformity in a beam's cross section.

UR - http://www.scopus.com/inward/record.url?scp=85096192756&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85096192756&partnerID=8YFLogxK

U2 - 10.1115/DETC2020-22073

DO - 10.1115/DETC2020-22073

M3 - Conference contribution

AN - SCOPUS:85096192756

T3 - Proceedings of the ASME Design Engineering Technical Conference

BT - 32nd Conference on Mechanical Vibration and Noise (VIB)

PB - American Society of Mechanical Engineers (ASME)

T2 - ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020

Y2 - 17 August 2020 through 19 August 2020

ER -

Computing natural frequencies and mode shapes of an axially moving non-uniform beam

Abstract

Publication series

Conference

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this