TY - GEN
T1 - Computing natural frequencies and mode shapes of an axially moving non-uniform beam
AU - Sinha, Alok
N1 - Publisher Copyright:
Copyright © 2020 ASME.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
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.
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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 -