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Determination Of Isopectral Rotating And Non-Rotating Beams

Electronic Theses of Indian Institute of Science

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Field Value
 
Title Determination Of Isopectral Rotating And Non-Rotating Beams
 
Creator Kambampati, Sandilya
 
Subject Isospectral Systems
Rotating Beams
Isopectral Beams
Non-rotating Beams
Isospectral Rotating Beams
Isospectral Non-Rotating Beams
Rotating Uniform Beam
Uniform Non-Rotating Beams
Non-Rotating Uniform Beams
Isospectral Non-Uniform Rotating Beams
Rotating Beam
Structural Engineering
 
Description In this work, rotating beams which are isospectral to non-rotating beams are studied. A rotating beam is isospectral to a non-rotating beam if both the beams have the same spectral properties i.e; both the beams have the same set of natural frequencies under a given boundary condition. The Barcilon-Gottlieb transformation is extended, so that it converts the fourth order governing equation of a rotating beam (uniform or non-uniform), to a canonical fourth order eigenvalue equation. If the coefficients in this canonical equation match with the coefficients of the non-rotating beam (non-uniform or uniform) equation, then the rotating and non-rotating beams are isospectral to each other. The conditions on matching the coefficients lead to a pair of coupled differential equations. We solve these coupled differential equations for a particular case, and thereby obtain a class of isospectral rotating and non-rotating beams. However, to obtain isospectral beams, the transformation must leave the boundary conditions invariant. We show that the clamped end boundary condition is always invariant, and for the free end boundary condition to be invariant, we impose certain conditions on the beam characteristics. The mass and stiffness functions for the isospectral rotating and non-rotating beams are obtained. We use these mass and stiffness functions in a finite element analysis to verify numerically the isospectral property of the rotating and non-rotating beams. Finally, the example of beams having a rectangular cross section is presented to show the application of our analysis. Since experimental determination of rotating beam frequencies is a difficult task, experiments can be easily conducted on these rectangular non-rotating beams, to calculate the frequencies of the isospectral rotating beams.
 
Contributor Ganguli, Ranjan
Mani, V
 
Date 2016-04-27T07:07:09Z
2016-04-27T07:07:09Z
2016-04-27
2012-08
 
Type Thesis
 
Identifier http://etd.iisc.ernet.in/handle/2005/2523
http://etd.ncsi.iisc.ernet.in/abstracts/3274/G25558-Abs.pdf
 
Language en_US
 
Relation G25558