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Non-uniform beams and stiff strings isospectral to axially loaded uniform beams and piano strings

Kambampati, Sandilya and Ganguli, Ranjan (2015) Non-uniform beams and stiff strings isospectral to axially loaded uniform beams and piano strings. In: ACTA MECHANICA, 226 (4). pp. 1227-1239.

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Official URL: http://dx.doi.org/10.1007/s00707-014-1238-6

Abstract

In this paper, we derive analytical expressions for mass and stiffness functions of transversely vibrating clamped-clamped non-uniform beams under no axial loads, which are isospectral to a given uniform axially loaded beam. Examples of such axially loaded beams are beam columns (compressive axial load) and piano strings (tensile axial load). The Barcilon-Gottlieb transformation is invoked to transform the non-uniform beam equation into the axially loaded uniform beam equation. The coupled ODEs involved in this transformation are solved for two specific cases (pq (z) = k (0) and q = q (0)), and analytical solutions for mass and stiffness are obtained. Examples of beams having a rectangular cross section are shown as a practical application of the analysis. Some non-uniform beams are found whose frequencies are known exactly since uniform axially loaded beams with clamped ends have closed-form solutions. In addition, we show that the tension required in a stiff piano string with hinged ends can be adjusted by changing the mass and stiffness functions of a stiff string, retaining its natural frequencies.

Item Type: Journal Article
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Additional Information: Copy right for this article belongs to the SPRINGER WIEN, SACHSENPLATZ 4-6, PO BOX 89, A-1201 WIEN, AUSTRIA
Keywords: NATURAL FREQUENCIES; CIRCULAR MEMBRANES; DENSITY
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering (Formerly, Aeronautical Engineering)
Date Deposited: 23 Apr 2015 07:39
Last Modified: 23 Apr 2015 07:39
URI: http://eprints.iisc.ernet.in/id/eprint/51354

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