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Benchmark analytical solutions from beams with shared eigenpair

Sarkar, Korak and Ganguli, Ranjan (2016) Benchmark analytical solutions from beams with shared eigenpair. In: INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, 106 . pp. 245-253.

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Official URL: http://dx.doi.org/10.1016/j.ijmecsci.2015.12.017

Abstract

Structures with governing equations having identical inertial terms but somewhat differing stiffness terms can be termed flexurally analogous. An example of such a structure includes an axially loaded non-uniform beam and an unloaded uniform beam, for which an exact solution exists. We find that there exist shared eigenpairs (frequency and mode shapes) for a particular mode between such structures. Non-uniform beams with uniform axial loads, gravity loaded beams and rotating beams are considered and shared eigenpairs with uniform beams are found. In general, the derived flexural stiffness functions (FSF's) for the non-uniform beams required for the existence of shared eigenpair have internal singularities, but some of the singularities can be removed by an appropriate selection of integration constants using the theory of limits. The derived functions yield an insight into the relationship between the axial load and flexural stiffness of axially loaded beam structures. The derived functions can serve as benchmark solutions for numerical methods. (C) 2016 Elsevier Ltd. All rights reserved.

Item Type: Journal Article
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Additional Information: Copy right for this article belongs to the PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
Keywords: Rotating beams; Shared eigenpair; Gravity-loaded beams; Free vibration; Test functions
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering (Formerly, Aeronautical Engineering)
Date Deposited: 06 Apr 2016 07:34
Last Modified: 07 Apr 2016 07:29
URI: http://eprints.iisc.ernet.in/id/eprint/53632

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