A note on the inverse mode shape problem for bars, beams, and plates

Sundaram, Meenakshi M and Ananthasuresh, GK (2013) A note on the inverse mode shape problem for bars, beams, and plates. In: INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 21 (1). pp. 1-16.

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Abstract

Motivated by the idea of designing a structure for a desired mode shape, intended towards applications such as resonant sensors, actuators and vibration confinement, we present the inverse mode shape problem for bars, beams and plates in this work. The objective is to determine the cross-sectional profile of these structures, given a mode shape, boundary condition and the mass. The contribution of this article is twofold: (i) A numerical method to solve this problem when a valid mode shape is provided in the finite element framework for both linear and nonlinear versions of the problem. (ii) An analytical result to prove the uniqueness and existence of the solution in the case of bars. This article also highlights a very important question of the validity of a mode shape for any structure of given boundary conditions.

Item Type:	Journal Article
Publication:	INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
Publisher:	TAYLOR & FRANCIS LTD
Additional Information:	Copyright for this article belongs to TAYLOR & FRANCIS LTD, ENGLAND
Keywords:	inverse mode shape problem;nonlinear eigenvalue problem;valid mode shape
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	07 Feb 2013 11:47
Last Modified:	07 Feb 2013 11:47
URI:	http://eprints.iisc.ac.in/id/eprint/45719

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