Inhomogeneous beams possessing an exponential mode shape

R. Gilat; I. Calio; I. Elishakoff

doi:10.1016/j.mechrescom.2010.04.003

Inhomogeneous beams possessing an exponential mode shape

R. Gilat, I. Calio, I. Elishakoff

Department of Civil Engineering

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

In this study inhomogeneous beams which posses exponential fundamental mode shapes are constructed. Closed-form solutions are derived for five cases of boundary conditions: (a) a beam with two free edges, (b) a cantilevered beam, (c) a beam that is clamped at both ends, (d) a simply supported beam and (e) a beam that is clamped at one end and simply supported at the other. The solutions can be utilized for axially varying the moment of inertia of the cross-section and/or functionally grading the material's modulus of elasticity in order to construct beams with prescribed vibration modes.

Original language	English
Pages (from-to)	417-426
Number of pages	10
Journal	Mechanics Research Communications
Volume	37
Issue number	4
DOIs	https://doi.org/10.1016/j.mechrescom.2010.04.003
State	Published - Jun 2010

Keywords

Exponential form
Inhomogeneous beam
Inverse problem
Prescribed vibration mode

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10.1016/j.mechrescom.2010.04.003

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abstract = "In this study inhomogeneous beams which posses exponential fundamental mode shapes are constructed. Closed-form solutions are derived for five cases of boundary conditions: (a) a beam with two free edges, (b) a cantilevered beam, (c) a beam that is clamped at both ends, (d) a simply supported beam and (e) a beam that is clamped at one end and simply supported at the other. The solutions can be utilized for axially varying the moment of inertia of the cross-section and/or functionally grading the material's modulus of elasticity in order to construct beams with prescribed vibration modes.",

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AU - Calio, I.

AU - Elishakoff, I.

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N2 - In this study inhomogeneous beams which posses exponential fundamental mode shapes are constructed. Closed-form solutions are derived for five cases of boundary conditions: (a) a beam with two free edges, (b) a cantilevered beam, (c) a beam that is clamped at both ends, (d) a simply supported beam and (e) a beam that is clamped at one end and simply supported at the other. The solutions can be utilized for axially varying the moment of inertia of the cross-section and/or functionally grading the material's modulus of elasticity in order to construct beams with prescribed vibration modes.

AB - In this study inhomogeneous beams which posses exponential fundamental mode shapes are constructed. Closed-form solutions are derived for five cases of boundary conditions: (a) a beam with two free edges, (b) a cantilevered beam, (c) a beam that is clamped at both ends, (d) a simply supported beam and (e) a beam that is clamped at one end and simply supported at the other. The solutions can be utilized for axially varying the moment of inertia of the cross-section and/or functionally grading the material's modulus of elasticity in order to construct beams with prescribed vibration modes.

KW - Exponential form

KW - Inhomogeneous beam

KW - Inverse problem

KW - Prescribed vibration mode

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Inhomogeneous beams possessing an exponential mode shape

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Keywords

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