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1986•International Journal for Numerical Methods in EngineeringRequires access

Effect of rotary inertia on vibration of tapered beams

Arvind Gupta

Open publisher page 5 citations

Abstract

Abstract Rotary inertia and dynamic‐correction rotary inertia matrices for a linearly tapered beam element of any cross‐sectional shape are derived in explicit form. Exact expressions for the required displacement functions are used in the derivation of these matrices. Variation of area and moment of inertia of the cross‐section along the axis of the element are exactly represented by simple functions involving shape factors. Vibration analysis results of a tapered cantilever beam of I‐section, obtained with and without the rotary inertia matrices are compared and effect of rotary inertia on vibration of tapered beams discussed.

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What this paper is about

Abstract Rotary inertia and dynamic‐correction rotary inertia matrices for a linearly tapered beam element of any cross‐sectional shape are derived in explicit form. Exact expressions for the required displacement functions are used in the derivation of these matrices. Variation of area and moment of inertia of the cross‐section along the axis of the element are exactly represented by simple functions involving shape factors. Vibration analysis results of a tapered cantilever beam of I‐section, obtained with and without the rotary inertia matrices are compared and effect of rotary inertia on vibration of tapered beams discussed.

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Available abstract

Abstract Rotary inertia and dynamic‐correction rotary inertia matrices for a linearly tapered beam element of any cross‐sectional shape are derived in explicit form. Exact expressions for the required displacement functions are used in the derivation of these matrices. Variation of area and moment of inertia of the cross‐section along the axis of the element are exactly represented by simple functions involving shape factors. Vibration analysis results of a tapered cantilever beam of I‐section, obtained with and without the rotary inertia matrices are compared and effect of rotary inertia on vibration of tapered beams discussed.

Key concepts: Rotary inertia, Moment of inertia, Inertia, Cantilever, Vibration, Beam (structure), Displacement (psychology), Euler's equations

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