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1972•International Journal for Numerical Methods in EngineeringRequires access

Bounds for eigenvalues in some vibration and stability problems

G. Venkateswara Rao, A. V. Krishna Mürty, A.K. Rao

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Abstract

Abstract In finite element displacement methods for vibration and stability problems, upper bounds to eigenvalues are ensured only if consistent and conforming elements arte used, whereas the use of other elements may yield an upper or a lower bound. Here a systematic perturbation of the mass (or geometric stiffness) matrix is used to generate two classes of eigenvalue sequences whose respective members tend to a common limit from opposite sides.

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What this paper is about

Abstract In finite element displacement methods for vibration and stability problems, upper bounds to eigenvalues are ensured only if consistent and conforming elements arte used, whereas the use of other elements may yield an upper or a lower bound. Here a systematic perturbation of the mass (or geometric stiffness) matrix is used to generate two classes of eigenvalue sequences whose respective members tend to a common limit from opposite sides.

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Available abstract

Abstract In finite element displacement methods for vibration and stability problems, upper bounds to eigenvalues are ensured only if consistent and conforming elements arte used, whereas the use of other elements may yield an upper or a lower bound. Here a systematic perturbation of the mass (or geometric stiffness) matrix is used to generate two classes of eigenvalue sequences whose respective members tend to a common limit from opposite sides.

Key concepts: Eigenvalues and eigenvectors, Eigenvalue perturbation, Vibration, Upper and lower bounds, Finite element method, Mathematics, Stiffness, Perturbation (astronomy)

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