Random Transverse Vibrations of Elastic Beams

Boyce, William E.; Goodwin, Bruce E.

doi:10.1137/0112052

Cited by 27 publications

(10 citation statements)

References 2 publications

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“…1 that both (13b) and (13c) provide better lower bounds for the experimental data than that provided by the perturbation estimate (14). (In this case the perturbation estimate apparently is also a lower bound but this is not known a priori.)…”

Section: Jomentioning

confidence: 87%

The transverse vibrations of a pipe containing flowing fluid: Methods of integral equations

Jones¹,

Goodwin²

1971

Quart. Appl. Math.

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Abstract.Methods are developed to study the problem described in the title. Improvable lower bounds for the first eigenvalue are obtained for the low velocity-thin pipe wall case. It is shown that the eigenvalue changes from real to imaginary as the fluid velocity increases through a "critical" velocity. It is the methods which we wish to emphasize in that while we discuss them only for the present problem they are very general and especially powerful when applied to differential equations with constant coefficients.

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Section: Jomentioning

confidence: 87%

The transverse vibrations of a pipe containing flowing fluid: Methods of integral equations

Jones¹,

Goodwin²

1971

Quart. Appl. Math.

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“…Even though many results from random initial value problems are applicable to random boundary value problems, the latter often raise questions which are unanswered by a study of the former. Boyce [5], [6], [7], Goodwin [9] and Haines [10], [11] have studied many properties of random eigenvalues and random eigenfunctions of a boundary value problem by a variety of techniques. BharuchaReid [4] and others have proved the existence and uniqueness of solutions to stochastic boundary value problems by using arguments from functional analysis and measure theory.…”

Section: Introductionmentioning

confidence: 99%

A monotone property of the solution of a stochastic boundary value problem

Day¹

1970

Quart. Appl. Math.

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“…The eigenfunction u is not random in this case because the eigenvalue X and the coefficients ak combine in just the right manner to eliminate the randomness in u. This case was treated in a paper by The general eigenvalue problem has been formulated and studied in different ways by Boyce [2,3,4,5,6,9], Goodwin [6,9], Haines [10], Purkert and vom Scheidt [12] and others. In the survey paper of Boyce [3], an asymptotic method is mentioned briefly for determining the eigenvalues and eigenfunctions of a randomly perturbed problem.…”

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confidence: 99%