Control of Vibrations of Elastically Fixed Objects Using Analysis of Eigenfrequencies

Fazullin, Z. Yu.; Madibaiuly, Zh.; Yermekkyzy, L.

doi:10.26577/ijmph.2020.v11.i2.04

Cited by 1 publication

(4 citation statements)

References 2 publications

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“…) ( 1 x y is an eigenfunction of problem ( 1), (10) Lemma 2 is proved similarly to Lemma 1. Note that spectral properties with respect to symmetric equivalence of spectral problem (1), (10) with axial load without ) (x k were investigated in [23].…”

Section: Problem Statement and Main Resultsmentioning

confidence: 91%

“…Control is achieved due to integral perturbations of the boundary conditions of the original problem. The research methods of this work are conceptually close to the methods of work [9,10]. Conditions on the boundary parameters for controlling the first eigenvalues are found (see Theorems 1, 2, 3).…”

Section: Introductionmentioning

confidence: 84%

“…In such problems, it is important to take into account the dependence of the boundary conditions on the spectral parameter and the singularity of the original problem as the coincidence of the spectrum with the entire complex plane. Along with the above questions, problems of control of some eigenvalues also arise [7][8][9][10]. In such problems, one of the important methods is the integral perturbation of the original problem.…”

Section: Introductionmentioning

confidence: 99%

“…It follows from condition(5) for the boundary parameter α that the second part of Theorem 1. Theorem 1 is proved.The previous Theorem 1 can be extended to control with several eigenvalues, which are important from the point of view of the application[7][8][9][10]. Let Int.…”

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confidence: 99%

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Control of Vibrations of a Beam with Nonlocal Boundary Conditions

Nurakhmetov

Jumabayev

Aniyarov

2021

ijmph

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In this article is considered the models of uniform Euler-Bernoulli beams with an arbitrary variable coefficient of foundation on a finite segment. The variable of foundation corresponds to the Winkler model. The control problem the first eigenvalues of the beam vibration is investigated. Two types of fastenings at the ends are considered: clamped-clamped and hinged-hinged. The control is based on the Kanguzhin algorithm through integral perturbations of one of the boundary conditions of the original problem. Conditions for the boundary parameters for controlling the first eigenvalues are found. First, a result is formulated regarding the control of the first eigenvalue of the oscillation of the Euler-Bernoulli beam with hinge fastening at both ends. The result is then extended to control with several eigenvalues for this beam, which are important from the point of view of the application. Such questions are especially relevant when studying the resonant natural frequencies of a mechanical system. A similar result was obtained for a Euler-Bernoulli beam with clamped fastening at both ends. Such results of eigenvalue control of a mechanical system contribute to the creation of various non-destructive testing devices that are widely used in technical acoustics.

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Section: Problem Statement and Main Resultsmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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