Identifying Nodes and Anti-Nodes of Complex Structures With Virtual Elements

Philip, Dennis; Dym, Clive L.; Wong, Wai-lun

doi:10.1006/jsvi.1997.1388

Cited by 8 publications

(13 citation statements)

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“…The second frequency has one maximum, two minima, while the third one has two maxima and three minima. These extrema correspond to the nodes and anti-nodes of the associated modes [13]. The minima and maxima approximately indicate the locations of anti-nodes and nodes respectively.…”

Section: Numerical Resultsmentioning

confidence: 98%

On the Eigenfrequencies of a Two-Part Beam–mass System

Kopmaz¹,

Tellı²

2002

Journal of Sound and Vibration

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Section: Numerical Resultsmentioning

confidence: 98%

On the Eigenfrequencies of a Two-Part Beam–mass System

Kopmaz¹,

Tellı²

2002

Journal of Sound and Vibration

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“…This limitation is not specific to our proposed IEP solution algorithm but is instead a fairly intuitive consequence of the underlying structural mechanics. In this case, attaching a lumped mass at any point along a beam can only decrease each natural frequency of the beam . By examining the natural frequencies of the combined beam‐mass system as the lumped element mass and attachment location are varied, as shown in Figure , we observe that the natural frequencies of the combined system can range between those of the bare beam (ie, the beam without any attachments) and those of a simply supported beam with an in‐span simple support.…”

Section: Resultsmentioning

confidence: 99%

“…Note that replacing the lumped mass with a grounded spring will change the range of achievable natural frequencies significantly. In general, attaching a lumped mass to a beam will lower the structure's natural frequencies, while attaching a grounded translational spring will increase the structure's natural frequencies . That being said, both cases converge in the limiting case: as the mass or stiffness increases, the dynamic response of the combined system approaches that of a beam with an in‐span pin (although in the case when an attached mass is increased the structure possesses a natural frequency that approaches zero in addition to natural frequencies that approach those of a beam with an in‐span pin).…”

Section: Resultsmentioning

confidence: 99%

A sensitivity‐based approach to solving the inverse eigenvalue problem for linear structures carrying lumped attachments

Dawson

Philip

2019

Numerical Meth Engineering

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This paper presents an efficient algorithm for designing dynamical systems to exhibit a desired spectrum of eigenvalues. Focusing on combined systems of linear structures carrying various lumped element attachments, we apply the assumed-modes method and the implicit function theorem to derive analytical expressions for eigenvalue sensitivities, which are used to efficiently determine the minimal set of structural modifications needed to achieve a set of desired eigenvalues. The proposed algorithm employs an adaptive step size, performs significantly better than existing approaches, and can be easily applied to a broad range of structures. Convergence properties and limitations on achievable eigenvalues are also discussed, and a number of case studies demonstrating the performance of the algorithm in a wide variety of different applications are also included. KEYWORDSinverse problem, structural design, structural dynamics, eigenvalue sensitivity Int J Numer Methods Eng. 2019;120:537-566.wileyonlinelibrary.com/journal/nme

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“…, it is relevant to be able to predict the antinode accurately, points of the maximum displacement. This is because one may want to install vibration absorbers or incorporate additional constrains to the system at this points in order to reduce the response of the system [2].…”

Section: Introductionmentioning

confidence: 99%

Vibration Characteristics of Beam Structure Attached with Vibration Absorbers at its Vibrational Node and Antinode by Finite Element Analysis

Ong¹,

Zainulabidin²

2020

J.Sci.Eng

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In this study, the vibration characteristics of fixed ends beam are analysed after attached with dynamic vibration absorbers at vibrational node and antinode by simulation using ANSYS APDL. This study aim to obtain the best location and optimum number of DVAs placed on the fixed ends beam in order to reduce vibration of beam. The dynamic vibration absorber were attached to the fixed ends beam vibrational node and antinode for a total of three modes of vibration. The 0.84 m long beam is modelled by ANSYS and divided into 21 elements where each element is 0.04 m. A harmonic force, Fo of 28.84 N is exerted at node 3 of beam element. Modal analysis and harmonic analysis are carried out in this study to obtain the natural frequency and frequency response of the beam respectively. The vibration characteristics of fixed ends beam without DVA and beam attached with DVAs were compared. The simulation results show reduction of vibration amplitude of the beam especially when the DVA were attached at the vibrational antinode. The DVA amplitude increase when amplitude of beam decreases. From this study, it is proved that DVAs absorb vibration of the beam structure. The best position to attach DVAs is the vibrational antinode based on the modes of vibration. The increment of DVAs number will not affect the percentage reduction of vibration amplitude as long as the DVAs are placed at optimum location.

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Identifying Nodes and Anti-Nodes of Complex Structures With Virtual Elements

Cited by 8 publications

References 0 publications

On the Eigenfrequencies of a Two-Part Beam–mass System

On the Eigenfrequencies of a Two-Part Beam–mass System

A sensitivity‐based approach to solving the inverse eigenvalue problem for linear structures carrying lumped attachments

Vibration Characteristics of Beam Structure Attached with Vibration Absorbers at its Vibrational Node and Antinode by Finite Element Analysis

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