Coupled bending and torsional vibration of a beam with in-span and tip attachments

Gökdağ, Hakan; Kopmaz, Osman

doi:10.1016/j.jsv.2004.11.019

Cited by 34 publications

(6 citation statements)

References 13 publications

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“…In general, for a large number of thinwalled beams used in practical engineering, the shear center and the mass centroid are not coincident, which results in a coupling of the bending and torsional modes of the oscillation that are independent in classical beams. Therefore, the coupled vibration between rigid motions of subsystems and thin-walled beams becomes more complicated than classical beams and needs to be clarified [38,39]. Oguamanam et al studied the coupled flexuraltorsional free vibration of thin-walled beams with tip mass attachments [38].…”

Section: Introductionmentioning

confidence: 99%

On the Forced Vibration of Bending-Torsional-Warping Coupled Thin-Walled Beams Carrying Arbitrary Number of 3-DoF Spring-Damper-Mass Subsystems

Chen

Liu

2022

Mathematics

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This paper presents an analytical transfer matrix modeling framework for the forced vibration of a bending-torsional-warping coupling Euler-Bernoulli thin-walled beam carrying an arbitrary number of three degree-of-freedom (DOF) spring-damper-mass (SDM) subsystems. The thin-walled beam is divided into a series of distinct sub-beams whose ends are connected to the SDM subsystems. The transfer matrix for each sub-beam is developed based on the exact shape functions of the bending-torsional-warping coupling Euler-Bernoulli theory. Each SDM system is modelled by a set of effective springs based on the dynamic condensation method. The governing matrix equation is formulated based on the compatibility conditions of the placement and the force at the common interfaces of two adjacent sub-beams. Then, a closed-form expression for the frequency response function of the thin-walled beam system is proposed. The results computed by the proposed method achieve good agreement with those obtained by the conventional finite-element method, which shows the accuracy and reliability of the proposed method. The effects of the system parameters on the vibration transmission and vibration isolation properties of the thin-walled beam system are studied. The presented method can simultaneously consider arbitrary number of SDM subsystems and boundary conditions. Furthermore, none of the associated matrices are larger than 12 × 12, which provides a significant computational advantage.

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Section: Introductionmentioning

confidence: 99%

On the Forced Vibration of Bending-Torsional-Warping Coupled Thin-Walled Beams Carrying Arbitrary Number of 3-DoF Spring-Damper-Mass Subsystems

Chen

Liu

2022

Mathematics

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“…Coupled vibrations in slender beam structures are effectively analysed by beam elements [7,8], as also shown in the present paper. Furthermore, external dampers and discrete masses directly influence the dynamic behaviour of beams with bending and torsion coupling, as investigated in [9,10,11] by both a finite element approach with beam elements as well as exact solutions.…”

Section: Introductionmentioning

confidence: 99%

Damping of coupled bending-torsion beam vibrations by spatially filtered warping position feedback

Hoffmeyer

Høgsberg

2020

Journal of Sound and Vibration

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“…Yani, normalde bu iki hareket bağımsız iken bu halde bağımlı hale gelmiştir. Gökdağ ve Kopmaz ilgili sistemdeki kirişi tek simetri eksenli bir kirişle değiştirerek benzer çalışmalar yapmışlardır [16]. Bu halde kirişin kendisi de bizatihi eğilme ve burulmanın kuplajlı (coupled) olduğu bir kiriştir.…”

Section: Gi̇ri̇ş (Introduction)unclassified

Multi-step diferansiyel transform metodu ile uç kütle eklentili kirişlerin serbest titreşim analizi

Kati¹,

Gökdağ²

2019

Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi

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 MDTM is applied for the first time to this problem  Verification with finite element model  Studying the influence of some parameters on the natural frequencies This research concerns a non-uniform beam with a three dimensional rigid tip mass whose center of gravity is not coincided with the attachment point of the beam and subjected to both torsional and flexural deformations in two orthogonal planes. A semi-numerical method called Multi-Step Differential Transform Method (MDTM) is employed to obtain natural frequencies and mode shapes of the system for two different boundary conditions, i.e. the left end clamped or free. The influence of tip mass dimensions, beam length and taper ratio on the natural frequencies are studied, and the finite element software (ANSYS) is employed to compare the results and confirm the accuracy of the model.

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Coupled bending and torsional vibration of a beam with in-span and tip attachments

Cited by 34 publications

References 13 publications

On the Forced Vibration of Bending-Torsional-Warping Coupled Thin-Walled Beams Carrying Arbitrary Number of 3-DoF Spring-Damper-Mass Subsystems

On the Forced Vibration of Bending-Torsional-Warping Coupled Thin-Walled Beams Carrying Arbitrary Number of 3-DoF Spring-Damper-Mass Subsystems

Damping of coupled bending-torsion beam vibrations by spatially filtered warping position feedback

Multi-step diferansiyel transform metodu ile uç kütle eklentili kirişlerin serbest titreşim analizi

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