Isogeometric method based in-plane and out-of-plane free vibration analysis for Timoshenko curved beams

Liu, Hongliang; Zhu, Xuefeng; Yang, Dan

doi:10.12989/sem.2016.59.3.503

Cited by 32 publications

(7 citation statements)

References 32 publications

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“…where, E and G are the Young and shear modulus, A is the area of the section of the beam, I t is the inertia of torsion, I n and I b are the moment of inertia of the cross section, k n and k b are the shear correction factors for the local n and b axes, respectively. According to isoparametric transformation [29,30], the relation between infinitesimal arch length s and the parametric coordinate  is defined as:…”

Section: Modeling Of the Compliant Mechanism With Isogeometric Analysismentioning

confidence: 99%

Design and Modeling of a Curved Beam Compliant Mechanism with Six Degrees of Freedom

et al. 2022

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Compliant mechanisms are widely used in cutting-edge scientific and technological fields such as precision engineering, micro-/nano-manipulation, or microelectronics. Hence, the demand for multi-degree-of-freedom compliant mechanisms has increased sharply. The structure of compliant mechanisms becomes increasingly complex with the increase of degrees of freedom. Here, a compliant mechanism with six degrees of freedom is proposed based on curved beams. The compliant mechanism has the advantages of simple structure and multi-degree-of-freedom. Using the isogeometric analysis method, a model of the mechanism is constructed. Static analysis show that six degrees of freedom can be generated. The prototype of the mechanism is developed by 3D printing. A loading test in six degrees of freedom is carried out. The output and input have high linear relations and the structure has low inter-directional coupling. We trust that this study provides a pioneering step towards the design of compliant mechanisms based on curved beam elements.

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Section: Modeling Of the Compliant Mechanism With Isogeometric Analysismentioning

confidence: 99%

Design and Modeling of a Curved Beam Compliant Mechanism with Six Degrees of Freedom

et al. 2022

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“…The analysis of these beam structures can be apparently carried out by utilizing the spatial beam formulations. However, in the case the cross-section is doubly symmetric or the cross-section height is small in comparison to the radius of [18,30,31]. In other words, the in-plane vibration of these beam structures can be performed independently with the out-of-plane vibration.…”

Section: Extensibility To Analysis Of Spatial Beamsmentioning

confidence: 99%

“…In particular, dynamic analysis of beam structures using the IGA approach has been studied in recent years. Several Timoshenko beam formulations have been presented in [13][14][15][16] for planar, and in [17,18] for spatial beam structures. Many types of beam are covered, i.e., straight [13], circular, elliptical, parabolic, and free-form beams [14][15][16], and several material models are involved, i.e., linear elastic, functionally graded materials [16].…”

Section: Introductionmentioning

confidence: 99%

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Dynamic multi-patch isogeometric analysis of planar Euler–Bernoulli beams

Borković

Nanakorn

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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This study presents a novel isogeometric Euler-Bernoulli beam formulation for in-plane dynamic analysis of multi-patch beam structures. The kinematic descriptions involve only displacements of the beam axis, which are approximated by non-uniform rational B-spline (NURBS) curves. Translational displacements of the control points are here considered as control variables. The motivation of this work is to propose a penalty-free method to handle in-plane dynamic analysis of multi-patch beam structures. A simple relation between cross-sectional rotations at the ends of the beams and control variables is derived, allowing the incorporation of the end rotations as degrees of freedom. This improved setting can straightforwardly tackle beam structures with many rigid multi-patch connections, a major challenging issue when using existing isogeometric Euler-Bernoulli beam formulations. Additionally, rotational boundary conditions are conveniently prescribed. Numerical examples with complicated beam structures such as circular arches and frames with kinks are considered to show the accuracy and performance of the developed formulation. The computed results are verified with those derived from the conventional finite element method, and the superior convergence properties of the proposed formulation are illustrated. We additionally discuss about the possible extension of the present approach to spatial beam structures.

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“…In this research, three coupled governing differential equations were derived via Hamilton's principle. Liu et al [29] addressed Inplane and out-of-plane free vibration analysis of Timoshenko curved beams based on the isogeometric method, and a practical scheme to avoid numerical locking in both of the two patterns is proposed in this paper.…”

Section: Introductionmentioning

confidence: 99%

Finite element model of circularly curved Timoshenko beam for in-plane vibration analysis

Nadi¹,

Raghebi²

2021

FME Transactions

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Curved beams are used so much in the arches and railway bridges and equipments for amusement parks. There are few reports about the curved beam with the effects of both the shear deformation and rotary inertias. In this paper, a new finite element model investigates to analyze In-Plane vibration of a curved Timoshenko beam. The Stiffness and mass matrices of the curved beam element was obtained from the force-displacement relations and the kinetic energy equations, respectively. Assembly of the elemental property matrices is simple and without need to transformation matrix because of using the local polar coordinate system. The natural frequencies of curved Euler-Bernoulli beam with large thickness are not sufficiently accurate. In this case, using the curved Timoshenko beam element is necessary. Moreover, the influence of vibration absorber is discussed on the natural frequencies of the curved beam.

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Isogeometric method based in-plane and out-of-plane free vibration analysis for Timoshenko curved beams

Cited by 32 publications

References 32 publications

Design and Modeling of a Curved Beam Compliant Mechanism with Six Degrees of Freedom

Design and Modeling of a Curved Beam Compliant Mechanism with Six Degrees of Freedom

Dynamic multi-patch isogeometric analysis of planar Euler–Bernoulli beams

Finite element model of circularly curved Timoshenko beam for in-plane vibration analysis

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