Stability of nonlinear periodic vibrations of 3D beams

Stoykov, Stanislav; Ribeiro, Pedro

doi:10.1007/s11071-011-0150-z

Cited by 22 publications

(17 citation statements)

References 33 publications

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“…Even though when the external force is applied only in z direction (in the case φ 0), the transverse displacement is excited, if there is small disturbance ( Figure 6 (b)). This phenomenon is due to symmetry-breaking bifurcation point, similar bifurcation point, but for clamped-clamped beams was presented in [19]. In Figure 5, the small excitation of comes from the Coriolis forces.…”

Section: Forced Vibrations Of Rotating Beamssupporting

confidence: 54%

Nonlinear Vibrations of Rotating 3d Tapered Beams With Arbitrary Cross Sections

Stoykov¹,

Margenov²

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. The geometrically nonlinear vibrations of 3D beams that rotate about a fixed axis are investigated by the p-version finite element method. The beams are considered to be tapered, i.e. with variable thickness along its length, and with arbitrary cross sections. The beam model is based on INTRODUCTIONRotating beams are used to model and investigate the dynamics of helicopter blades, jet engine turbine blades, robot arms, wind turbine blades, etc. Many studies have been performed for modeling rotating beams about a fixed axis. The linear natural frequencies of beams that rotate with constant speed were investigated by many researchers, for example in [1][2][3][4][5]. Works that consider geometrically nonlinear models of rotating beams may be found, for example [6][7][8]. In what concerns modern wind turbine blades, most of them are constructed with load carrying box girder inside the blade and shells on the surface of the blade [9]. The purpose of the box girder is to make the blade stronger and stiffer while the shells around the box girder form the aerodynamic shape. Thus, the dynamic behavior of the wind turbine blade might be determined mainly from the load carrying box, even though the shells contribute small bending strength.In the current work, a model of beams rotating about a fixed axis with constant speed of rotation is presented. A setting angle and a rigid hub are included in the model. The equation of motion is derived in the rotating coordinate system, and the rotation is taken into account by the inertia forces [10]. The beam may vibrate in space, i.e. it may perform longitudinal, torsional and bending deformations, the model is based on Timoshenko's theory for bending and assumes that under torsion, the cross section deforms only in longitudinal direction due to warping [11]. Geometrical type of nonlinearity is considered and the equation of motion is derived by the principle of virtual work.Thin-walled box beams with linearly varying thickness and width are investigated. First, the derived model is validated by generating a fine mesh of three-dimensional finite elements. Then, the influence of the setting angle and the speed of rotation on the natural frequencies is examined. Forced vibrations of rotating beams due to harmonic forces are presented.

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Section: Forced Vibrations Of Rotating Beamssupporting

confidence: 54%

Nonlinear Vibrations of Rotating 3d Tapered Beams With Arbitrary Cross Sections

Stoykov¹,

Margenov²

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…The dimension of the local mass and stiffness matrices is 4 × 4. Mass proportional and frequency dependent damping [17] is introduced in the system.…”

Section: Validationmentioning

confidence: 99%

Scalable parallel implementation of shooting method for large-scale dynamical systems. Application to bridge components

Stoykov

Margenov

2016

Journal of Computational and Applied Mathematics

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a b s t r a c tThe mathematical models applied to real-life engineering structures result into large-scale dynamical systems. The efficient computation of their dynamical characteristics requires the usage of advanced numerical methods with parallel algorithms. The shooting method, in combination with a continuation method, presents a powerful tool for analyzing and investigating the dynamical characteristics of such systems. The efficiency and scalability of the shooting method are analyzed in the current paper for linear and nonlinear equations. Its applicability to large-scale systems is demonstrated by structural component of bridge discretized by three-dimensional finite elements.

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“…Admittedly, there are alternative and efficient methods that treat nonlinear problems in the frequency domain, such as the harmonic balance [5], the incremental harmonic balance [6] and the shooting methods [7]. Those, however, do not cancel the value of the proposed methodology, which could be effectively applied for a variety of nonlinear structural dynamics problems as well.…”

Section: Introductionmentioning

confidence: 99%

Second-order nonlinear dynamics of catenary pipelines subjected to bi-chromatic excitations

Chatjigeorgiou

2015

Applied Mathematical Modelling

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Please cite this article as: I.K. Chatjigeorgiou, Second-order nonlinear dynamics of catenary pipelines subjected to bi-chromatic excitations, Appl. Math. Modelling (2014), doi: http://dx. AbstractThe purpose of this study is to investigate the 2D nonlinear dynamics of catenary pipelines for marine applications approaching the solution in the frequency domain. The proposed methodology is seeking the transfer functions and in particular the quadratic magnification factors of the involved dynamic components assuming a bi-chromatic excitation, namely, a signal which arises from the superposition of two different sinusoidal harmonics. The sought solution is achieved by employing a perturbation technique that expands all dynamic components into series of perturbations relatively to a scaling factor, whilst the mathematical processing is performed into the complex space. The adopted procedure results in a series of problems which are solved separately and successively.Also, separate mathematical systems are derived for the sum-and the difference-frequency problems. The numerical results are obtained using a centered-differences approximation of the final set of ordinary differential equations. The correlation of the structural model with marine applications required the employment of a proper procedure for linearizing the nonlinear drag force at second-order. Finally, it is remarked that the outlined methodology can be effectively extended to polychromatic excitations and to the 3D space as well.

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Stability of nonlinear periodic vibrations of 3D beams

Cited by 22 publications

References 33 publications

Nonlinear Vibrations of Rotating 3d Tapered Beams With Arbitrary Cross Sections

Nonlinear Vibrations of Rotating 3d Tapered Beams With Arbitrary Cross Sections

Scalable parallel implementation of shooting method for large-scale dynamical systems. Application to bridge components

Second-order nonlinear dynamics of catenary pipelines subjected to bi-chromatic excitations

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