Free vibration and stability analysis of a cantilever beam axially loaded by an intermittently attached tendon

Ondra, Václav; Titurus, Branislav

doi:10.1016/j.ymssp.2021.107739

Cited by 18 publications

(34 citation statements)

References 48 publications

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“…As in the previous studies [21,24], substituting the normal mode forms into Eqs. (1), ( 2) and (3) allows one to eliminate time and rewrite the PDEs into a system of first order ordinary differential equations (ODEs) that, together with the BCs, define a boundary value problem.…”

Section: Numerical Free Vibration Analysismentioning

confidence: 99%

“…At the tip, their displacements are identical and the tendon-induced axial force contributes to the shear and moment boundary conditions of the beam. Unlike [23,24], no other connectivity conditions were enforced since the tendon is free to vibrate inside the beam.…”

Section: Theoretical Modelmentioning

confidence: 99%

“…In order to evaluate the modal properties (natural frequencies and mode shapes) of the beam-tendon system, the same procedure as in [21,24] is used. The excitation forces and moments in Eq.…”

Section: Numerical Free Vibration Analysismentioning

confidence: 99%

“…It was found that the beam-tendon system exhibits reduction in the beam's natural frequencies due to the tendon-induced axial force as well as veering between beam-dominated and tendon-dominated modes. These findings were further numerically examined in [22] for rotating pre-twisted beams and for a system with intermittently attached tendon in [23,24]. It was shown that although the rotation has a considerable effect on the tendon, the tendon is still able to influence the modal characteristics of the beam significantly.…”

Section: Introductionmentioning

confidence: 99%

“…In all these studies, the tendon was attached to the beam's tip so that the place of the attachment coincided with the shear centre of the beam. Moreover, in the experimental studies [20,21,24] a cantilever beam with a double symmetry cross-section has been used so the elastic and mass axis were the same. A mono-symmetric channel cross-section was however also experimentally studied in [27], but the effect of the tendon placement has not been systemically investigated.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Theoretical and experimental free vibration analysis of a beam-tendon system with an eccentrically placed tendon

Ondra

Titurus

2019

Thin-Walled Structures

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Theoretical and experimental free vibration analysis of a beam-tendon system is presented in this paper. The system consists of a thin-walled cantilever beam with an open cross-section and a tip mass which is loaded by an eccentrically placed tendon. The novel beam-tendon system is modelled using a set of partial differential equations and numerical free vibration analysis is conducted using a boundary problem solver. The results are thoroughly validated using a bench-top experiment and a high-fidelity finite element model. The effect of the tendon location on the frequency-loading diagrams is systematically investigated for the first time. The results demonstrate that the location of the tendon significantly influences natural frequency shifts caused by the applied axial load and it is observed that some natural frequencies can even increase with the increasing compressive axial loading for certain locations of the tendon. In addition, veering between the beam-dominated and tendon-dominated modes is studied and the structural stability of the system is discussed. The paper concludes with suggestions of practical applications of a beam-tendon system with an eccentrically placed tendon.

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Section: Numerical Free Vibration Analysismentioning

confidence: 99%

Section: Theoretical Modelmentioning

confidence: 99%

Section: Numerical Free Vibration Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Theoretical and experimental free vibration analysis of a beam-tendon system with an eccentrically placed tendon

Ondra

Titurus

2019

Thin-Walled Structures

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Green functions for three-point boundary value problems governed by differential equation systems with applications to Timoshenko beams

Kiss

Szeidl

2023

Acta Mech

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The present paper is devoted to the issue of the Green function matrices that belongs to some three-point boundary- and eigenvalue problems. A detailed definition is given for the Green function matrices provided that the considered boundary value problems are governed by a class of ordinary differential equation systems associated with homogeneous boundary and continuity conditions. The definition is a constructive one, i.e., it provides the means needed for calculating the Green function matrices. The fundamental properties of the Green function matrices—existence, symmetry properties, etc.—are also clarified. Making use of these Green functions, a class of three-point eigenvalue problems can be reduced to eigenvalue problems governed by homogeneous Fredholm integral equation systems. The applicability of the novel findings is demonstrated through a Timoshenko beam with three supports.

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Nonlinear aeroelastic analysis of a damped elastica-aerofoil system

Jayatilake

Titurus

2022

Nonlinear Dyn

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This work formulates a comprehensive model of a nonlinear aeroelastic system developed for the analysis of complex aeroelastic phenomena related to structural and aerodynamic nonlinearities. The system is formulated as a two-dimensional cantilevered elastica with a rigid airfoil section firmly attached at its tip undergoing large displacements in the crosswind conditions. The system can demonstrate a wide range of domain specific as well as coupled nonlinear phenomena. The structural model is developed by means of the Rayleigh–Ritz approach, with shape functions discretizing both vertical and horizontal displacements and Lagrangian multipliers enforcing inextensibility. Damping is modeled based on a non-local strain-based mechanism in the Kelvin–Voigt arrangement. The resulting structural model is examined through studying the behavior under a follower load and with a tip-attached tendon under tension to study the shape convergence properties and the alignment of the results with known characteristics in the literature. The ONERA dynamic stall model is used to model the aerodynamics of the problem to accurately capture post-stall behavior at large deformations. The LCO responses of the aeroelastic problem are evaluated through time-marched simulations, and the combined airspeed–damping interactions are studied in this manner.

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Free vibration and stability analysis of a cantilever beam axially loaded by an intermittently attached tendon

Cited by 18 publications

References 48 publications

Theoretical and experimental free vibration analysis of a beam-tendon system with an eccentrically placed tendon

Theoretical and experimental free vibration analysis of a beam-tendon system with an eccentrically placed tendon

Green functions for three-point boundary value problems governed by differential equation systems with applications to Timoshenko beams

Nonlinear aeroelastic analysis of a damped elastica-aerofoil system

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