Flexural and torsional non-linear free vibrations of beams using a p-version finite element

Alonso, Raquel; Ribeiro, Pedro

doi:10.1016/j.compstruc.2007.11.008

Cited by 10 publications

(1 citation statement)

References 14 publications

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“…[14][15] studied the free flexural-torsional vibrations of beams and obtained nonlinear normal modes by expansion of the equations of motion employing the Galerkin technique and neglecting the crosssection warping. Lopes and Ribeiro [16] studied also the nonlinear flexural-torsional free vibrations of beams employing a FEM solution and neglecting the longitudinal and rotary inertia as well as the cross-section warping. Duan [17] presented a FEM formulation for the nonlinear free vibration problem of thin-walled curved beams of asymmetric cross-section based on a simplified displacement field.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Effects in Elastic Flexural-Torsional Vibrations of Beams of Arbitrary Cross Section

Sapountzakis

Dikaros²

2010

CSENG

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In this paper a boundary element method is developed for the nonlinear flexural-torsional dynamic analysis of beams of arbitrary, simply or multiply connected, constant cross section, undergoing moderate large deflections and rotations under general boundary conditions, taking into account the effects of rotary and torsional warping inertia. Four boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to the angle of twist and solved using the Analog Equation Method, a BEM based method. The geometric, inertia, torsion and warping constants are evaluated employing the Boundary Element Method. The proposed model takes into account, both the Wagner's coefficients and the shortening effect. Numerical examples are worked out to illustrate the efficiency, wherever possible the accuracy, the range of applications of the developed method as well as the influence of the nonlinear effects to the response of the beam.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Effects in Elastic Flexural-Torsional Vibrations of Beams of Arbitrary Cross Section

Sapountzakis

Dikaros²

2010

CSENG

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Stability of nonlinear periodic vibrations of 3D beams

Stoykov

Ribeiro

2011

Nonlinear Dyn

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The geometrically nonlinear periodic vibrations of beams with rectangular cross section under harmonic forces are investigated using a p-version finite element method. The beams vibrate in space; hence they experience longitudinal, torsional, and nonplanar bending deformations. The model is based on Timoshenko's theory for bending and assumes that, under torsion, the cross section rotates as a rigid body and is free to warp in the longitudinal direction, as in Saint-Venant's theory. The theory employed is valid for moderate rotations and displacements, and physical phenomena like internal resonances and change of the stability of the solutions can be investigated. Green's nonlinear strain tensor and Hooke's law are considered and isotropic and elastic beams are investigated. The equation of motion is derived by the principle of virtual work. The differential equations of motion are converted into a nonlinear algebraic form employing the harmonic balance method, and then solved by the arc-length continuation method. The variation of the amplitude of vibration in space with the excitation frequency of vibration is determined and pre-S. Stoykov ( ) · P.

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Nonlinear flexural–torsional dynamic analysis of beams of variable doubly symmetric cross section—application to wind turbine towers

Sapountzakis

Dikaros

2013

Nonlinear Dyn

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Flexural and torsional non-linear free vibrations of beams using a p-version finite element

Cited by 10 publications

References 14 publications

Nonlinear Effects in Elastic Flexural-Torsional Vibrations of Beams of Arbitrary Cross Section

Nonlinear Effects in Elastic Flexural-Torsional Vibrations of Beams of Arbitrary Cross Section

Stability of nonlinear periodic vibrations of 3D beams

Nonlinear flexural–torsional dynamic analysis of beams of variable doubly symmetric cross section—application to wind turbine towers

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