Nonlinear free vibrations of centrifugally stiffened uniform beams at high angular velocity

In this paper, we study the bending nonlinear free vibrations of a centrifugally stiffened beam with uniform cross-section and constant angular velocity. The nonlinear intrinsic equations of motion used here are geometrically exact and specific to beams exhibiting large amplitude displacements and r...

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Bibliographic Details
Published in:Journal of sound and vibration 2016-09, Vol.379, p.177-190
Main Authors: Bekhoucha, F., Rechak, S., Duigou, L., Cadou, J.M.
Format: Article
Language:English
Subjects:
Angular velocity
Chemical Sciences
Critical rotating velocity
Equations of motion
Free vibration
Galerkin method
Galerkin methods
High rotating velocity
Material chemistry
Mathematical analysis
Mathematical models
Nonlinear free vibration
Nonlinearity
Shear effect
Timoshenko beams
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Summary:In this paper, we study the bending nonlinear free vibrations of a centrifugally stiffened beam with uniform cross-section and constant angular velocity. The nonlinear intrinsic equations of motion used here are geometrically exact and specific to beams exhibiting large amplitude displacements and rotations associated with small strains. Based on the Timoshenko beam model, these equations are derived from Hamilton׳s principle, in which the warping is considered. All coupling terms are considered including Coriolis terms. The studied beams are isotropic with clamped-free boundary conditions. By combining the Galerkin method with the harmonic balance method, the equations of motion are converted into a quadratic function treated with a continuation method: the Asymptotic Numerical Method, where the generalized displacement vector is presented as a series expansion. While analysing the effect of the angular velocity, we determine the amplitude versus frequency variations which are plotted as backbone curves. Considering the first lagging and flapping modes, the changes in beam behaviour from hardening to softening are investigated and identified as a function of the angular velocity and the effect of shear. Particular attention is paid to high angular velocities for both Euler–Bernoulli and Timoshenko beams and the natural frequencies so obtained are compared with the results available in the literature.
ISSN:0022-460X
1095-8568
DOI:10.1016/j.jsv.2016.05.045