Free and forced large amplitude vibrations of periodically inhomogeneous slender beams

Wind turbine blades are designed to be thin and flexible elements. Because unstable dynamic behaviour can affect the life of the rotor, it is crucial to understand the instability of non-linear behaviour caused by large deflections. The present study undertakes both a stability analysis of the non-linear response and an experimental validation of a simplified model for a wind turbine blade based on a cantilever beam. The model is formulated taking into account large geometric deflections and assuming a Galerkin approach. The model is validated experimentally in a wind tunnel with aluminium beams of differing geometry. Analysis of the dynamic response using phase planes reveals that the degree of instability is related to the amplitude of the excitation and the stiffness characteristics.

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“…( 16), in y = L, the Eqs. (19) and (20) are obtained. These equations describe the distribution of fluid over the blade.…”

Section: Wind Excitation Forcementioning

confidence: 99%

“…While phase planes have been applied as a qualitative technique for analysing the dynamic stability of thin structures under considerable excitation amplitudes [19] and [20], phase planes should better pictorially represent the chaotic motion.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Instability of a Wind Turbine Blade Due to Large Deflections: An Experimental Validation

Lopez-Lopez

Robles-Ocampo

Sevilla-Camacho

et al. 2020

SV-JME

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“…Tomczyk and Szczerba [15], Tomczyk et al [16]), dynamics of beams (cf. Domagalski [17], Domagalski et al [18], Domagalski and Jędrysiak [19]), statics of plates with a dense system of ribs (cf. Marczak et al [20]), dynamics of sandwich plates (cf.…”

Section: Introductionmentioning

confidence: 99%

The Stability Analysis of Periodic Beams Interacting with Periodic Elastic Foundation with the Use of the Tolerance Averaging Technique

Marczak

Jędrysiak

2021

Materials

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In this paper a stability analysis of microperiodic beams resting on the periodic inhomogeneous foundation is carried out. The main issue of this considerations, which is the analytical solution to the governing equations characterised by periodic, highly oscillating and non-continuous coefficients, is overwhelmed by the application of the tolerance averaging technique. As a result of such application, the governing equation is transformed into a form with constant coefficients which can be solved using well-known mathematical methods. In several calculation examples, the convergence of the results of two derived averaged models is examined, as well as the convergence of the lowest value of the critical force parameter derived from the averaged models with the FEM model. The results prove the superiority of the presented analytical solution over the FEM analysis in the optimisation process.

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“…Plates, beams, and shells as the most famous continuous structures can be found as building blocks of many mechanical/civil systems; Polus and Szumigala [1] analysed aluminium-concrete composite beams using a three-dimensional finite element technique and found very good agreement between experiments and theory. Domagalski [2] considered periodically inhomogeneous beams and examined the vibration behaviour in the absence of loadings and subject to external loadings via the Galerkin techniques for frequency-amplitude responses. In some applications, their nonlinear response becomes important.…”

Section: Introductionmentioning

confidence: 99%

“…There are a limited number of investigations in the literature which considered nonlinearities [2,[10][11][12]. Correa et al [13], for an Euler-Bernoulli beam under a moving load, developed a dynamic model using the finite element (FE) model in the pressure of non-smooth frictional damping.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear coupled moving-load excited dynamics of beam-mass structures

Ghayesh

Farokhi

Zhang

et al. 2020

Archiv.Civ.Mech.Eng

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Investigated in this paper is the first on the moving-load-caused nonlinear coupled dynamics of beam-mass systems. A constant value load excites the beam-mass system where its position on the beam-mass system changes periodically. The energy contribution of the moving load is included via a virtual work formulation. The kinetic energy of the mass together with the beam as well as energy stored in the beam after deflection is formulated. Hamilton's principle gives nonlinear equations of the beam-mass system under a moving load in a coupled transverse/longitudinal form. A weighted-residual-based discretisation gives a 20 degree of freedom which is numerically integrated via continuation/time integration along with Floquet theory techniques. The resonance dynamics in time, frequency, and spatial domains is investigated. As we shall see, torus bifurcations are present for some beam-mass structure parameters as well as travelling waves. A finite element analysis is performed for a simpler linear version of the problem for to-some-extend verifications.

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Free and forced large amplitude vibrations of periodically inhomogeneous slender beams

Cited by 15 publications

References 20 publications

Dynamic Instability of a Wind Turbine Blade Due to Large Deflections: An Experimental Validation

Dynamic Instability of a Wind Turbine Blade Due to Large Deflections: An Experimental Validation

The Stability Analysis of Periodic Beams Interacting with Periodic Elastic Foundation with the Use of the Tolerance Averaging Technique

Nonlinear coupled moving-load excited dynamics of beam-mass structures

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