Helicopter rotor dynamics by finite element time approximation

Borri, M.

doi:10.1016/0898-1221(86)90092-1

Cited by 94 publications

(43 citation statements)

References 7 publications

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“…The simulation of the dynamics of rotor blades and similar systems has long been a challenge and a test bed for time-integration algorithms for structural dynamics [38][39][40][41][42][43]. The slender geometry of the blades renders the system prone to dynamic instability, and the need to compute accurate solutions for long periods of time, to conserve linear and angular momentum, and to accurately distribute the energy across the frequency spectrum place stringent tests on time-integration methods.…”

Section: Numerical Examplesmentioning

confidence: 99%

Variational time integrators

Lew

Marsden

Ortiz

et al. 2004

Numerical Meth Engineering

212

215

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SUMMARYThe purpose of this paper is to review and further develop the subject of variational integration algorithms as it applies to mechanical systems of engineering interest. In particular, the conservation properties of both synchronous and asynchronous variational integrators (AVIs) are discussed in detail. We present selected numerical examples which demonstrate the excellent accuracy, conservation and convergence characteristics of AVIs. In these tests, AVIs are found to result in substantial speed-ups, at equal accuracy, relative to explicit Newmark. A mathematical proof of convergence of the AVIs is also presented in this paper. Finally, we develop the subject of horizontal variations and configurational forces in discrete dynamics. This theory leads to exact path-independent characterizations of the configurational forces acting on discrete systems. Notable examples are the configurational forces acting on material nodes in a finite element discretisation; and the J-integral at the tip of a crack in a finite element mesh.

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Section: Numerical Examplesmentioning

confidence: 99%

Variational time integrators

Lew

Marsden

Ortiz

et al. 2004

Numerical Meth Engineering

212

215

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show abstract

“…Since the transition matrix is uniquely defined, any choice of the integer in Eq. (A15) would act as a shift in the frequency content of Z j , such that all triads {ω j n , ξ j n , φ j n } remain exactly the same, as first observed by Borri (1986) and later discussed by Peters et al (2011).…”

Section: A1 Floquet Theory In Continuous Timementioning

confidence: 64%

Periodic stability analysis of wind turbines operating in turbulent wind conditions

Riva

Cacciola²,

Bottasso

2016

Wind Energ. Sci.

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Abstract. The formulation is model-independent, in the sense that it does not require knowledge of the equations of motion of the periodic system being analyzed, and it is applicable to an arbitrary number of blades and to any configuration of the machine. In addition, as wind turbulence can be viewed as a stochastic disturbance, the method is also applicable to real wind turbines operating in the field.The characteristics of the new method are verified first with a simplified analytical model and then using a high-fidelity multi-body model of a multi-MW wind turbine. Results are compared with those obtained by the well-known operational modal analysis approach.

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“…Thus, we will be working with shape functions similar to those of Eqs. (6) - (8). In addition, note that tlie time derivatives of u and Su do not appear in the formulation.…”

Section: Weak Principle For Optimal Controlmentioning

confidence: 99%

Weak Hamiltonian finite element method for optimal control problems

Hodges

Bless

1991

Journal of Guidance, Control, and Dynamics

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A temporal finite element method based on a mised form of the Hamiltonian n-eal; principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the nionient a and displacements do not appear therein; instead, only the virtual momenta and virtual displaceinents are differentiated with respect to time. Based on the duality that is obser\-cd to esist between the mixed form of Hamilton's weak principle and variational principles governing classical optiinal control problems, a temporal finite element forinulation of the latter can be developed in a rather straightforward manner. Several n-ell-l;nowl problelxs in dynamics and optimal control are illustrated. The esample dynamics problem inr-olws a time-marching problem. As optimal control esaniples, elementary trajectory optimizat ion problems are treated.

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Helicopter rotor dynamics by finite element time approximation

Cited by 94 publications

References 7 publications

Variational time integrators

Variational time integrators

Periodic stability analysis of wind turbines operating in turbulent wind conditions

Weak Hamiltonian finite element method for optimal control problems

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