Higher Order Normal Form and Period Averaging

Leung, A.Y.T.; Zhang, Q.C.

doi:10.1006/jsvi.1998.1752

Cited by 21 publications

(12 citation statements)

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“…Here only the period averaged Normal Form is presented as developed in Leung and Qichang (1998). Before discussing the period averaged Normal Form, a Lie group definition for the Normal Form is required.…”

Section: Period Averaged Normal Formmentioning

confidence: 99%

Bifurcation analysis and limit cycle oscillation amplitude prediction methods applied to the aeroelastic galloping problem

Vio

Dimitriadis

Cooper

2007

Journal of Fluids and Structures

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Section: Period Averaged Normal Formmentioning

confidence: 99%

Bifurcation analysis and limit cycle oscillation amplitude prediction methods applied to the aeroelastic galloping problem

Vio

Dimitriadis

Cooper

2007

Journal of Fluids and Structures

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“…Operatorial equation (99) could be rewritten as advanced methods (such as the normal form method) can be used to avoid secular terms [25,26,27,29,30,32,33,34], but such an application for the present problem is really tricky due to the dimension of the problem which is infinite. It is also assumed that the following expansion can be written, and identifying terms in ε n , for each integer n > 0, we then obtain…”

Section: Formal Perturbations Methods For Solving Nonlinear Dynamicalmentioning

confidence: 99%

Non-linear viscoelastodynamic equations of three-dimensional rotating structures in finite displacement and finite element discretization

Desceliers¹,

Soize²

2004

International Journal of Non-Linear Mechanics

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This paper deals with the nonlinear viscoelastodynamics of three-dimensional rotating structure undergoing finite displacement. In addition, the nonlinear dynamics is studied with respect to geometrical and mechanical perturbations. On part of the boundary of the structure, a rigid body displacement field is applied which moves the structure in a rotation motion. A time dependent Dirichlet condition is applied to another part of the boundary. For instance, this corresponds to the cycle step of a helicopter rotor blade. A surface force field is applied to a third part of the boundary and depends on the time history of the structural displacement field. For example, this might corresponds to general unsteady aerodynamics forces applied to the structure. The objective of this paper is to model the nonlinear dynamic behavior of such a rotating viscoelastic structure undergoing finite displacements, and to allow small geometrical and mechanical (mass, constitutive equations) perturbations analysis to be performed.The model is constructed by the introduction of a reference configuration which is deduced from the nonlinear steady boundary value problem. A constitutive equation deduced from the Coleman and Noll theory concerning the viscoelasticity in finite displacement is used. Thereafter, the weak formulation of the boundary value problem is constructed and discretized using the finite element method. In order to simplify the mathematical study of the equations, multilinear forms are introduced in the algebraic calculation and their mathematical properties are presented.

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“…The algebraic code developed by Leung and Zhang) 23 ) has been extended to solve aeroelastic problems. Considering the aeroelastic problems, it is found that Equation 10is not sufficient for obtaining normal forms and therefore a modified version of the NFT method is constructed using the expression…”

Section: Limit-cycle Predictionmentioning

confidence: 99%

“…However, the influence of non-linearities on modern aircraft is becoming of increasing importance" 1 . These non-linearities can be structural (free-play, backlash, cubic stiffness), aerodynamic (nonlinear damping, moving shocks) or control (time delays, non-linear control laws) based and can result in behaviour such as limit-cycle oscillations (LCO) that cannot occur in a linear system' 23 '. With the increasing use of increasingly sophisticated technology (e.g.…”

Section: Introductionmentioning

confidence: 99%

Limit-cycle oscillation prediction for non-linear aeroelastic systems

et al. 2002

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This paper describes part of an investigation into the prediction and characterisation of limit cycle oscillations occurring in non-linear aeroelastic systems. Through the use of a modified version of normal form theory, it is shown how it is possible to predict the limit-cycle oscillations and characterise their stability. The approach is analytical and does away with the need for an excessive amount of time marching iterative numerical simulation of the system. The methodology is demonstrated upon a simple two degrees-of-freedom aeroelastic wing model with cubic stiffness. A good agreement was obtained between the analytical prediction and numerical simulations.

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Higher Order Normal Form and Period Averaging

Cited by 21 publications

References 0 publications

Bifurcation analysis and limit cycle oscillation amplitude prediction methods applied to the aeroelastic galloping problem

Bifurcation analysis and limit cycle oscillation amplitude prediction methods applied to the aeroelastic galloping problem

Non-linear viscoelastodynamic equations of three-dimensional rotating structures in finite displacement and finite element discretization

Limit-cycle oscillation prediction for non-linear aeroelastic systems

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