A high dimensional harmonic balance approach for an aeroelastic airfoil with cubic restoring forces

Liu, L.; Dowell, Earl H.; Thomas, Jeffrey P.

doi:10.1016/j.jfluidstructs.2006.09.005

Cited by 58 publications

(21 citation statements)

References 13 publications

(17 reference statements)

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“…The base flow is taken to be spatially uniform; such a flow is physically stable to any linear disturbance. Projecting the linearized Euler equations onto the random basis leads to a linear ROM (53), written here aṡ…”

Section: Test Case: Random Basismentioning

confidence: 99%

Reduced order modeling of fluid/structure interaction.

Barone¹,

Kalashnikova²,

Segalman³

et al. 2009

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This report describes work performed from October 2007 through September 2009 under the Sandia Laboratory Directed Research and Development project titled "Reduced Order Modeling of Fluid/Structure Interaction." This project addresses fundamental aspects of techniques for construction of predictive Reduced Order Models (ROMs). A ROM is defined as a model, derived from a sequence of high-fidelity simulations, that preserves the essential physics and predictive capability of the original simulations but at a much lower computational cost. Techniques are developed for construction of provably stable linear Galerkin projection ROMs for compressible fluid flow, including a method for enforcing boundary conditions that preserves numerical stability. A convergence proof and error estimates are given for this class of ROM, and the method is demonstrated on a series of model problems. A reduced order method, based on the method of quadratic components, for solving the von Karman nonlinear plate equations is developed and tested. This method is applied to the problem of nonlinear limit cycle oscillations encountered when the plate interacts with an adjacent supersonic flow. A stability-preserving method for coupling the linear fluid ROM with the structural dynamics model for the elastic plate is constructed and tested. Methods for constructing efficient ROMs for nonlinear fluid equations are developed and tested on a one-dimensional convectiondiffusion-reaction equation. These methods are combined with a symmetrization approach to construct a ROM technique for application to the compressible Navier-Stokes equations.

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Section: Test Case: Random Basismentioning

confidence: 99%

Reduced order modeling of fluid/structure interaction.

Barone¹,

Kalashnikova²,

Segalman³

et al. 2009

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“…Note that the flutter boundary U * L is independent of the nonlinear coefficient η. Lee et al [4] found a secondary Hopf bifurcation as U * increases further, where a jump of the amplitudes is detected (see Figures 2 and 3). Liu et al [6] used the high-dimensional HB method to study the secondary Hopf bifurcation and found that to capture the secondary bifurcation, as many as 9 (or 5 dominant) harmonics have to be considered.…”

Section: Resultsmentioning

confidence: 99%

“…In practice, the integral and the nonlinear terms make it difficult to analytically study the dynamic behavior of the system. In order to eliminate the integral terms, Lee et al [4][5][6] introduced the following four new variables…”

Section: Equations Of Motionsmentioning

confidence: 99%

“…Lee et al [4] studied the aeroelastic system by considering two dominant harmonics and by an improved HB1 method, respectively. Recently, the high-dimensional HB method was further improved to investigate the aeroelastic motions of an airfoil [5,6]. Essentially, the incremental harmonic balance (IHB) method is a semianalytical method for nonlinear dynamic systems.…”

Section: Introductionmentioning

confidence: 99%

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Highly Accurate Solution of Limit Cycle Oscillation of an Airfoil in Subsonic Flow

Zhang

Chen

Liu

et al. 2011

Advances in Acoustics and Vibration

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The homotopy analysis method (HAM) is employed to propose a highly accurate technique for solving strongly nonlinear aeroelastic systems of airfoils in subsonic flow. The frequencies and amplitudes of limit cycle oscillations (LCOs) arising in the considered systems are expanded as series of an embedding parameter. A series of algebraic equations are then derived, which determine the coefficients of the series. Importantly, all these equations are linear except the first one. Using some routine procedures to deduce these equations, an obstacle would arise in expanding some fractional functions as series in the embedding parameter. To this end, an approach is proposed for the expansion of fractional function. This provides us with a simple yet efficient iteration scheme to seek very-high-order approximations. Numerical examples show that the HAM solutions are obtained very precisely. At the same time, the CPU time needed can be significantly reduced by using the presented approach rather than by the usual procedure in expanding fractional functions.

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“…And the freeplay and hysteresis are the typical nonsmooth nonlinearities arising from aeroelastic systems. They can result in complex nonlinear dynamic responses, such as limit cycle oscillations (LCOs), bifurcations, and chaos [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

A Highly Accurate Approach for Aeroelastic System with Hysteresis Nonlinearity

Cui

Xie

Huang³

et al. 2017

International Journal of Aerospace Engineering

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We propose an accurate approach, based on the precise integration method, to solve the aeroelastic system of an airfoil with a pitch hysteresis. A major procedure for achieving high precision is to design a predictor-corrector algorithm. This algorithm enables accurate determination of switching points resulting from the hysteresis. Numerical examples show that the results obtained by the presented method are in excellent agreement with exact solutions. In addition, the high accuracy can be maintained as the time step increases in a reasonable range. It is also found that the Runge-Kutta method may sometimes provide quite different and even fallacious results, though the step length is much less than that adopted in the presented method. With such high computational accuracy, the presented method could be applicable in dynamical systems with hysteresis nonlinearities.

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A high dimensional harmonic balance approach for an aeroelastic airfoil with cubic restoring forces

Cited by 58 publications

References 13 publications

Reduced order modeling of fluid/structure interaction.

Reduced order modeling of fluid/structure interaction.

Highly Accurate Solution of Limit Cycle Oscillation of an Airfoil in Subsonic Flow

A Highly Accurate Approach for Aeroelastic System with Hysteresis Nonlinearity

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