Comparative Analysis of Computational Methods for Limit-Cycle Oscillations

Gopinath, Arathi K.; Beran, Philip S.; Jameson, Antony

doi:10.2514/6.2006-2076

Cited by 22 publications

(15 citation statements)

References 11 publications

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“…In order to find the amplitudes and periods of the limit cycles excited by the fluid flow over the plate, a cyclic method similar to [70,71] is employed. In this method, the modal amplitudes α n and period of vibration for the system T are sought such that…”

Section: Fluid-structure Interactionmentioning

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: Fluid-structure Interactionmentioning

confidence: 99%

Reduced order modeling of fluid/structure interaction.

Barone¹,

Kalashnikova²,

Segalman³

et al. 2009

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“…The HB method can offer over one order of magnitude reduction in computational effort when compared against time domain methods. 5,[7][8][9] An overview of different variations of the Harmonic Balance method, such as high-dimensional, incremental, or elliptic HB methods is given by Dimitriadis.…”

Section: Introductionmentioning

confidence: 99%

The Influence of Structural Variability on Limit Cycle Oscillation Behaviour

Hayes¹,

Marques²,

Yao³

2014

15th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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Modal analysis is a popular approach used in structural dynamic and aeroelastic problems due to its efficiency. The response of a structure is composed of the sum of orthogonal eigenvectors or modeshapes and corresponding modal frequencies. This paper investigates the importance of modeshapes on the aeroelastic response of the Goland wing subject to structural uncertainties. The wing undergoes limit cycle oscillations (LCO) as a result of the inclusion of polynomial stiffness nonlinearities. The LCO computations are performed using a Harmonic Balance approach for speed, the modal properties of the system are extracted from MSC NASTRAN. Variability in both the wing's structure and the store centre of gravity location is investigated in two cases:-supercritical and subcritical type LCOs. Results show that the LCO behaviour is only sensitive to change in modeshapes when the nature of the modes are changing significantly.

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“…Although the HB method employs global basis functions resulting in system matrices with no sparsity, it offers better temporal convergence than spectral element and cyclic methods [20]. Additionally, convergence problems can occur for the spectral element method during the transition between unstable and stable branches of a subcritical LCO [7], the HB method does not encounter this problem.…”

Section: Introductionmentioning

confidence: 98%

Prediction of limit cycle oscillations under uncertainty using a Harmonic Balance method

Hayes

Marques

2015

Computers & Structures

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The Harmonic Balance method is an attractive solution for computing periodic responses and can be an alternative to time domain methods, at a reduced computational cost. The current paper investigates using a Harmonic Balance method for simulating limit cycle oscillations under uncertainty. The Harmonic Balance method is used in conjunction with a nonintrusive polynomial-chaos approach to propagate variability and is validated against Monte Carlo analysis. Results show the potential of the approach for a range of nonlinear dynamical systems, including a full wing configuration exhibiting supercritical and subcritical bifurcations, at a fraction of the cost of performing time domain simulations. Prediction of Limit Cycle Oscillations under Uncertainty using a Harmonic Balance MethodRichard Hayes, Simão P. Marques 1, School of Mechanical and Aerospace EngineeringQueen's University Belfast, Belfast, UK, BT9 5AH AbstractThe Harmonic Balance method is an attractive solution for computing periodic responses and can be an alternative to time domain methods, at a reduced computational cost. The current paper investigates using a Harmonic Balance method for simulating limit cycle oscillations under uncertainty. The Harmonic Balance method is used in conjunction with a nonintrusive polynomial-chaos approach to propagate variability and is validated against Monte Carlo analysis. Results show the potential of the approach for a range of nonlinear dynamical systems, including a full wing configuration exhibiting supercritical and subcritical bifurcations, at a fraction of the cost of performing time domain simulations.

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Comparative Analysis of Computational Methods for Limit-Cycle Oscillations

Cited by 22 publications

References 11 publications

Reduced order modeling of fluid/structure interaction.

Reduced order modeling of fluid/structure interaction.

The Influence of Structural Variability on Limit Cycle Oscillation Behaviour

Prediction of limit cycle oscillations under uncertainty using a Harmonic Balance method

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