Analysis of Nonlinear Aeroelastic Panel Response Using Proper Orthogonal Decomposition

Mortara, Sean; Slater, J. C.; Beran, Philip S.

doi:10.1115/1.1687389

Cited by 14 publications

(6 citation statements)

References 10 publications

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“…For a stationary wall, specifying the acoustically-reflecting boundary condition amounts to setting the incoming characteristic, V 5 , equal to the outgoing characteristic, V 4 . When the wall velocity is u w ≡ u w (x, y,t), the following relation satisfies (57):…”

Section: Solid Wall Acoustically-reflecting Boundary Conditionmentioning

confidence: 99%

“…Dowell [51] considered the same problem and used a Galerkin approximation to model the mode shapes of the plate, while introducing an additional basis for the membrane motion that was coupled nonlinearly to the mode shapes through a weighted residuals technique. Other related aero-elastic problems include incompressible flow [52,53,54], turbulent flow modeled as a random process [55], reduced order models of the full fluid field [56,19], and cylindrical bending assumptions for the plate [51,57,58], which effectively reduce the problem to that of a beam.…”

Section: Introductionmentioning

confidence: 99%

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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: Solid Wall Acoustically-reflecting Boundary Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reduced order modeling of fluid/structure interaction.

Barone¹,

Kalashnikova²,

Segalman³

et al. 2009

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show abstract

“…As the authors expected for this problem, eigenvalues of S T S rapidly diminished in magnitude, indicating rapid convergence and the potential for a very low-order model [11]. In terms of the energy measure of the sampled data, the first three displacement modes represented 99.9% of the total Branches of LCO solutions for different numbers of sin modes are found to converge quickly to the LCO branch obtained through time integration of the spatially discretized equations formulated in Section 2.5.…”

Section: The Reduced Order Panel Problemmentioning

confidence: 88%

“…In the second problem, the aeroelastic response of a nonlinear panel is studied with the Cyclic ROM using a low-order formulation expressed with both POD and analytically defined modes. Time integration of the low-order model, like that reported elsewhere [11], yielded baseline results.…”

Section: Introductionmentioning

confidence: 92%

A Reduced Order Cyclic Method for Computation of Limit Cycles

Beran

Lucia

2005

Nonlinear Dyn

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A reduced order cyclic method was developed to compute limit-cycle oscillations for large, nonlinear, multidisciplinary systems of equations. Method efficacy was demonstrated for two simplified models: a typical-section airfoil with nonlinear structural coupling and a nonlinear panel in high-speed flow. The cyclic method was verified to maintain second-order temporal accuracy, yield converged limit cycles in about 10 Newton iterates, and provide precise estimates of cycle frequency. This method was projected onto a low-order space using a set of variables governing the amplitudes of empirically derived modes, which were computed with the proper orthogonal decomposition. In this reduced order form, the cyclic Jacobian was greatly compressed, allowing accurate limit cycle solutions to be very efficiently computed. Nomenclature s = Time step normalized by period t = Time step x = Panel node spacing γ = Ratio of specific heats λ = Reduced velocity (airfoil); pressure parameter (panel) µ = Mass ratio = Mode matrix ν = Poisson's ratio, 0.3 M ∞ = Freestream Mach number N f = Number of variables N m = Number of modes N t = Number of time intervals in oscillation N x = Number of nodes on panel (excluding end points) p = Pressure T = Oscillation period w = Panel deflection v = Panel velocity, ∂w/∂t

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“…For a chronological development of this approach including the seminal paper by Romanowski [22], the reader may consult [22][23][24][25][26][27][28][29]. There is a discussion of the eigenmode and/or POD mathematical technique in most of these papers and readily accessible accounts are available in [3][4][5][6].…”

Section: Eigenmodes and Pod Modesmentioning

confidence: 99%

Some Recent Advances in Nonlinear Aeroelasticity

Dowell

2021

A Modern Course in Aeroelasticity

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This brings the discussion of nonlinear aeroelasticity up to date. See the earlier discussion in Chap. 11. Much of the recent advances are based on new understanding of such subjects as limit cycle oscillations due to structural non-linearities, including freeplay, and fluid nonlinearities associated with unsteady separated flow including self excited flow oscillations variously called buffet or non-synchronous vibration.As the reader now knows, aeroelasticity is the field that examines, models and seeks to understand the interaction of the forces from an aerodynamic flow and the deformation of an elastic structure. The forces produce deformation, but the structural deformation in turn changes the aerodynamic forces. This feedback between force and deformation leads to a variety of dynamic responses of the fluid and the structure including flutter (a Hopf bifurcation), limit cycle oscillations and sometimes chaos. Selected recent advances in nonlinear aeroelasticity and fluid-structure interaction are reviewed to identify and model the fundamental elements that they share. Topics discussed include the following. following. 1 1 This chapter is based upo a AIAA SDM lecture given in 2010.

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Analysis of Nonlinear Aeroelastic Panel Response Using Proper Orthogonal Decomposition

Cited by 14 publications

References 10 publications

Reduced order modeling of fluid/structure interaction.

Reduced order modeling of fluid/structure interaction.

A Reduced Order Cyclic Method for Computation of Limit Cycles

Some Recent Advances in Nonlinear Aeroelasticity

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