Flutter Equation as a Piecewise Quadratic Eigenvalue Problem

Eller, David

doi:10.2514/1.40653

Cited by 7 publications

(3 citation statements)

References 4 publications

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“…However, the PQI method tracks all eigenvalues very well. It is noted that the eigenvalues with jgj > k should be considered to be dubious, regardless of the method of solution [5].…”

Section: Illustrative Examplementioning

confidence: 98%

“…However, It is necessary to track the eigenvalues in the PQI method. The PQI method in Eller's scheme is C 1 continuous on the stability boundary, offering inherent facility to reduce the possible discontinuities at large damping values to arbitrarily small levels [5]. Therefore, neither mode tracking nor blending of roots is required on the boundaries.…”

Section: Mode Tracking Schemementioning

confidence: 99%

“…This approach, however, does not impose any constraints on the derivatives of interpolation functions so that the eigenvalues may be discontinuous on the segment boundaries, exhibiting gaps or overlaps. Eller [5] proposed an improved scheme by dividing the reduced frequency range into n 2 segments with n 1 breakpoints, keeping the continuity of the function derivatives on the segment boundaries. Nevertheless, the previous studies on the piecewise quadratic interpolation (PQI) method mainly focused on the interpolation improvements.…”

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confidence: 99%

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Flutter Analysis: Using Piecewise Quadratic Interpolation with Mode Tracking and Wind-Tunnel Tests

Huang

Qian

Zhao

et al. 2010

Journal of Aircraft

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= reference length of half-chord b j = breakpoint of the jth segment c 0 , c 1 , c 2 , c 3 , c 4 = coefficients of interpolation polynomial D = generalized damping matrix fV = cubic spline function of flow velocity f i = frequency corresponding to the flow velocity at the ith step g = added structural damping for k method Im = imaginary part of complex number j = sequence number of segment K = generalized stiffness matrix k = reduced frequency k j = the jth reduced frequency in which the generalized aerodynamic matrix is computed M = Mach number M = generalized mass matrix n = number of reduced frequencies for computing aerodynamic influence matrices n a = number of frequency data in a set p = Laplace variable Q s p = rational function approximation for generalized aerodynamic matrix Q 0 j , Q 1 j , Q 2 j = complex-valued coefficient matrices of the jth segment q = vector of generalized coordinates V = flow velocity V i = flow velocity at the ith step = flow density

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“…However, the PQI method tracks all eigenvalues very well. It is noted that the eigenvalues with jgj > k should be considered to be dubious, regardless of the method of solution [5].…”

Section: Illustrative Examplementioning

confidence: 98%

Section: Mode Tracking Schemementioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Flutter Analysis: Using Piecewise Quadratic Interpolation with Mode Tracking and Wind-Tunnel Tests

Huang

Qian

Zhao

et al. 2010

Journal of Aircraft

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Aeroelastic flutter analysis considering modeling uncertainties

Lokatt

2017

Journal of Fluids and Structures

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A semi-analytical approach for flutter analysis of a high-aspect-ratio wing

et al. 2020

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We present a hybrid, semi-analytical approach to perform an eigenvalue-based flutter analysis of an Unmanned Aerial Vehicle (UAV) wing. The wing has a modern design that integrates metal and composite structures. The stiffness and natural frequency of the wing are calculated using a Finite Element (FE) model. The modal parameters are extracted by applying a recursive technique to the Lanczos method in the FE model. Subsequently, the modal parameters are used to evaluate the flutter boundaries in an analytical model based on the p-method. Two-degree-of-freedom bending and torsional flutter equations derived using Lagrange’s principle are transformed into an eigenvalue problem. The eigenvalue framework is used to evaluate the stability characteristics of the wing under various flight conditions. An extension of this eigenvalue framework is applied to determine the stability boundaries and corresponding critical flutter parameters at a range of altitudes. The stability characteristics and critical flutter speeds are also evaluated through computational analysis of a reduced-order model of the wing in NX Nastran using the k- and pk-methods. The results of the analytical and computational methods are found to show good agreement with each other. A parametric study is also carried out to analyse the effects of the structural member thickness on the wing flutter speeds. The results suggest that changing the spar thickness contributes most significantly to the flutter speeds, whereas increasing the rib thickness decreases the flutter speed at high thickness values.

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Flutter Equation as a Piecewise Quadratic Eigenvalue Problem

Cited by 7 publications

References 4 publications

Flutter Analysis: Using Piecewise Quadratic Interpolation with Mode Tracking and Wind-Tunnel Tests

Flutter Analysis: Using Piecewise Quadratic Interpolation with Mode Tracking and Wind-Tunnel Tests

Aeroelastic flutter analysis considering modeling uncertainties

A semi-analytical approach for flutter analysis of a high-aspect-ratio wing

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