Generalized Linear Servo-Aero-Viscoelasticity: Theory and Applications

Merrett, Craig G.; Hilton, Harry H.

doi:10.2514/6.2008-1997

Cited by 8 publications

(7 citation statements)

References 2 publications

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“…From exact values are arbitrary; however, the range was selected to include higher order derivatives that may occur when more terms are used in a conventional Prony series [1]. In Figs.…”

Section: Discussionmentioning

confidence: 99%

“…(1) to (3). The δ n are distinct non-integers and the derivatives D δ n = d δ n /dt δ n are defined in the Fourier sense [36].…”

Section: Fractional Derivative Constitutive Relationsmentioning

confidence: 98%

“…In the example above DO F = 2. The historic aeroelastic stability criteria must be replaced by aero-viscoelastic creep torsional divergence and bendingtorsion flutter stability criteria [1,5,6] stability criteria…”

Section: Torsional Divergence: Steady Aerodynamics With Quasi-static mentioning

confidence: 99%

“…1) has brought forth the need to switch from aeroelastic analyses to aero-viscoelastic ones 1 [1][2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

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Fractional order derivative aero-servo-viscoelasticity

Merrett

Hilton

2015

Int. J. Dynam. Control

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Divergence and flutter of lifting surfaces obeying fractional derivative (FD) viscoelastic material constitutive relations under separate fractional derivative servo-controls are analytically investigated. The analytical and computational complexities of FD formulations are examined and compared to Prony series formulations, which are the equivalent of integer derivative viscoelastic characterizations. An approximate formulation is offered that facilitates the Fourier transform but not the evaluation of the convolution integrals. Stability in the form flutter and torsional divergence of a two DOF system is investigated in the Laplace transform space by modified Nyquist plots. Illustrative examples demonstrate that the use of Prony series modulus/compliance characterizations offers a much simpler path to stability determinations in real time than the quest for intersections of curves of flight speeds and frequencies associated with fractional derivative representations.

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“…From exact values are arbitrary; however, the range was selected to include higher order derivatives that may occur when more terms are used in a conventional Prony series [1]. In Figs.…”

Section: Discussionmentioning

confidence: 99%

“…(1) to (3). The δ n are distinct non-integers and the derivatives D δ n = d δ n /dt δ n are defined in the Fourier sense [36].…”

Section: Fractional Derivative Constitutive Relationsmentioning

confidence: 98%

Section: Torsional Divergence: Steady Aerodynamics With Quasi-static mentioning

confidence: 99%

“…1) has brought forth the need to switch from aeroelastic analyses to aero-viscoelastic ones 1 [1][2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fractional order derivative aero-servo-viscoelasticity

Merrett

Hilton

2015

Int. J. Dynam. Control

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“…Elastic and viscoelastic flutter under time dependent velocities has been analyzed in [9 -11], while an extensive bibliography on viscoelastic flutter is presented and evaluated in [13]. In [14] it has been proved that during bending of non-homogeneous and/or of unsymmetrical viscoelastic beams, the neutral axis and the shear center line translate and rotate in time.…”

Section: Introductionmentioning

confidence: 99%

The Influence of Unsymmetrical Bending and Torsion on Elastic and Viscoelastic Wing Flutter

Merrett¹,

Hilton²

2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials ConferenceSelf Cite

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The analysis in this paper considers the effects of in-plane bending, i.e. about the vertical axis, on torsional and plunging bending as well as flutter instabilities in any one or more bending modes (DOFs) present. The inclusion of the in-plane bending displacements and in particular their associated velocities changes the problem from a linear one to a nonlinear one for slow flying vehicles such as UAVs and MAVs. In both instances the spatial dependences of the five governing relations are eliminated by Galerkin's method. The resulting nonlinear elastic ODEs are solved by using the Runge-Kutta numerical approach. The equivalent viscoelastic relations are nonlinear integral ordinary differential equations (IODEs) with variable coefficients, which unfortunately also can only be solved numerically thus making general parametric solutions, studies and conclusions unreachable. A number of illustrative problem examples with results are presented and discussed. The character and stability (flutter) of the solutions are examined. NOMENCLATURE a = distance as fraction of b from center of twist to aerodynamic center a ij , b ijkl = relaxation modulus coefficientsexternal vibratory force g, g w , g θ = structural damping coefficient k = reduced frequency N = summation limit in modulus, compliance Prony series O[n] = order n P , Q = viscoelastic differential operators t = time u = generalized displacement V, V (t) = free stream air velocity w = bending deflection x = {x 1 , x 2 , x 3 } = Cartesian coordinates α = trim angle of attack α = angle of zero lift α = Eq. (10) α r = rigid body angle of attack ∆p = aerodynamic pressure kl = strain components λ = exponent ρ air = air density σ kl = stress components θ = torsional deflection τ klmn = relaxation time ω = frequency 2

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Generalized viscoelastic designer functionally graded auxetic materials engineered/tailored for specific task performances
Hilton
¹
,
Lee
²
,
Fouly
³

2008
Mech Time-Depend Mater
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Generalized Linear Servo-Aero-Viscoelasticity: Theory and Applications

Cited by 8 publications

References 2 publications

Fractional order derivative aero-servo-viscoelasticity

Fractional order derivative aero-servo-viscoelasticity

The Influence of Unsymmetrical Bending and Torsion on Elastic and Viscoelastic Wing Flutter

Generalized viscoelastic designer functionally graded auxetic materials engineered/tailored for specific task performances

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