Aeroelastic response of composite rotor blades considering transverse shear and structural damping

Jung, Sung Nam; Kim, Seung Jo

doi:10.2514/3.12059

Cited by 13 publications

(9 citation statements)

References 16 publications

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“…Good correlation between these two results is obtained. 22 9.408 GPa (1.364 £ 10 6 psi) G 23 2.541 GPa (0.3686 £ 10 6 psi) G 13 4.304 GPa (0.6242 £ 10 6 psi) G 12 5.157 GPa (0.7479 £ 10 6 psi) Table 4. Tables 5 and 6 show the correlation of the free vibration results obtained by the present mixed method with experimental data and also with those obtained by other analyses: theoretical results from Abarcar and Cunniff 27 based on a exibility approach, numerical results from Suresh and Nagaraj 28 using a stiffness approach and a torsional warping function based on a minimal strain energy, numerical results from Hodges et al 29 based on a nite element approach, and numerical results from Stemple and Lee 25 based on a detailed nite element modeling.…”

Section: A Rotating Box Beammentioning

confidence: 98%

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Refined Structural Dynamics Model for Composite Rotor Blades

2001

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A re ned one-dimensional beam formulation based on a mixed approach has been developed for structural dynamics analyses of rotating and nonrotating composite beams and blades of general section shape with openor closed-section contours. The theory uses a mixed variational approach and accounts for the effects of elastic coupling, shell-wall thickness, warping, warping restraint, and transverse shear deformations. The analysis is validated against experimental data and other analytical results for composite cantilevered beams of various cross sections. Good correlation is achieved for all of the cases considered. The in uence of wall thickness and transverse shear on the free vibration characteristics of composite beams with either bending-torsion or extension-torsion coupling is investigated. For a bending-torsion coupled beam, the in uence of wall thickness becomes important when the thickness-to-depth ratio of the beam reaches about 30%. The frequency error in neglecting transverse shear exibility is about 50% for a bending-torsion coupled composite box beam with a slenderness ratio of 5.modi ed laminate stiffnesses; Eq. (6) A n" ; A n· ; : : : ; A°¿ = semi-inverted coef cients; Eq. (7a) E 1 ; E 2 = Young's moduli in principal directions f x ; f y ; f z ; f Á ; f ! = shear ow components G 12 = shear modulus k 2 A = radius of gyration M x x ; M s s ; M xs = moments for the shell segment M y ; M z = beam bending moments M ! = warping torsion m k 2 m 1 ; m k 2 m 2 = mass moment of inertia mk 2 m = polar mass moment of inertia, mk 2 m 1 C mk 2 m 2 N = axial force of beam N xn ; N sn = transverse shear stress resultants for the shell N x x ; N ss ; N xs = membrane stress resultants for the shell segment Q y ; Q z = transverse shear forces T s = St. Venant torque U; V ; W = beam displacements u; v t ; v n = shell-wall displacements; Eq. (1) x; s; n = coordinate systems of shell wall x; y; z = undeformed beam coordinates y ;¯z = cross section rotations of beam°x n = transverse shear strain of shell°x y ;°x z = transverse shear strains of beam " x x ; " ss ; " xs = membrane strains of shell · x x ; · ss ; · xs = curvatures of the midsurface of shell º 12 = Poisson's ratio in principal plane ½ = mass density 8 R = semicomplementary energy function; Eq. (8) Á = elastic twist deformation Ä = rotational speed, rpm N ! = sectorial area; Eq. (4a)

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Section: A Rotating Box Beammentioning

confidence: 98%

“…Property Dimensions E 11 75.8 GPa (11 £ 10 6 psi) E 22 5.51 GPa (0.8 £ 10 6 psi) G 23 2.07 GPa (0.3 £ 10 6 psi) G13…”

Section: Table 7 Materials Properties and Dimensions Of Kevlar-epoxy Imentioning

confidence: 99%

Refined Structural Dynamics Model for Composite Rotor Blades

2001

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“…The same kinematic relations and constitutive relations that are given by Ref. 6 for the composite box model are used in the present formulation. In case of thin-walled construction of boxbeam, the internal shear stresses for the equivalent load applying at shear center are distributed in a form as shown in Fig.…”

Section: Problem Formulationmentioning

confidence: 98%

“…6. The deformation of the blade in space is described by u, v, w, and <p, which are, respectively, axial, lead-lag, flap, and elastic twist deformations.…”

Section: Problem Formulationmentioning

confidence: 99%

“…In the present work, the formulation of Ref. 6, which considers the effects of transverse shear flexibility, torsion warping, and two-dimensional in-plane behavior, is extended to analyze arbitrary lay-up geometry including antisymmetric configuration. Numerical simulations are performed for a specific antisymmetric configuration to identify the transverse shear behavior on the aeroelastic stability of composite rotor.…”

Section: Introductionmentioning

confidence: 99%

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Effect of transverse shear on aeroelastic stability of a composite rotor blade

Jung

Kim

1995

AIAA Journal

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IntroductionI N the analysis point of view, the composite rotor blade has typically been analyzed through the one-dimensional beam assumption since the spanwise length of rotor blades is generally much longer than their lateral dimensions. In developing the beam theory, there may be coupling among extension, bending, and torsional deformations. These couplings generally invalidate the Euler-Bernoulli assumption: plane sections remain plane and are perpendicular to the elastic axis. The assumption leads to underestimation of beam displacements, especially in case of bending, because of constant shear distribution across the beam section. Moreover, for a composite beam in bending, this distribution of shear is nearly parabolic (piecewise in general). 1 The use of the shear correction factor (SCF) may be the most economical one for the transverse shear behavior without largely sacrificing the required accuracy of solution. In addition, warping and warping inhibition effects are to be considered in the analysis. 2 Therefore, an appropriate analytical model capturing these behaviors is inevitable to get more enhanced results from the aeroelastic analysis of a composite rotor blade.Hong and Chopra 3 used the nonlinear kinematic model of Hodges and Dowell 4 and extended it to the case of composite rotor. They used a simplified beam model, in which the transverse shear flexibility was not included in the formulation. Smith and Chopra 5 modified this one to include the transverse shear effects and other secondary structural modeling effects. They focused on the behavior of an elastically tailored composite blade and presented various results for vibratory hub loads of box-beam having different ply configurations, but they did not go further to consider the sectional distribution of shear stresses. To improve the theoretical results, an alternative approach, which has been developed by Jung and Kirn 6 for the effects of transverse shear and structural damping on the aeroelastic response of composite rotor blades in hover, involved the usage of SCF to account for the sectional distribution of shear stresses. They showed that the effects of transverse shear and structural damping can have a key role on the flutter boundary of the rotor, but the lay-up structure is confined to symmetric configuration only. In the present work, the formulation of Ref. 6, which considers the effects of transverse shear flexibility, torsion warping, and two-dimensional in-plane behavior, is extended to analyze arbitrary lay-up geometry including antisymmetric configuration. Numerical simulations are performed for a specific antisymmetric configuration to identify the transverse shear behavior on the aeroelastic stability of composite rotor. Problem FormulationThe rotor structure is idealized as a laminated composite boxbeam whose constituent laminae are characterized by different ply orientation angles and different material and thickness properties as depicted in Ref. 6. The deformation of the blade in space is described by u, v, w, and

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Transverse shear behavior on the aeroelastic stability of composite rotor blades

Jung

Kim

1996

KSME Journal

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Aeroelastic response of composite rotor blades considering transverse shear and structural damping

Cited by 13 publications

References 16 publications

Refined Structural Dynamics Model for Composite Rotor Blades

Refined Structural Dynamics Model for Composite Rotor Blades

Effect of transverse shear on aeroelastic stability of a composite rotor blade

Transverse shear behavior on the aeroelastic stability of composite rotor blades

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