Validation of the Variational Asymptotic Beam Sectional Analysis

Yu, Wenbin; Volovoi, Vitali; Hodges, Dewey H.; Hong, Xianyu

doi:10.2514/2.1545

Cited by 242 publications

(83 citation statements)

References 17 publications

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“…where the 3×3 submatrices R, S, and T , which make up the cross-sectional flexibility matrix, may be computed by VABS for various initial curvatures [Cesnik and Hodges 1997;Yu et al 2002;Hodges 2006]. When the reference line of the beam is chosen to be coincident with a cross-section shear center, the shear-torsion elastic couplings S 21 and S 31 vanish for that section.…”

Section: Validationmentioning

confidence: 99%

“…As a more powerful alternative than analytical treatments for determining cross-sectional elastic constants, one may use VABS (variational asymptotic beam sectional analysis) [Cesnik and Hodges 1997;Yu et al 2002;Hodges 2006] to numerically calculate all the cross-sectional elastic constants, including the stretch-bending coupling term. Based on results obtained from VABS, it is easy to show that there is another term that depends on initial curvature and reflects shear-twist coupling.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stability studies for curved beams

Chang¹,

Hodges²

2009

J. Mech. Solids Struct.

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The paper presents a concise framework investigating the stability of curved beams. The governing equations used are both geometrically exact and fully intrinsic; that is, they have no displacement and rotation variables, with a maximum degree of nonlinearity equal to two. The equations of motion are linearized about either the reference state or an equilibrium state. A central difference spatial discretization scheme is applied, and the resulting linearized ordinary differential equations are cast as an eigenvalue problem. The scheme is validated by comparing predicted numerical results for prebuckling deformation and buckling loads for high arches under uniform pressure with published analytical solutions. This is a conservative system of forces despite their being modeled as distributed follower forces. The results show that the stretch-bending coupling term must be included in order to accurately calculate the prebuckling curvature and bending moment of high arches. In addition, the lateral-torsional buckling instability of curved beams under tip moments is investigated. Finally, when a curved beam is loaded with nonconservative forces, resulting dynamic instabilities may be found through the current framework.

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Section: Validationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability studies for curved beams

Chang¹,

Hodges²

2009

J. Mech. Solids Struct.

View full text Add to dashboard Cite

show abstract

“…where the 3 × 3 submatrices R, S, and T , which make up the cross-sectional flexibility matrix, are computed by VABS [Cesnik and Hodges 1997;Yu et al 2002;Hodges 2006] for various initial curvatures. Though not essential, to make the shear-torsion elastic couplings S 21 = S 31 = 0, the stiffness matrix may be recomputed at the cross-sectional shear center.…”

Section: Validationmentioning

confidence: 99%

“…The Variational Asymptotic Beam Sectional (VABS) analysis [Cesnik and Hodges 1997;Yu et al 2002;Hodges 2006] can be used to numerically calculate this coupling term. Based on results obtained from VABS, it is easy to show that there is another term, which also depends on initial curvature but reflects shear-torsion coupling.…”

Section: Introductionmentioning

confidence: 99%

Vibration characteristics of curved beams

Chang

Hodges

2009

J. Mech. Mater. Struct.

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The paper presents a concise framework studying the coupled vibration of curved beams, whether the curvature is built-in or is caused by loading. The governing equations used are both geometrically exact and fully intrinsic, with a maximum degree of nonlinearity equal to two. For beams with initial curvature, the equations of motion are linearized about the reference state. For beams that are curved because of the loading, the equations of motion are linearized about the equilibrium state. A central difference spatial discretization scheme is applied, and the resulting linearized ordinary differential equations are cast as an eigenvalue problem. Numerical examples are presented, including: (1) validation of the analysis for both in-plane and out-of-plane vibration by comparison with published results, and (2) presentation of results for vibration of curved beams with free-free, clamped-clamped, and pinned-pinned boundary conditions. For coupled vibration, the numerical results also exhibit the low-frequency mode transition or veering phenomenon. Substantial differences are also shown between the natural frequencies of curved beams and straight beams, and between initially curved and bent beams with the same geometry.

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“…The results of the VAM cross-sectional analysis have been validated in [Yu et al 2002b] and [Yu and Hodges 2004]. VABS solutions have been compared with those of the three-dimensional elasticity solution.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic response of an accelerating composite rotor blade using perturbations

Ghorashi

Nitzsche

2009

J. Mech. Mater. Struct.

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The general nonlinear intrinsic differential equations of a composite beam are solved in order to obtain the elastodynamic response of an accelerating rotating hingeless composite beam. The solution utilizes the results of the linear variational asymptotic method applied to cross-sectional analysis. The integration algorithm implements the finite difference method in order to solve the transient form of the nonlinear intrinsic differential equations. The motion is analyzed since the beam starts rotating from rest, until it reaches the steady state condition. It is shown that the transient solution of the nonlinear dynamic formulation of the accelerating rotating beam converges to the steady state solution obtained by an alternative integration algorithm based on the shooting method. The effects of imposing perturbations on the steady state solution have also been analyzed and the results are shown to be compatible with those of the accelerating beam. Finally, the response of a nonlinear composite beam with embedded anisotropic piezocomposite actuators is illustrated. The effect of activating actuators at various directions on the steady state forces and moments generated in a rotating beam has been analyzed. These results can be used in controlling the nonlinear elastodynamic response of adaptive rotating beams.A list of symbols can be found starting on page 713.

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Validation of the Variational Asymptotic Beam Sectional Analysis

Cited by 242 publications

References 17 publications

Stability studies for curved beams

Stability studies for curved beams

Vibration characteristics of curved beams

Nonlinear dynamic response of an accelerating composite rotor blade using perturbations

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