On triply coupled vibrations of thin-walled beams with arbitrary cross-section

Prokić, Aleksandar

doi:10.1016/j.jsv.2003.11.053

Cited by 30 publications

(17 citation statements)

References 9 publications

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“…[13] examined the behavior of thin-walled beams using one warping function valid for open and closed cross sections. More about modelling of the open and closed thin-walled beams can also be found, for example, in [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

An efficient 3D numerical beam model based on cross sectional analysis and Ritz approximations

Stoykov

Manoach

Margenov

2015

Z. Angew. Math. Mech.

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A 3D beam model, i.e. a beam that may deform in space and experience longitudinal and torsional deformations, is developed considering Timoshenko's theory for bending and assuming that the cross section rotates as a rigid body but may deform in longitudinal direction due to warping. The cross sectional properties are firstly calculated and then inserted at the equation of motion. The beam is assumed to be with an arbitrary cross section, with linearly varying thickness and width, and with an initial twist. The model is appropriate for open and closed thin-walled cross sections, and also for solid cross sections. The objective of the current research is to demonstrate that complex beam structures can be modeled accurately with reduced number of degrees of freedom.

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Section: Introductionmentioning

confidence: 99%

An efficient 3D numerical beam model based on cross sectional analysis and Ritz approximations

Stoykov

Manoach

Margenov

2015

Z. Angew. Math. Mech.

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“…Some researchers have employed the assumptions of TTT (Thin Tube Theory) and the nonuniform torsion theory with an additional degree of freedom for nonuniform warping that is the rate of angle of twist [23][24][25][26][27][28][29][30][31][32][33][34] or an independent warping parameter [35][36]. Egidio et al [37] describe the non-linear warping of open crosssection thin-walled beams in terms of the flexural and torsional curvatures.…”

Section: Introductionmentioning

confidence: 99%

Generalized Warping Effect in the Dynamic Analysis of Beams of Arbitrary Cross Section

Dikaros¹,

Sapountzakis²,

Argyridi³

et al. 2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…Such a beam when subjected to lateral loads or a twisting moment is expected to warp. The thin-walled beam theories that allow us to include warping can be mainly divided into two categories: Vlasov beam theory [4,5,22,43,129] and Benscoter beam theory [8,13,18,20,26,130,131]. In this study, the derivation is based on Benscoter beam theory where the warping degree of freedom is considered independent of the rate of twist.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Analysis of a Thin-Walled Beam with a Crack

Kunaporn¹,

Singh²,

Patil³

et al. 2010

51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Probabilistic Analysis of a Thin-walled Beam with a CrackChalitphan Kunaporn (ABSTRACT) It is reasonable to assume that an aircraft might experience some in-flight discrete source damage caused by various incidents. It is, thus, necessary to evaluate the impact of such damage on the performance of the aircraft. This study is focused on evaluating the effect of a simple discrete damage in an aircraft wing on its static and dynamic response.The damaged wing is modeled by a thin-walled beam with a longitudinal crack the response of which can be obtained analytically. As uncertainties are present in the location and size of the crack as well as in the applied loads, their effects are incorporated into the framework consisting of structural response, crack propagation and aeroelasticity.The first objective of this study is to examine the effect of damage represented by a crack on the wing flexibility that influences its deformation and aero-elastic divergence characteristics. To study this, the thin-walled beam is modeled by Benscoter thin-walled beam theory combined with Gunnlaugsson and Pedersen compatibility conditions to accurately account for the discontinuity at the interface of the cracked and uncracked beam segments. Instead of conducting a detailed finite element analysis, the solution is obtained in an exact sense for general distributed loads representing the wind pressure effects. This analytical approach is shown to provide very accurate values for the global beam response compared with the detailed finite element shell analysis. This analytical solution is, then, used to study the beam response probabilistically. The crack location and size are assumed to be uncertain and are, thus, characterized by random variable. For a specified limit state, the probability of failure can be conveniently calculated by the first order second moment analysis using the safety index approach. The same analytical solution is also used to study the aero-elastic divergence characteristics of a wing, the inner structure of which is represented by a thin-walled beam with a crack of uncertain size and position along the beam.iii The second objective of this study is to examine the time growth of a crack under dynamic gust type of loading to which a wing is likely to be exposed during flight.Damage propagating during operation further deteriorates the safety of the aircraft and it is necessary to study its time growth so that its impact on the performance can be evaluated before it reaches its unstable state. The proposed framework for the crack growth analysis is based on classical fracture mechanics where the remaining flight time is obtained by Monte Carlo simulation in which various uncertainties are taken into account. To obtain equivalent cyclic loading required for crack growth analysis, random vibration analysis of the thin-walled beam is conducted for stochastic wind load defined by a gust load spectral density function. The probability of failure represented by the crack size approaching the critical crack size wit...

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On triply coupled vibrations of thin-walled beams with arbitrary cross-section

Cited by 30 publications

References 9 publications

An efficient 3D numerical beam model based on cross sectional analysis and Ritz approximations

An efficient 3D numerical beam model based on cross sectional analysis and Ritz approximations

Generalized Warping Effect in the Dynamic Analysis of Beams of Arbitrary Cross Section

Probabilistic Analysis of a Thin-Walled Beam with a Crack

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