Coupled Flexural–torsional Vibrations of Timoshenko Beams

Bercin, A.N.; Tanaka, Michihiko

doi:10.1006/jsvi.1997.1110

Cited by 68 publications

(27 citation statements)

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“…Jun et al [86] in 2004 employed the concepts from a publication of Bercin and Tanaka [12] so as to derive the analytical expressions of the response of a mono-symmetric thin-walled beams subjected to random excitations using combined approach of the normal mode superposition and frequency response.…”

Section: Reliability Methodsmentioning

confidence: 99%

“…Early works based on this theory did not include the effect of restraining warping such as in [10] while later works that include warping stiffness can be found in [12,13,[18][19][20][21][22][23]]. …”

Section: Timoshenko's Theorymentioning

confidence: 99%

“…Hallauer [32] Bercin and Tanaka [12] in 1997 employed the method proposed by Banerjee and Williams [36] to obtain numerical results for the case of a thin-wall beam of monosymmetric crosssection. They found that the effects of warping stiffness, shear deformation and rotary inertia were significant for the modal frequency when the thickness of cross-section increases.…”

Section: Thin-walled Beam Of Discontinuous Cross Sectionsmentioning

confidence: 99%

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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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Section: Reliability Methodsmentioning
confidence: 99%

Section: Timoshenko's Theorymentioning
confidence: 99%

Section: Thin-walled Beam Of Discontinuous Cross Sectionsmentioning
confidence: 99%

See 1 more Smart Citation
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
0
0
0
0
View full text Add to dashboard Cite
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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“…The first seven natural frequencies for the beams given in Fig. 2 are obtained by including and excluding the effect of warping stiffness when the spinning speed is zero, and compared with the results by Bercin and Tanaka (1997), as shown in Table 3. It is observed that when the effect of warping is neglected, the errors associated with it become increasingly large as the modal index increases.…”

Section: Validationmentioning
confidence: 99%

Modeling and analysis for coupled flexural-torsional spinning beams with unsymmetrical cross sections
Wang
¹
,
Li
²
,
Jiang
³

2017
jtam
6
0
2
0
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The structural modeling and dynamic properties of a spinning beam with an unsymmetrical cross section are studied. Due to the eccentricity and spinning, transverse deflections along the two principal directions and the torsional motion about the longitudinal axis are coupled. The structural model of the beam is established based on the Hamilton principle and by incorporating the torsional inertia. Moreover, because of its significant influence on characteristics for the non-circular cross-sectional beam, the warping effect is considered in the formulation. The proposed model is effectively validated in two cases: the spinning beam with a symmetric cross section and the cantilevered beam with an unsymmetrical cross section. Then the effects of the spinning speed on natural frequencies and mode shapes are investigated. Numerical results reveal that the critical speed is altered with respect to noncoincidence of the centroid and the shear center. For the beams with strong warping rigidities, the warping effect cannot be neglected due to significant influence on natural frequencies.

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“…In their paper, Bercin and Tanaka [1] studied mainly the warping effect in coupled bending±torsional vibration analysis of a Timoshenko beam. Also they have reviewed brie¯y a few groups of theories related with the subject.…”

Section: Introductionmentioning
confidence: 99%

Comments on Coupled Flexural-Torsional Vibrations of Timoshenko Beams
Cortínez
¹
,
Piován
²
,
Rossi
³

1999
Journal of Sound and Vibration
4
0
1
0
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Coupled Flexural–torsional Vibrations of Timoshenko Beams

Cited by 68 publications

References 0 publications

Probabilistic Analysis of a Thin-Walled Beam with a Crack

Probabilistic Analysis of a Thin-Walled Beam with a Crack

Modeling and analysis for coupled flexural-torsional spinning beams with unsymmetrical cross sections

Comments on Coupled Flexural-Torsional Vibrations of Timoshenko Beams

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