An experimental-theoretical correlation study of non-linear bending and torsion deformations of a cantilever beam

Dowell, Earl H.; Traybar, Joseph J; Hodges, Dewey H.

doi:10.1016/0022-460x(77)90501-6

Cited by 88 publications

(40 citation statements)

References 2 publications

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“…Note that the first comparisons of the Hodges-Dowell theory with the experiments [15] showed significant deficiencies of the moderate deformation nonlinear beam theory at the largest experimental loading conditions. Rosen and Friedmann [17], using an improved, 3rd-order nonlinear beam formulation showed considerable improvement, but this approach is still subject to the limitations of a theory developed using an ordering scheme.…”

Section: Introductionmentioning

confidence: 99%

“…Static data from the experiment has been widely used (e.g., [15,16]), to evaluate nonlinear beam theories -not always with satisfactory results. Note that the first comparisons of the Hodges-Dowell theory with the experiments [15] showed significant deficiencies of the moderate deformation nonlinear beam theory at the largest experimental loading conditions.…”

Section: Introductionmentioning

confidence: 99%

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An Examination of Selected Problems in Rotor Blade Structural Mechanics and Dynamics

Hopkins¹,

Ormiston²

2006

J. Am. Helicopter Society

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The deformation of rotorcraft blades are frequently classified as moderate, exceeding the small deformation limitation of typical beam finite elements. Advances in computer capabilities have made possible an implementation of a hybrid element combining rigid and flexible body kinematics in the Rotorcraft Comprehensive Analysis System (RCAS). Two challenges to new software are to verify the correctness of the implementation and to ascertain whether it represents an improvement. Comparisons are made to analytical results, to measurements from the "Princeton Beam" and Maryland vacuum chamber experiments, and to UH-60 flight test data. Inspection of these comparisons lead to the conclusion that the results obtained with RCAS correlate well with analytical and experimental results, sometimes representing significant improvements.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Examination of Selected Problems in Rotor Blade Structural Mechanics and Dynamics

Hopkins¹,

Ormiston²

2006

J. Am. Helicopter Society

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show abstract

“…This is true not only at the micro-and nanoscale, but also for macroscopic structures such as airplane wings. 18,19 Consequently, an effort to predict the dynamics of the nonlinear response and the parameters governing it has recently gained momentum. [20][21][22] Nonlinearity in the dynamic response of mechanical structures can have a multitude of origins, 8,23 including transduction effects (actuation/detection), 21 material properties (nonlinear constitutive relations), 24 nonideal boundary conditions, 25,26 damping mechanisms, 27,28 adsorption/desorption processes, 29 and geometric/inertial effects.…”

Section: Introductionmentioning

confidence: 99%

Nonlinearity in nanomechanical cantilevers

et al. 2013

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Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro-and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development. In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its predictions deviate strongly from our measurements for the nonlinearity of the fundamental flexural mode, which show a systematic dependence on aspect ratio (length/width) together with random scatter. This contrasts with the second mode, which is always found to be in good agreement with theory. These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation.

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“…Those that do, often present calculations with simplified models whose correspondence with the experimental system is established at a qualitative level only [6][7][8][9][10][11]. In other cases, models are derived from first principles [12][13][14], and may sometimes provide good quantitative matches as well [15][16][17][18][19]: however, such systems are usually weakly nonlinear and have easily modeled physics (e.g., Euler-Bernoulli beams, possibly under axial loads, undergoing not-too-large oscillations, with possibly nonstandard boundary conditions [20]).…”

Section: Introductionmentioning

confidence: 99%

Resonance, Parameter Estimation, and Modal Interactions in a Strongly Nonlinear Benchtop Oscillator

Nandakumar

Chatterjee

2005

Nonlinear Dyn

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We study the vibrations of a strongly nonlinear, electromechanically forced, benchtop experimental oscillator. We consciously avoid first-principles derivations of the governing equations, with an eye towards more complex practical applications where such derivations are difficult. Instead, we spend our effort in using simple insights from the subject of nonlinear oscillations to develop a quantitatively accurate model for the single-mode resonant behavior of our oscillator. In particular, we assume an SDOF model for the oscillator; and develop a structure for, and estimate the parameters of, this model. We validate the model thus obtained against experimental free and forced vibration data. We find that, although the qualitative dynamics is simple, some effort in the modeling is needed to quantitatively capture the dynamic response well. We also briefly study the higher dimensional dynamics of the oscillator, and present some experimental results showing modal interactions through a 0:1 internal resonance, which has been studied elsewhere. The novelty here lies in the strong nonlinearity of the slow mode.

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An experimental-theoretical correlation study of non-linear bending and torsion deformations of a cantilever beam

Cited by 88 publications

References 2 publications

An Examination of Selected Problems in Rotor Blade Structural Mechanics and Dynamics

An Examination of Selected Problems in Rotor Blade Structural Mechanics and Dynamics

Nonlinearity in nanomechanical cantilevers

Resonance, Parameter Estimation, and Modal Interactions in a Strongly Nonlinear Benchtop Oscillator

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