Abstract
Cantilever beams can often be used as representative models for more complex systems and can accurately display the expected behavior of these systems under different loads. The health of a cantilever beam after being subjected to harmonic excitation at its second resonance frequency is determined using a nondestructive health monitoring technique. Nonlinear Modal Tracking assumes a second order differential equation that factors in mass, stiffness, and damping of the beam with a cubic nonlinearity parameter. Research so far has confirmed that a drastic shift in this nonlinear term is a result of crack initiation and an indicator of the beam’s transition from healthy to unhealthy. Application of this Nonlinear Modal Tracking can be beneficial in monitoring the health of structures in order to predict catastrophic failure. The purpose of this study was to investigate several new techniques and conditions to verify the robustness of the model.
This experimental study included three newly considered beam geometries and then induced cracks using stress concentrations. Additionally, multiple frequency excitation was considered, and noise was added to the excitation frequency. This method of study is vital to future implementation of Nonlinear Modal Tracking in more complex systems. The technique successfully predicted the onset of beam failure during 5 of 6 beam experiments.
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Abbreviations
- Ω:
-
Excitation Frequency
- ∝:
-
Nonlinear parameter
- A:
-
Vertical displacement
- c:
-
Damping
- D ξ :
-
Bending stiffness
- F:
-
Input force
- L:
-
Length of total beam
- m:
-
Mass
- NDE:
-
Nondestructive evaluation technique
- NMT:
-
Nonlinear modal tracking
- s:
-
Horizontal displacement
- t:
-
Time
References
Doebling, S.W., Farrar, C.R., Prime, M.B.: A summary review of vibration-based damage identification methods. Shock Vib. Dig. 30, 91 (1998)
Bovsunovsky, A.P., Bovsunovsky, O.: Crack detection in beams by means of the driving force parameters variation at non-linear resonance vibrations. Key Eng. Mater. 347, 413–420 (2007)
Andreaus, U., Casini, P., Vestroni, F.: Nonlinear features in the dynamic response of a cracked beam under harmonic forcing. In: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, vol. 6, pp. 2083–2089. ASME, Long Beach, CA (2005)
Doughty, T.A., Leineweber, M.J.: Investigating nonlinear models for health monitoring in vibrating structures. Mech. Solids, Struct. Fluids. 11, 57–62 (2009)
Doughty, T.A., Dally, M.R., Bacon, M.R., Etzel, N.G.: Nonlinear Model Tracking for Varying System Geometries, pp. 167–175. Springer, New York (2013)
Doughty, T.A., Higgins, N.S., Etzel, N.G.: Nonlinear model tracking in application to failed nondestructive evaluations. Mech. Solids, Struct. Fluids; Vib., Acoust. Wave Propag. 8, 1009–1016 (2011)
Doughty, T.A.: Effect of nonlinear parametric model accuracy in crack prediction and detection. In: Experimental and Applied Mechanics, vol. 6, pp. 549–556. Springer, New York (2010)
Khiem, N.T., Lien, T.V.: Multi-crack detection for beam by the natural frequencies. J. Sound Vib. 273(1), 175–184 (2004)
Loutridis, S., Douka, E., Hadjileontiadis, L.J.: Forced vibration behaviour and crack detection of cracked beams using instantaneous frequency. NDT E Int. 38(5), 411–419 (2005)
Lee, Y.Y., Liew, K.M.: Detection of damage locations in a beam using the wavelet analysis. Int. J. Struct. Stab. Dyn. 1(3), 455–465 (2001)
Gudmundson, P.: Changes in modal parameters resulting from small cracks. Proc. Int. Modal Anal. Conf. Exhib. 2, 690–697 (1984)
Kim, J.-T., Ryu, Y.-S., Cho, H.-M., Stubbs, N.: Damage identification in beam-type structures: frequency-based method vs mode-shape-based method. Eng. Struct. 25(1), 57–67 (2003)
Doughty, T.A., Belle-Isle, A.W., Pendowski, N.: Experimental validation of nonlinear model tracking with varying conditions. In: Topics in Modal Analysis and Testing, vol. 10, pp. 139–153. Springer International Publishing, New York (2016)
Doughty, T.A., Davies, P., Bajaj, A.K.: A comparison of three techniques using steady state data to identify non-linear modal behavior of an externally excited cantilever beam. J. Sound Vib. 249(4), 785–813 (2002)
Doughty, T.A., Hector, M.J.: Numerical enhancement of nonlinear model tracking for health monitoring. In: Dynamics of Civil Structures, vol. 2, pp. 191–199. Springer International Publishing, New York (2015)
Crespo da Silva, M.R.M., Glynn, C.C.: Nonlinear flexural-flexural-torsional dynamics of inextensional beams. II. Forced motions. J. Struct. Mech. 6(4), 449–461 (1978)
Benaroya, H., Nagurka, M.L.: Mechanical Vibration: Analysis, Uncertainties, and Control. CRC/Taylor & Francis, Boca Raton, FL (2010)
Doughty, T.A.: System identification of modes in nonlinear structures. Ph.D. Thesis, Ray W. Herrick Laboratories, School of Mechanical Engineering, Purdue University (2002)
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Doughty, T.A., Blaser, A.K., Johnston, J.R. (2017). Monitoring the Health of a Cantilever Beam Using Nonlinear Modal Tracking. In: Niezrecki, C. (eds) Structural Health Monitoring & Damage Detection, Volume 7. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-54109-9_7
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DOI: https://doi.org/10.1007/978-3-319-54109-9_7
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