Modeling Approach for Predicting the Rate of Frequency Change of Notched Beam Exposed to Gaussian Random Excitation

Habtour, Ed; Paulus, Mark; Dasgupta, Abhijit

doi:10.1155/2014/164039

Cited by 10 publications

(9 citation statements)

References 18 publications

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“…After the location of the crack, an inverse method inspired from the literature is used to estimate the crack depth [34]. First, the localized crack position is used to plot one of the frequencies as function of the crack depth.…”

Section: Crack Quantificationmentioning

confidence: 99%

Crack Detection through the Change in the Normalized Frequency Shape

Dahak¹,

Touat²,

Benkedjouh³

2018

Vibration

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Abstract:The objective of this work is to use natural frequencies for the localization and quantification of cracks in beams. First, to study the effect of the crack on natural frequencies, a finite element model of Euler-Bernoulli is presented. Concerning the damaged element, the stiffness matrix is calculated by the theory of fracture mechanics, by inverting the flexibility matrix. Then, in order to detect damage, we are going to show that the shape given by the change in the natural frequencies is as function of the damage position only. Thus, the crack is located by the correlation between the shape of the measured frequencies and those obtained by the finite elements, where the position that gives the calculated shape which is the most similar to the measured one, indicates the crack position. After the localization, an inverse method will be applied to quantify the damage. Finally, an experimental application is presented to show the real applicability of the method, in which the crack is introduced by using an Electrical Discharge Machining. The results confirm the applicability of the method for the localization and the quantification of cracks.

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Section: Crack Quantificationmentioning

confidence: 99%

Crack Detection through the Change in the Normalized Frequency Shape

Dahak¹,

Touat²,

Benkedjouh³

2018

Vibration

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“…The presence of cracks in a structure is usually detected by adopting a linear approach through the monitoring of changes in the structure's dynamic response features [27][28][29]. Several studies have reported analytical and experimental results for vibration of cracked Euler-Bernoulli beams and the effects of surface cracks on fundamental frequencies and vibration modes of beams [30][31][32]. Few researchers uncovered nonlinear dynamic behavior of beam structures with single crack in the time history and frequency spectrum [33][34][35].…”

Section: Nonlinear Dynamics Of Undamaged and Damaged Structuresmentioning

confidence: 99%

Detection of fatigue damage precursor using a nonlinear vibration approach

Habtour

Cole

Riddick

et al. 2016

Struct. Control Health Monit.

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SUMMARYA nonlinear dynamic methodology is developed for detecting and estimating fatigue damage precursor in isotropic metal structures, prior to fatigue crack initiation, based on measurement of changes in the structure nonlinear response to harmonic base excitation. As an example, a damage precursor feature was extracted for cantilever beams by quantifying the reduction in the nonlinear stiffness because of localized microscopic material softening. The nonlinear dynamic analytical model parametrically tracks changes in the nonlinear structural stiffening as a function of the structural response and the loading cycles. Experimental results are obtained by exciting the base of cantilever beams at various amplitude levels. At high response amplitudes, the beams experience three competing simultaneous nonlinear dynamic mechanisms: (i) stiffening because of high response amplitude at the fundamental mode; (ii) softening because of inertial forces; and (iii) softening because of localized microscopic material damage caused by cyclic micro-plasticity. The third mechanism-a potential precursor to fatigue crack initiation in the structure-resulted in a cumulative softening because of early accumulation of cyclic fatigue damage and is the focus of this study. The loading intensity and the number of cycles influenced the relative contribution of these dynamic mechanisms. Nanoindentation studies near the beam clamped boundary were conducted to confirm the fatigue degradation in the local mechanical properties as a function of loading cycles. The proposed detection method is simple to implement and detects the presence of damage precursors but lacks the resolution to discern spatial distributions of the damage intensity. Based on prior knowledge of the structural dynamic characteristics of the beam and using the proposed methodology, damage level and stiffness reduction can be detected and estimated based on changes in the nonlinear structural response. The nonlinear stiffness term in the equation of motion is found to be very sensitive to the proposed fatigue damage precursor, making it an effective method for monitoring structural degradation prior to crack developments. The proposed methodology provides new insights and constitutes a significant step toward the development of new inspection techniques.

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“…The model applied linear elastic fracture mechanics for crack propagation and included the shift in frequency that resulted from the crack growth. Habtour et al [114] developed an FEM model to predict the stress intensity and natural frequency during damage accumulation. The analytical model developed by Paulus et al was coupled with the FEM to predict TTF for complex geometries for which stress intensity values were not available.…”

Section: Uniaxial Loadingmentioning

confidence: 99%

Review of Response and Damage of Linear and Nonlinear Systems under Multiaxial Vibration

Habtour

Connon

Pohland

et al. 2014

Shock and Vibration

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A review of past and recent developments in multiaxial excitation of linear and nonlinear structures is presented. The objective is to review some of the basic approaches used in the analytical and experimental methods for kinematic and dynamic analysis of flexible mechanical systems, and to identify future directions in this research area. In addition, comparison between uniaxial and multiaxial excitations and their impact on a structure’s life-cycles is provided. The importance of understanding failure mechanisms in complex structures has led to the development of a vast range of theoretical, numerical, and experimental techniques to address complex dynamical effects. Therefore, it is imperative to identify the failure mechanisms of structures through experimental and virtual failure assessment based on correctly identified dynamic loads. For that reason, techniques for mapping the dynamic loads to fatigue were provided. Future research areas in structural dynamics due to multiaxial excitation are identified as (i) effect of dynamic couplings, (ii) modal interaction, (iii) modal identification and experimental methods for flexible structures, and (iv) computational models for large deformation in response to multiaxial excitation.

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Modeling Approach for Predicting the Rate of Frequency Change of Notched Beam Exposed to Gaussian Random Excitation

Cited by 10 publications

References 18 publications

Crack Detection through the Change in the Normalized Frequency Shape

Crack Detection through the Change in the Normalized Frequency Shape

Detection of fatigue damage precursor using a nonlinear vibration approach

Review of Response and Damage of Linear and Nonlinear Systems under Multiaxial Vibration

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