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Forced Nonlinear Vibrations of a One-Dimensional Bar with Arbitrary Distributions of Hysteretic Damage

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Abstract

An analytical model is presented which predicts the forced, nonlinear response of a bar with arbitrarily distributed damage. Damage, which is either described by quadratic hysteresis, or due to dislocations interacting with point defects distributed along the dislocations’ glide planes, is considered. The wave equation is solved by means of a perturbation approach. Resonance frequency shift caused by damage-induced material softening, nonlinear attenuation, and higher harmonics’ generation are evaluated. For damage which is described by quadratic hysteresis, this model recovers the well-known dependence of the three acoustic quantities mentioned above on the source’s strength. On the other hand, for damage due to dislocations, both frequency shift and nonlinear attenuation present a distinctive nonlinear behavior the origin of which resides in the stress dependence of the fraction of dislocations breaking away from the point defects. Furthermore, different distributions of damage having the same integrated intensity are shown to generate nonlinear effects of increasing magnitude as their spatial extent decreases. Finally, it is suggested that, once the effect of the source’s strength is removed, spectral features may be used to assess the spatial extent of damage.

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Authors and Affiliations

  1. Hesjakollen 111 A, 5142 , Bergen, Norway

    Claudio Pecorari

  2. Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W. 19th Ave, Columbus, OH , 43210, USA

    Daniel A. Mendelsohn

Authors
  1. Claudio Pecorari
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  2. Daniel A. Mendelsohn
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Correspondence to Claudio Pecorari.

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Pecorari, C., Mendelsohn, D.A. Forced Nonlinear Vibrations of a One-Dimensional Bar with Arbitrary Distributions of Hysteretic Damage. J Nondestruct Eval 33, 239–251 (2014). https://doi.org/10.1007/s10921-014-0228-x

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  • DOI: https://doi.org/10.1007/s10921-014-0228-x

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