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Hysteretic damping and causality

  • Clasical Problems of Linear Acoustics and Wave Theory
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Abstract

It is proven that linear oscillatory systems with hysteretic damping in the form of complex stiffness and/or complex elastic moduli satisfy the causality principle: the response of such a system to an arbitrary external force cannot appear earlier than the onset of the force. The proof, based on a rigorous solution to the problem of forced oscillations, is presented in detail for an oscillator with a complex stiffness, as well as in a brief explanation for a system with N mass. It is also shown that these systems are Lyapunov-unstable. A comparison is made to other linear hysteretic damping models.

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Authors and Affiliations

  1. Blagonravov Institute of Mechanical Engineering Research, Russian Academy of Sciences, Malyi Kharitonievskii per. 4, Moscow, 101990, Russia

    Yu. I. Bobrovnitskii

Authors
  1. Yu. I. Bobrovnitskii
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Correspondence to Yu. I. Bobrovnitskii.

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Original Russian Text © Yu.I. Bobrovnitskii, 2013, published in Akusticheskii Zhurnal, 2013, Vol. 59, No. 3, pp. 291–295.

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Bobrovnitskii, Y.I. Hysteretic damping and causality. Acoust. Phys. 59, 253–256 (2013). https://doi.org/10.1134/S1063771013030032

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  • DOI: https://doi.org/10.1134/S1063771013030032

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