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Stability of a flat arch subjected to deterministic and stochastic loads taking into account nonlocal damping

Abstract

In the example of a flat arch, a problem of vibrational stability of systems subjected to deterministic and stochastic loads is considered taking into account the geometric nonlinearity and nonlocal damping of a material, which is characteristic of certain types of composites and nanomaterials. To study the stability of arch motion within the deterministic statement of the problem (stability in the sense of Lyapunov) and the stability in the almost certain stochastic statement, a method is used which is based on the calculation of the maximal Lyapunov’s exponent. The influence of damping and loading parameters on the degree of system stability is analyzed.

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Additional information

Original Russian Text © V.D. Potapov, 2013, published in Problemy Mashinostroeniya i Nadezhnosti Mashin, 2013, No. 6, pp. 9–16.

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Potapov, V.D. Stability of a flat arch subjected to deterministic and stochastic loads taking into account nonlocal damping. J. Mach. Manuf. Reliab. 42, 450–456 (2013). https://doi.org/10.3103/S1052618813060101

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Keywords

  • Machinery Manufacture
  • Maximal Lyapunov Exponent
  • Viscoelastic System
  • Arch Length
  • Stochastic Load