Non-linear dynamics of size-dependent Euler–Bernoulli beams with topologically optimized microstructure and subjected to temperature field

A. V. Krysko, J. Awrejcewicz, S. P. Pavlov, K. S. Bodyagina, M. V. Zhigalov, V. A. Krysko

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3 Citations (Scopus)


This paper is devoted to the investigation of non-linear dynamics of non-homogeneous beams with a material optimally distributed along the height and length of the beam. The study was initiated by topological optimization for the given boundary and loading conditions, which yielded maximum stiffness of a beam microstructure. As a result, the beam with an optimized microstructure exhibiting non-homogeneity in two directions, i.e. along beam thickness and length, was obtained. In the second step, a beam model was derived based on the kinematic Euler–Bernoulli hypotheses and the modified couple stress theory including the von Kármán geometric non-linearity and heat flow action obeying the Duhamel–Neumann law. Both static and dynamic behaviour of the optimized (non-homogeneous) and homogeneous beams were studied for different values of the material length-dependent parameter and temperature. Differences and peculiarities in static and dynamic problems were illustrated and discussed. In particular, the influence of the scale size parameter on chaotic beam dynamics was investigated. Also, scenarios of transition into deterministic chaos were detected and analysed for both homogeneous and optimized beams.

Original languageEnglish
Pages (from-to)75-86
Number of pages12
JournalInternational Journal of Non-Linear Mechanics
Publication statusPublished - 1 Sep 2018



  • Chaos
  • Dynamics
  • Euler–Bernoulli beam
  • Microstructures
  • Optimization
  • Statics

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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