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

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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
Volume104
DOIs
Publication statusPublished - 1 Sep 2018

Fingerprint

Euler-Bernoulli Beam
Temperature Field
Nonlinear Dynamics
Microstructure
Temperature distribution
Dependent
Chaos theory
Kinematics
Stiffness
Heat transfer
Topological Optimization
Deterministic Chaos
Couple Stress
Geometric Nonlinearity
Heat Flow
Dynamic Problem
Dynamic Behavior
Temperature
Scenarios

Keywords

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

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

Non-linear dynamics of size-dependent Euler–Bernoulli beams with topologically optimized microstructure and subjected to temperature field. / Krysko, A. V.; Awrejcewicz, J.; Pavlov, S. P.; Bodyagina, K. S.; Zhigalov, M. V.; Krysko, V. A.

In: International Journal of Non-Linear Mechanics, Vol. 104, 01.09.2018, p. 75-86.

Research output: Contribution to journalArticle

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