On the Bolotin's reduced beam model versus various boundary conditions

Igor I. Andrianov, Jan Awrejcewicz, Wim T. van Horssen

Research output: Contribution to journalArticleScientificpeer-review


This paper is devoted to the construction of asymptotically correct simplified models of nonlinear beam equations for various boundary conditions. V.V. Bolotin mentioned that in some cases (e.g., if compressed load is near the buckling value), the so-called „nonlinear inertia“ must be taken into account. The effect of nonlinear inertia on the oscillations of the clamped-free beam is investigated in many papers. Bolotin used some physical assumption and did not compare the order of nonlinear terms in original equations. Below we propose our method for deriving those, which we will named “Bolotin's equations“. This approach is based on fractional analysis of original boundary value problems.
Original languageEnglish
Article number103505
Number of pages10
JournalMechanics Research Communications
Publication statusPublished - 2020


  • Asymptotics
  • Beam
  • Boundary conditions
  • PDE
  • Vibrations

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