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

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

doi:10.1016/j.mechrescom.2020.103505

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

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

Mathematical Physics

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Abstract

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 language	English
Article number	103505
Number of pages	10
Journal	Mechanics Research Communications
Volume	105
DOIs	https://doi.org/10.1016/j.mechrescom.2020.103505
Publication status	Published - 2020

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Asymptotics
Beam
Boundary conditions
PDE
Vibrations

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10.1016/j.mechrescom.2020.103505

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KW - Asymptotics

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KW - Vibrations

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

Abstract

Bibliographical note

Keywords

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