The role of parameters of smallness in deduction of approximated theories for deterministic dynamics of beams

Babilio, Enrico; Lenci, Stefano

doi:10.1051/matecconf/20168301001

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Bolotin's Approximation For a Clamped-clamped Beam1

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2019

2024

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Cited by 3 publications

(1 citation statement)

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“…In addition, we use the expression for curvature proposed in [17][18][19][20] . This curvature is known as material, normalized, flexural or mechanical curvature Let us assume that…”

Section: Bolotin's Approximation For a Clamped-clamped Beammentioning

confidence: 99%

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

Andrianov¹,

Awrejcewicz

Horssen

2020

Mechanics Research Communications

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“…In addition, we use the expression for curvature proposed in [17][18][19][20] . This curvature is known as material, normalized, flexural or mechanical curvature Let us assume that…”

Section: Bolotin's Approximation For a Clamped-clamped Beammentioning

confidence: 99%

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

Andrianov¹,

Awrejcewicz

Horssen

2020

Mechanics Research Communications

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Asymptotic analysis of geometrically nonlinear beam vibrations: Kirchhoff and Bolotin equations

Andrianov,

Koblik

2024

Z Angew Math Mech

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The paper analyzes various approximate models of geometrically nonlinear vibrations of a beam. In practice, simplified equations are often based on the quasi‐static Kirchhoff hypothesis—neglecting axial inertia. This hypothesis is justified with the prescribed end‐displacements of the beam in the axial direction. Under dead loading, quasi‐static Kirchhoff hypothesis results in a linear equation. The corresponding approximate equations obtained in this paper are based on the asymptotic procedure. The ratio of bending stiffness to reduced tensile/compressive stiffness is taken as a small parameter. Axial inertia is taken into account in the equation of the first approximation. Introduced by V.V. Bolotin concept “nonlinear inertia” is discussed. The most common errors in using the quasi‐static Kirchhoff hypothesis are analyzed.

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