A comprehensive analysis of hardening/softening behaviour of shearable planar beams with whatever axial boundary constraint

Lenci, Stefano; Clementi, Francesco; Rega, Giuseppe

doi:10.1007/s11012-016-0374-6

Cited by 54 publications

(33 citation statements)

References 19 publications

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“…This paper continues the investigations reported in [1][2][3] where the nonlinear free transverse oscillations of a planar Timoshenko beam have been investigated for different boundary conditions in the axial direction. The motivation behind this research is the observation, well documented in the literature, that axially restrained beams exhibit hardening behaviour of the backbone curve, while axially free beams have softening behaviour.…”

Section: Introductionsupporting

confidence: 77%

“…They confirmed the results previously obtained using reduced-order models, and also provided an experimental verification of the phenomenon. A more detailed literature survey can be found in [2].…”

Section: Introductionmentioning

confidence: 99%

“…The expressions of the nonlinear correction coefficient ω 2 were obtained; in particular, the function ω 2 (κ) was determined. In [2], a detailed investigation of the effects of slenderness, end spring stiffness, axial and rotational inertia, and of the shear stiffness is reported. Finally, in [3], the analytical results are compared with finite element method (FEM) numerical simulations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Axial–transversal coupling in the free nonlinear vibrations of Timoshenko beams with arbitrary slenderness and axial boundary conditions

Lenci

Rega

2016

Proc. R. Soc. A.

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The nonlinear free oscillations of a straight planar Timoshenko beam are investigated analytically by means of the asymptotic development method. Attention is focused for the first time, to the best of our knowledge, on the nonlinear coupling between the axial and the transversal oscillations of the beam, which are decoupled in the linear regime. The existence of coupled and uncoupled motion is discussed. Furthermore, the softening versus hardening nature of the backbone curves is investigated in depth. The results are summarized by means of behaviour charts that illustrate the different possible classes of motion in the parameter space. New, and partially unexpected, phenomena, such as the changing of the nonlinear behaviour from softening to hardening by adding/removing the axial vibrations, are highlighted.

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Section: Introductionsupporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Axial–transversal coupling in the free nonlinear vibrations of Timoshenko beams with arbitrary slenderness and axial boundary conditions

Lenci

Rega

2016

Proc. R. Soc. A.

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“…Arguments in favor of the former can be found in [1-3, 6, 9]. On the other hand, in [10][11][12][13][14] the latter is treated as the better choice.…”

Section: A Remark On the Moment-curvature Relationmentioning

confidence: 99%

“…The assumptions (14) inserted in Eq. (5), neglecting all terms whose order of magnitude is certainly smaller than , the bending curvature (5) takes the form…”

Section: Approximationmentioning

confidence: 99%

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

Babilio

Lenci

2016

MATEC Web Conf.

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On the static condensation of initially not rectilinear beams

Lenci,

Sorokin

2023

Z Angew Math Mech

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Two weakly nonlinear integral equations of motion commonly used in the literature to study the nonlinear dynamics of straight and initially not rectilinear Euler‐Bernoulli beams, respectively, are further investigated. Attention is focused on the process known as “static condensation”, which consists of neglecting the axial inertia in the exact, fully nonlinear system of equations of motion to determine the axial displacement as a function of the transversal one. The novelty of the paper relies on showing that, contrarily to expectation and somehow surprisingly, the integral equation for beams with a not rectilinear initial configuration cannot be obtained by the static condensation process starting from the exact, fully nonlinear, equations of motion, apart from a very particular and specific case. On the contrary, it is confirmed the well‐known result that for rectilinear beams the integral equation can be obtained by the static condensation. This highlights a major difference between the two integral equations in terms of reliability and allows us a better understanding of the integral equation of rectilinear beams, underlying its stronger mathematical background than the classical counterpart for not straight beams (i.e., its being obtainable from the exact, fully nonlinear, equations of motion via static condensation), which provides it with a “special” behavior and makes it more trustworthy.

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A comprehensive analysis of hardening/softening behaviour of shearable planar beams with whatever axial boundary constraint

Cited by 54 publications

References 19 publications

Axial–transversal coupling in the free nonlinear vibrations of Timoshenko beams with arbitrary slenderness and axial boundary conditions

Axial–transversal coupling in the free nonlinear vibrations of Timoshenko beams with arbitrary slenderness and axial boundary conditions

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

On the static condensation of initially not rectilinear beams

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