A Simple Model for Predicting the Nonlinear Dynamic Behavior of Elastic Systems Subjected to Friction

Bennati, Stefano; Barsotti, Riccardo; Migliaccio, Giovanni

doi:10.1007/978-3-030-41057-5_115

Cited by 2 publications

(5 citation statements)

References 12 publications

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“…Hence, a sticking phase may begin only if a friction force no greater than F k is required at the first instant the relative velocity vanishes, otherwise the sliding phase will continue, as also discussed in [27,28]. According to the rule introduced here, a sticking phase following a sliding phase may begin at any time t * at which the relative velocity vanishes only if the following condition holds: m ..…”

Section: The Friction Law: a Modified Version Of The Coulomb's Formul...mentioning

confidence: 95%

Section: Figurementioning

confidence: 99%

“…We begin by considering the simple scheme depicted in Figure 4, in which a rigid block (G) is connected elastically to a first rigid support (A) and is in frictional contact with a second rigid support (B). Preliminary results concerning this one degree-of-freedom model have been presented by the authors in [11,27,28]. The analytical description of the system's stick and slip phases is outlined in Section 2 for Coulomb-like friction forces between the rigid block and moving support B.…”

Section: Figurementioning

confidence: 99%

“…In the next sections, both the sticking and sliding phases are discussed in detail. Here, as in [27,28], we only recall that during any sticking phase, the velocity of the rigid block coincides with that of the moving support B, while during any sliding phase, the explicit expression of the block's motion is the following:…”

Section: Event-driven Solution Of the Equation Of Motionmentioning

confidence: 99%

“…This section takes up a particular set of sliding limit cycles discussed in a preliminary investigation by the authors of [27,28]. More precisely, we consider a block that is undergoing periodic motion and assume the block slides over the moving support B without ever sticking to it.…”

Section: Sliding Limit Cyclesmentioning

confidence: 99%

See 4 more Smart Citations

Non-Linear Dynamics of Simple Elastic Systems Undergoing Friction-Ruled Stick–Slip Motions

Barsotti,

Bennati,

Migliaccio

2024

CivilEng

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The stick–slip phenomenon is a jerking motion that can occur while two objects slide over each other with friction. There are several situations in which this phenomenon can be observed: between the slabs of the friction dampers used to mitigate vibrations in buildings, as well as between the components of the base isolation systems used for seismic protection. The systems of this kind are usually designed to work in a smooth and flawless manner, but under particular conditions undesired jerking motions may develop, yielding complex dynamic behavior even when only a few degrees of freedom are involved. A simplified approach to the problems of this kind leads to the mechanical model of a rigid block connected elastically to a rigid support and at the same time with friction to a second rigid support, both the supports having a prescribed motion. Despite the apparent simplicity of this model, it is very useful for studying important features of the non-linear dynamics of many physical systems. In this work, after a suitable formulation of the problem, the equations of motion are solved analytically in the sticking and sliding phases, and the influence of the main parameters of the system on its dynamics and limit cycles is investigated and discussed.

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Section: The Friction Law: a Modified Version Of The Coulomb's Formul...mentioning

confidence: 95%

Section: Figurementioning

confidence: 99%

Section: Figurementioning

confidence: 99%

Section: Event-driven Solution Of the Equation Of Motionmentioning

confidence: 99%

Section: Sliding Limit Cyclesmentioning

confidence: 99%

See 3 more Smart Citations

Non-Linear Dynamics of Simple Elastic Systems Undergoing Friction-Ruled Stick–Slip Motions

Barsotti,

Bennati,

Migliaccio

2024

CivilEng

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On the role of different nonlinear damping forms in the dynamic behavior of the generalized Beck’s column

Migliaccio,

D’Annibale

2024

Nonlinear Dyn

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The influence of internal and external nonlinear damping forms on the dynamics of a generalized Beck’s column, namely a visco-elastic cantilever beam, subjected to conservative and non-conservative loads at its free end, is investigated. A variational principle provides the equations of motion of the system, which are properly recast into an integro-differential form. The linear stability analysis of the system is then carried out and bifurcation points are detected in the space of parameters associated with the conservative and non-conservative loads. Starting from Hopf’s bifurcation points, a post-critical analysis, based on the Method of Multiple Scales is directly performed on the continuous system, avoiding any a-priori discretization. This method provides the bifurcation equations whose analysis reveals the double nature of nonlinear damping, which can be beneficial or detrimental in terms of stable or unstable bifurcated equilibria. It is found that both the internal and external forms of nonlinear damping can turn a supercritical instability of the system into a subcritical one, thus revealing another destabilizing effect of damping, beyond the very well-known one occurring in the linear field. Numerical simulations, grounded on a Galerkin discretization of the original system, confirm the analytical findings.

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A Simple Model for Predicting the Nonlinear Dynamic Behavior of Elastic Systems Subjected to Friction

Cited by 2 publications

References 12 publications

Non-Linear Dynamics of Simple Elastic Systems Undergoing Friction-Ruled Stick–Slip Motions

Non-Linear Dynamics of Simple Elastic Systems Undergoing Friction-Ruled Stick–Slip Motions

On the role of different nonlinear damping forms in the dynamic behavior of the generalized Beck’s column

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