Experimental evidence of bifurcating nonlinear normal modes in piecewise linear systems

Giannini, Oliviero; Casini, Paolo; Vestroni, Fabrizio

doi:10.1007/s11071-010-9827-y

Cited by 17 publications

(4 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…the friction force for the AS is greater than that for the DS) and the anticlockwise drooping loops have been observed in the pure sliding regime in engineering applications. Moreover, the hysteretic loops have been experimentally observed in the presliding regime based on the compliance property between the asperities induced by the spring-like behaviour as described in (Casini et al, 2012;Giannini et al, 2011). As a result, there is velocity overshooting during the initiation of stick-slip motion between the bodies in contact.…”

Section: Introductionmentioning

confidence: 99%

Modelling and analysis of dynamic frictional interactions of vibro-driven capsule systems with viscoelastic property

Liu

Cang

2019

European Journal of Mechanics - A/Solids

View full text Add to dashboard Cite

This paper studies the dynamic frictional interactions of the underactuated vibro-driven capsule systems with the viscoelastic property. Frictional dynamics of the capsule systems is an active research domain, while the online implementation and control of the friction models are still intractable tasks. This paper investigates the frictional characteristics of the capsule systems in the dynamic regime, including particularly the non-reversible drooping and hysteresis. Firstly, the frictional interaction dynamics is modelled and characterized using a combined physics-based and analytical-based approach. Subsequently, the qualitative changes in the capsule dynamics and friction-induced vibrational responses that triggered by multiple control parameters are discussed. It is found that the capsule dynamics is mainly periodic, and the motion velocity of the capsule systems can be controlled by appropriate tuning of the control parameters around the identified control points. Simulation results have a good agreement with the experimentally observed frictional characteristics. The effectiveness of the proposed method is verified in terms of satisfaction of the energy requirements and quenching of the friction-induced vibrations. It is also found that the frictional interaction dynamics of the capsule systems can be predicted for a wide range of vibrational behaviours. Finally, the importance of a concrete understanding and accurate description of the dynamic friction at the sliding substrate is highlighted.

show abstract

Section: Introductionmentioning

confidence: 99%

Modelling and analysis of dynamic frictional interactions of vibro-driven capsule systems with viscoelastic property

Liu

Cang

2019

European Journal of Mechanics - A/Solids

View full text Add to dashboard Cite

show abstract

“…A number of studies exist for the static and dynamic analysis of structuresupport problem with unilateral connection (e.g. [26][27][28][29][30][31]), but, mostly, they assume that the location of the contact and non-contact zones are given as prior information, or they are limited to the systems with limited DOFs. An indepth understanding is still incomplete, as the ongoing challenge is to perform the time integration procedure in a predictive and efficient way.…”

Section: Introductionmentioning

confidence: 99%

Non-linear modal analysis of structural components subjected to unilateral constraints

Attar

Karrech

Regenauer-Lieb

2017

Journal of Sound and Vibration

View full text Add to dashboard Cite

In this paper, we present a detailed numerical study of the non-linear dynamics in structural components under unilateral contact constraints. Here, the unilateral term characterises the constitutive law of the restoring force in the constraints as they only sustain elastic reactions in one direction, either compressive or tensile.Thus, the non-differentiability of the contact law at the discontinuity point is the only source of non-linearity. In our approach, the discrete lattice method (DLM) is used to treat the continuous system as a piecewise linear model. Thus, the trajectory of each node in the discrete model would be a sequence of smooth solutions with the switching times between them. The application of the one-step integration scheme allows us to detect the occurrence of contact (i.e. the instants that the lattice nodes cross the discontinuity boundary) and consequently update the active Preprint submitted to Elsevier 31 October 2016 constraints. We also consider embedding the bisection algorithm into the time integration procedure to localise the instants at which the nodes cross the boundary and minimise the accumulative error. Subsequently, the resulting unconditionally stable integration scheme is utilised as the modelling tool in combination with the shooting technique to perform a novel non-smooth modal analysis. In analogy with the smooth non-linear systems, the evolution of non-smooth periodic motions is presented in the frequency-stiffness plots. We apply our method to obtain non-linear normal modes (NNMs) for a number of representative problems, including a barobstacle system, a beam-substrate system and a granular chain with tensionless interactions. These numerical examples demonstrate the efficiency of the solution procedure to trace the family of energy-independent non-linear modes across the range of contact stiffnesses. Moreover, the stability analysis of the modes on the plot backbone reveal that they may become unstable due to the interaction with the higher modes or bifurcation of a new NNM with a period equal to the integer multiple of the main mode period. Our results also indicate that the bilinear formula can accurately predict the non-linear frequencies only if the corresponding mode exhibits a smooth character, regardless of the commutativity conditions of the system stiffness matrix. However, it is obvious that the assumption of smooth bilinear behaviour for non-linear modes is not generally valid. This highlights the importance of the present numerical framework for the computation of non-smooth resonance frequencies.

show abstract

“…For two oscillators (n=2) a periodic sticking motion was found. A coupled bilinear oscillator with a free end was considered in [39,40]. The analysis was based on combining the eigenfrequencies from alternating linear states, however out of 4 possibilities only two were considered in the approximation presented.…”

Section: Introductionmentioning

confidence: 99%

Structure of resonances and formation of stationary points in symmetrical chains of bilinear oscillators

Dyskin

Pasternak

Shufrin

2014

Journal of Sound and Vibration

View full text Add to dashboard Cite

Dynamics of strongly non-linear systems can in many cases be modelled by bilinear oscillators, which are the oscillators whose springs have different stiffnesses in compression and tension. This underpins the analysis of a wide range of phenomena, from oscillations of fragmented structures, connections and mooring lines to deformation of geological media. Single bilinear oscillators were studied previously and the presence of multiple resonances both super-and sub-harmonic was found. Less attention was paid to systems of multiple bilinear oscillators that describe many natural and engineering processes such as for example the behaviour of fragmented solids. Here we fill this gap concentrating on the simplest case-1D symmetrical chains of bilinear oscillators. We show that the presence and structure of resonances in a symmetric chain of bilinear oscillators with fixed ends depends upon the number of oscillating masses. Two elementary chains act as the basic ones: a single mass bilinear chain (a mass connected to the fixed points by two bilinear springs) that behaves as a linear oscillator with a single resonance and a two mass chain that is a coupled bilinear oscillator (two masses connected by three bilinear springs). The latter has multiple resonances. We demonstrate that longer chains either do not have resonances or get decomposed, during the resonance, into either the single mass or two mass elementary chains with stationary masses in between. The resonance frequencies are inherited from the basic chains of decomposition. We show that if the number of masses is odd the chain can be decomposed into the single mass bilinear chains separated by stationary masses. It then inherits the resonances of the single mass bilinear chain. The chains with the number of masses minus 2 divisible by 3 can be decomposed into the two mass bilinear chains separated by stationary masses and inherit the resonances of the two mass chains. The chains whose lengths satisfy both criteria (such as chains with 5, 11, 17 … masses) allow both types of resonances.

show abstract

Experimental evidence of bifurcating nonlinear normal modes in piecewise linear systems

Cited by 17 publications

References 29 publications

Modelling and analysis of dynamic frictional interactions of vibro-driven capsule systems with viscoelastic property

Modelling and analysis of dynamic frictional interactions of vibro-driven capsule systems with viscoelastic property

Non-linear modal analysis of structural components subjected to unilateral constraints

Structure of resonances and formation of stationary points in symmetrical chains of bilinear oscillators

Contact Info

Product

Resources

About