49 research outputs found
Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators
Many engineering structures are composed of weakly coupled sectors assembled
in a cyclic and ideally symmetric configuration, which can be simplified as
forced Duffing oscillators. In this paper, we study the emergence of localized
states in the weakly nonlinear regime. We show that multiple spatially
localized solutions may exist, and the resulting bifurcation diagram strongly
resembles the snaking pattern observed in a variety of fields in physics, such
as optics and fluid dynamics. Moreover, in the transition from the linear to
the nonlinear behaviour isolated branches of solutions are identified.
Localization is caused by the hardening effect introduced by the nonlinear
stiffness, and occurs at large excitation levels. Contrary to the case of
mistuning, the presented localization mechanism is triggered by the
nonlinearities and arises in perfectly homogeneous systems
On the effect of the loading apparatus stiffness on the equilibrium and stability of soft adhesive contacts under shear loads
The interaction between contact area and frictional forces in adhesive soft contacts is receiving much attention in the scientific community due to its implications in many areas of engineering such as surface haptics and bioinspired adhesives. In this work, we consider a soft adhesive sphere that is pressed against a rigid substrate and is sheared by a tangential force where the loads are transferred to the sphere through a normal and a tangential spring, representing the loading apparatus stiffness. We derive a general linear elastic fracture mechanics solution, taking into account also the interaction between modes, by adopting a simple but effective mixed-mode model that has been recently validated against experimental results in similar problems. We discuss how the spring stiffness affects the stability of the equilibrium contact solution, i.e. the transition to separation or to sliding
On unified crack propagation laws
The anomalous propagation of short cracks shows generally exponential fatigue crack growth but the dependence on stress range at high stress levels is not compatible with Parisâ law with exponent . Indeed, some authors have shown that the standard uncracked SN curve is obtained mostly from short crack propagation, assuming that the crack size a increases with the number of cycles N as where h is close to the exponent of the Basquinâs power law SN curve. We therefore propose a general equation for crack growth which for short cracks has the latter form, and for long cracks returns to the Parisâ law. We show generalized SN curves, generalized KitagawaâTakahashi diagrams, and discuss the application to some experimental data. The problem of short cracks remains however controversial, as we discuss with reference to some examples
Numerical and experimental analysis of the bi-stable state for frictional continuous system
Unstable friction-induced vibrations are considered an annoying problem in several fields of engineering. Although several theoretical analyses have suggested that friction-excited dynamical systems may experience sub-critical bifurcations, and show multiple coexisting stable solutions, these phenomena need to be proved experimentally and on continuous systems. The present work aims to partially fill this gap. The dynamical response of a continuous system subjected to frictional excitation is investigated. The frictional system is constituted of a 3D printed oscillator, obtained by additive manufacturing that slides against a disc rotating at a prescribed velocity. Both a finite element model and an experimental setup has been developed. It is shown both numerically and experimentally that in a certain range of the imposed sliding velocity the oscillator has two stable states, i.e. steady sliding and stickâslip oscillations. Furthermore, it is possible to jump from one state to the other by introducing an external perturbation. A parametric analysis is also presented, with respect to the main parameters influencing the nonlinear dynamic response, to determine the interval of sliding velocity where the oscillator presents the two stable solutions, i.e. steady sliding and stickâslip limit cycle
On notch and crack size effects in fatigue, Parisâ law and implications for Wöhler curves
As often done in design practice, the Wöhler curve of a specimen, in the absence of more direct information, can be crudely retrieved by interpolating with a power-law curve between static strength at a given conventional low number of cycles N0 (of the order of 10-103), and the fatigue limit at a âinfinite lifeâ, also conventional, typically Nâ=2Î106 or Nâ=107 cycles. These assumptions introduce some uncertainty, but otherwise both the static regime and the infinite life are relatively well known. Specifically, by elaborating on recent unified treatments of notch and crack effects on infinite life, and using similar concepts to the static failure cases, an interpolation procedure is suggested for the finite life region. Considering two ratios, i.e. toughness to fatigue threshold FK=KIc/DKth, and static strength to endurance limit, FR =sR /Ds0, qualitative trends are obtained for the finite life region. Parisâ and Wöhlerâs coefficients fundamentally depend on these two ratios, which can be also defined âsensitivitiesâ of materials to fatigue when cracked and uncracked, respectively: higher sensitivity means stringent need for design for fatigue. A generalized Wöhler coefficient, kâ, is found as a function of the intrinsic Wöhler coefficient k of the material and the size of the crack or notch. We find that for a notched structure, k<kâ<m, as a function of size of the notch: in particular, kâ=k holds for small notches, then kâ decreases up to a limiting value (which depends upon Kt for mildly notched structures, or on FK and FR only for severe notch or crack). A perhaps surprising return to the original slope k is found for very large blunt notches. Finally, Parisâ law should hold for a distinctly cracked structure, i.e. having a long-crack; indeed, Parisâ coefficient m is coincident with the limiting value of kâlim. The scope of this note is only qualitative and aims at a discussion over unified treatments in fatigue