Quasi Zero Stiffness (QZS) devices have received widespread interest due to their potential applications in vibration isolation and as nonlinear energy sinks. However, as the stiffness is driven ...towards zero, the response becomes dominated by the effects of damping and friction. This places a strong emphasis on accurate modelling of these effects if realistic results are to be achieved. This work analyses and experimentally demonstrates the complex responses that can occur in a frictional QZS device, including isolated response regions and non-sinusoidal responses. This is done using a simple device recently developed by the authors that allows accurate adjustment of the nonlinear force–displacement curve. Furthermore, high frequency disturbances on the frictional system are shown to introduce a damping effect on the low frequency behaviour, and an equivalent linear damping coefficient is derived.
Through the reading and the analysis, a posteriori, of Studio Monestiroli's projects for the Cimitero Maggiore of Voghera and the Cemetery on the island of San Michele in Venice, the text identifies ...in some specific elements, which build the place of the dead, the reasons of sense and form for the representation of the sepulchral space. The comparison of the two works also leads to a profound questioning of the permanent architectural elements that contribute to the representation of the cult of the dead. Protecting and preserving through the relationship that these elements establish with the place and, at the same time, questioning the relationship between architecture and nature.
The so-called Isola Rizza treasure, now conserved in the Museum of Castelvecchio, it was found by chance in this locality of the Veronese plain in 1872. Some brief updates on this treasure are ...proposed on the basis of the most recent research, with the intention of highlighting some themes that may arouse further research in the future. Finally, through the analysis of two manuscripts by Luigi Bennassuti conserved in Biblioteca Civica of Verona and in Biblioteca Capitolare of Verona, compiled a short distance after that discovery, the data of which are put in relation with the cadastral data, the identification of the area of concealment and some aspects of the conditions of the finds at the time of discovery and of the social context are specified.
The study of linear mechanical structures with discrete nonlinear attachments is a widespread field in structural dynamics as it is important in many areas of engineering. A common type of ...nonlinearity is a hardening spring, which can be described by a cubic polynomial representing the force-deflection relationship. The frequency response of a system consisting of a hardening spring and a mass is characterized by an amplitude-dependent resonance frequency, that increases as the displacement of the mass increases. The way in which the resonance of a nonlinear attachment interacts with the resonance of a linear host structure has already been discussed in the literature, however little attention has been paid to the interaction of the nonlinear resonance with a fixed anti-resonance of the host structure. This paper aims to fill this gap by addressing the physical aspects of the interaction between an anti-resonance and a resonance due to a nonlinear resonant attachment. A two-degrees-of-freedom system representing a general structure with two modes of vibration is used as a host structure to which a nonlinear resonant device is attached. The host structure has a fixed anti-resonance prior to the nonlinear device being attached to the structure, and the influence of this device on the anti-resonance is investigated. This is achieved by using the harmonic balance method and a numerical continuation algorithm. In the study, it was found that the anti-resonance interacts with the nonlinear resonance, where some of the peaks bend toward higher frequencies because of the hardening stiffness. Further increasing the nonlinearity, results in an isola being formed inside the main frequency response curve. When the motion is extremely high, quasi-periodic or chaotic-like responses are observed in specific frequency regions.
•Investigation of Resonance and Anti-Resonance Interactions in Nonlinear Mechanical Structures.•Novel Study on the Influence of Nonlinear Attachments on Fixed Anti-Resonance Frequencies.•Harmonic Balance Method and Numerical Continuation Algorithm Used to Analyze Nonlinear Resonance Interactions.
The escalation of the health conditions concerning the recent emergency amplifies the problems already expressed by the evolution of the urban organism. The alternation between the appropriate need ...for confinement of the inhabitants in limited groups and the policies of social distancing aiming at stemming the spread of contagion of a virus that is as lethal as it is peculiar, proposes, in these current times, a general reflection on the composition of the forma urbis to refine settlement grammars that, in the face of the expansion and dispersion of the informal city of the twentieth century outlines, on the other hand, in the concentration and discontinuity of the built-up areas, in the identifiability of a finished figure of the settlements, in the control of the void as the primary space of agricultural production and sociability, the operational conditions to define the characters of a plausible urban dimension.
In this work, we have mathematically modeled a 1DOF parametric oscillator with stiffness-hardening characteristics and dry friction and investigated both experimentally and numerically the ...bifurcation dynamics. The system consists of a cart moving along a linear rolling guide widely used in the industry. It has a stiffness comprised of two components: a linear time-variable part generated by a rotating rod of a rectangular cross-section and a nonlinear hardening stiffness caused by magnetic springs. In the case of nonlinear resistance of motion in a rolling bearing, regardless of the true nature of this phenomenon, it was modeled as the sum of viscous damping and the second component mathematically equivalent to dry friction. The trivial solution was observed to be stable in the whole range of parametric excitation frequencies. But there is a frequency range where the system is bistable, a periodic attractor coexists with the stable equilibrium position, and the branch of the periodic orbit is isolated, i.e., not connected with the equilibrium position, and forms an Isola. This distinguishes the analyzed system from the commonly investigated parametric oscillators, including the classical Mathieu equation and its various versions. Our work perfectly agreed between the numerical simulations and the experimental data. Moreover, the mathematical model for different friction values is investigated, showing the transition between the system without dry friction and the actual rig. The stability of the equilibrium position is tested, and the bifurcation dynamics of periodic orbits are presented using numerical continuation methods, obtaining complete agreement between the results obtained using different ways.
•1DOF parametric oscillator with dry friction is investigated experimentally.•Bistability of experimental oscillator is observed.•Bifurcation dynamics of the oscillator is investigated.•Isolated branches of periodic solutions are shown.•Effect of dry friction on the properties of the parametric oscillator is revealed.
This work presents a conceptually simple experiment consisting of a cantilever beam with a nonlinear spring at the tip. The configuration allows manipulation of the relative spacing between the modal ...frequencies of the underlying linear structure, and this permits the deliberate introduction of internal resonance. A 3:1 resonance is studied in detail; the response around the first mode shows a classic stiffening response, with the addition of more complex dynamic behaviour and an isola region. Quasiperiodic responses are also observed but in this work the focus remains on periodic responses. Predictions using Normal Form analysis and continuation methods show good agreement with experimental observations. The experiment provides valuable insight into frequency responses of nonlinear modal structures, and the implications of nonlinearity for vibration tests.
•Experimental demonstration of 3:1 internal resonance in an easy to reproduce structure with transparent underlying physics.•Experimental demonstration of isolated region in frequency response.•Normal forms/backbone analysis of the free structure used to explain the rich dynamics seen.•Reasonable match with continuation analysis in AUTO; the revealed structure of bifurcations sheds further light on the response of the forced and damped system.
Meta-materials are utilized for bringing passive attenuation solution especially in the acoustics and vibration domains. Generally speaking, they are composed of an array or a chain of meta-cells. ...Here the vibratory energy exchanges between particles of a nonlinear meta-cell are studied. The meta-cell is composed of an outer mass which houses an inner mass with a compound nonlinear restoring forcing term. It is globally non-smooth, containing pure cubic and piece-wise linear terms, which constitutes a new type of nonlinearity for such mass-in-mass cells. The complexified form of system equations is treated by the multiple time scale method to find out its fast and slow dynamics, leading to determination of the slow invariant manifold as well as the singular and equilibrium points of the system. The compound nonlinear restoring forcing function of the inner mass makes the global geometry of the slow invariant manifold to be different from those of systems with pure cubic nonlinearities, for example, including four singular lines and two distinct unstable zones. Amplitude dependency of the frequency of such a nonlinear system in the conservative form is represented by the backbone curves. Furthermore, detected equilibrium points for different external forcing amplitudes are represented by three-dimensional frequency response curves. Finally, analytical predictions are confronted with numerical results obtained by direct time integration of the system equations. An application of such system can be the passive control of main systems via embedding another nonlinear oscillator inside it. Moreover, such system can also be extended in the form of an array to create meta-materials.
•A mass-in-mass meta-cell with a compound nonlinearity is studied.•The complexified form of system equations is treated by the multiple time scale method.•Fast and slow system dynamics are detected.•The system can present periodic and/or non-periodic responses.
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