Preface to the special issue on “Recent developments in structural nonlinear dynamics”

Nonlinear Dynamics, Nov 2016

Angelo Luongo, Sara Casciati

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Preface to the special issue on “Recent developments in structural nonlinear dynamics”

Preface to the special issue on “Recent developments in structural nonlinear dynamics” Angelo Luongo 0 1 Sara Casciati 0 1 0 S. Casciati University of Catania , Siracusa , Italy 1 A. Luongo Department of Civil, Construction-Architectural and Environmental Engineering, University of L'Aquila , Via Ospedale S. Salvatore 6, 67100 L'Aquila , Italy - Recent studies on the dynamics of mechanical systems show that a proper nonlinear modelling allows not only a correct understanding of the system behavior, especially in some classical paradoxical phenomena, but also improving the performance of controllers and energy harvesting devices. Remarkably, nonlinearities might involve detrimental or beneficial effects on the post-critical behavior, which can be exploited in the design process. Moving our steps based on these observations, the main topics discussed in this special issue are summarized as follows. In Hao et al. (2016), a two sided damping constraint control strategy is proposed to improve the performance of a quasi-zero stiffness isolator. This strategy consists of switching the damping of the isolator between the soft- and hard-modes based on a preset value of the relative displacement (PRD). For an adequately chosen PRD value, it is shown that the damping control approach can lower the isolation frequency, enhance the effectiveness of the isolation in high frequencies, and prevent the severity of end-stop impacts. In Ture Savadkoohi et al. (2016), the 1:1 resonant behavior of mechanical systems with rheologies, where the main oscillators are coupled with nonlinear energy sink(s), is studied at different time scales. Invariants of the systems at fast time scale are detected, while possible periodic and strongly modulated regimes around their invariants are traced at slow time scales. This methodology provides some insight to be used in the design of the nonlinear energy sinks for passively controlling and/or energy harvesting of the main oscillators. The effectiveness of the nonlinear energy sink in controlling the limit cycle oscillations of a nonlinear aeroelastic system is assessed in Bichiou et al. (2016). The system consists of a rigid airfoil elastically mounted on linear and nonlinear springs. The results show that the nonlinear energy sink has a limited impact on the system’s response in terms of effectively delaying the onset of flutter, changing the type of instability or reducing the amplitude of the limit cycle oscillations. In D’Annibale (2016), the effects of several linear and passive piezoelectric controllers on the limit-cycle at the Hopf bifurcation triggered by a follower force acting on a Ziegler’s column endowed with a Van der Pollike nonlinear damping are investigated. It is shown that the piezoelectric-based control specifically designed to increment the critical bifurcation load of the system, can also have, quite surprisingly, a detrimental effect on its nonlinear dynamics, by giving rise to the occurrence of the hard loss of stability phenomenon. In Belhaq and Hamdi (2016), a delayed van der Pol oscillator with time-varying delay amplitude is coupled to an electromagnetic energy harvesting device. The vibration source is due to self-excitations, and the influence of different system parameters on the performance of the quasi-periodic (QP) vibration-based energy harvesting is reported and discussed. In particular, it is shown that the modulation of the delay amplitude gives rise to large-amplitude QP vibrations in a broadband of the parameters near and far from the resonance. The self-excited angular dynamics of elastically restrained rigid-bodies in uniform compressible laminar flows is numerically investigated in Kleiman et al. (2016). The results reveal a critical angle-of-attack beyond which the flow becomes unsteady. Periodic limit-cycles are observed for a low Reynolds number flow. These self-excited oscillations evolve to ultrasubharmonic, quasiperiodic and non-stationary chaoticlike dynamics with increasing Reynolds number. The Nicolai paradox, concerning the loss of stability of a column subjected to an evanescent follower torque, is analyzed in the nonlinear regime in Luongo and Ferretti (2016). It is shown that, under certain circumstances, nonlinearities can limit the amplitude of the post-critical oscillations. The existence of unsafe initial conditions is discussed, and the dangerous effects of the follower torque, also in nonlinear regime, are highlighted. A nonlinear extended regularized model of a taut string carrying a moving point mass is proposed in Gavrilov et al. (2016) with the intent to contribute to the solution of the paradox of particle’s discontinuous trajectory. The main features of this model is to introduce the coupling between transversal and longitudinal motions of the string under the assumption of a nondissipative mass-string system. The non-zero limit vertical position of the point mass causes the emergence of a wave resistance force that hinders the approach of the end support. Thus, the solution is continuous, but to reach the remote support is not always possible, depending on a dimensionless parameter given by the ratio between the point mass weight and the prestress tension. The analysis of the effects of a local control procedure on the global dynamical behavior of a noncontact Atomic Force Microscopy (AFM) reduced order model is performed in Settimi and Rega (2016). The aim consists of identifying the design parameters ranges able to guarantee a reliable operation of the AFM by avoiding the instabilities of the micro-cantilever beam. In particular, the AFM dynamic integrity is assessed by drawing the erosion profiles of the basins of attraction of the system bounded solutions under horizontal parametric excitation. The stability thresholds in the proximity of the resonance regions are assessed for varying initial conditions of the forcing amplitude and the tip sample distance. The implementation of a cell mapping method towards the distributed computing of large-scale basins of attraction is discussed in Belardinelli and Lenci (2016). A parallel implementation using a multicore environment is pursued, and two types of cores are considered; namely, the integrator core and the memory core. When the integrator core finds an attractor, it sends the information to the memory core to process and add it to the database if it does not already exist there. A proper balance between memory operations and numerical integrations is the key to obtain the optimal performance of the proposed algorithm. The editors are grateful to the authors and the reviewers for their cooperation, and to the journal publisher for giving them the opportunity to publish these contributions together.


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Angelo Luongo, Sara Casciati. Preface to the special issue on “Recent developments in structural nonlinear dynamics”, Nonlinear Dynamics, 2016, DOI: 10.1007/s11071-016-3178-2