Limiting phase trajectories and the origin of energy localization in nonlinear oscillatory chains

We demonstrate that the modulation instability of the zone boundary mode in a finite (periodic) Fermi-Pasta-Ulam chain is the necessary but not sufficient condition for the efficient energy transfer by localized excitations. This transfer results from the exclusion of complete energy exchange between spatially different parts of the chain, and the excitation level corresponding to that turns out to be twice more than threshold of zone boundary mode's instability. To obtain this result one needs in far going extension of the beating concept to a wide class of finite oscillatory chains. In turn, such an extension leads to description of energy exchange and transition to energy localization and transfer in terms of 'effective particles' and Limiting Phase Trajectories. The 'effective particles' appear naturally when the frequency spectrum crowding ensures the resonance interaction between zone boundary and two nearby nonlinear normal modes, but there are no additional resonances. We show that the Limiting Phase Trajectories corresponding to the most intensive energy exchange between 'effective particles' can be considered as an alternative to Nonlinear Normal Modes, which describe the stationary process

Suppression Aeroelastic Instability Using Broadband Passive Targeted Energy Transfers, Part 1: Theory

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76103/1/AIAA-24062-636.pd

On the dynamics of a nonlinear energy harvester with multiple resonant zones

The dynamics of a nonlinear vibration energy harvester for rotating systems is investigated analytically through harmonic balance, as well as by numerical analysis. The electromagnetic harvester is attached to a spinning shaft at constant speed. Magnetic levitation is used as the system nonlinear restoring force for broadening the resonant range of the oscillator. The system is modelled as a Duffing oscillator with linear frequency variation under static, as well as harmonic excitation. Behaviour charts and backbone curves are extracted for the fundamental harmonic response and validated against frequency response curves for selected cases, using direct numerical integration. It is found that variation in stiffness, together with asymmetric forcing, gives rise to a novel structure of multiple resonant zones, incorporating mono-stable and bi-stable dynamics. Contrary to previously considered bi-stable energy harvesters, cross-well oscillations are realized through a transition from single-well potential energy to double-well with forward frequency sweep. Furthermore, in-well_oscillations present a hardening behaviour, unlike the well-known softening in-well response of bi-stable Duffing oscillators. The analysis shows that the proposed system has multiple resonant responses to a frequency sweep, influenced by consecutive interacting backbone curves similar to a multi-modal system. This combined effect of the transition to bi-stable dynamics and the hardening in-well oscillations induces resonant response of the harvester over multiple distinct frequency ranges. Thus, the system exhibits a broadened frequency response, enhancing its energy harvesting potential

Experimental testing of a large 9-story structure equipped with multiple nonlinear energy sinks subjected to an impulsive loading

ABSTRACT Building structures can be critically affected by impulsive loads such as blasts, collisions, gusts, and pulse dominated earthquakes. The addition of nonlinear energy sinks (NESs) in buildings has been proposed as a means to rapidly and passively dissipate the energy in a system exposed to this type of loading. This rapid dissipation occurs because the essential nonlinearity of the NES allows it to resonate with any mode of the structure and engage in targeted energy transfer, the nearly oneway transfer of energy to the NES where it is locally dissipated. Additionally, the NES couples the modes of the structure and facilitates the transfer of energy from the lower modes of the structure to the higher modes, where it can be dissipated at a reduced time scale. In this study the experimental performance of a system of multiple NESs in a large 9-story test structure is discussed. Two different types of NESs are used, each of which employ a different type of restoring force; one type of NES utilizes a smooth restoring force that is roughly cubic, while the other utilizes a linear restoring force coupled with one-sided vibro-impacts. To load this system, an impulse-like ground motion is applied via a large shake table. The results of this study show that the system of NESs greatly improves the performance of the structure across a wide range of impulse amplitudes by reducing and very rapidly attenuating its response

Study of the relative humidity dependence of aerosol light-scattering in southern Spain

This investigation focuses on the characterisation of the aerosol particle hygroscopicity. Aerosol particle optical properties were measured at Granada, Spain, during winter and spring seasons in 2013. Measured optical properties included particle light-absorption coefficient (sap) and particle light-scattering coefficient (ssp) at dry conditions and at relative humidity (RH) of 85 +/- 10%. The scattering enhancement factor, f(RH=85%), had a mean value of 1.5 +/- 0.2 and 1.6 +/- 0.3 for winter and spring campaigns, respectively. Cases of high scattering enhancement were more frequent during the spring campaign with 27% of the f(RH=85%) values above 1.8, while during the winter campaign only 8% of the data were above 1.8. A Saharan dust event (SDE), which occurred during the spring campaign, was characterised by a predominance of large particles with low hygroscopicity. For the day when the SDE was more intense, a mean daily value of f(RH=85%)=1.3 +/- 0.2 was calculated. f(RH=85%) diurnal cycle showed two minima during the morning and afternoon traffic rush hours due to the increase in non-hygroscopic particles such as black carbon and road dust. This was confirmed by small values of the single-scattering albedo and the scattering Angstrom exponent. A significant correlation between f(RH=85%) and the fraction of particulate organic matter and sulphate was obtained. Finally, the impact of ambient RH in the aerosol radiative forcing was found to be very small due to the low ambient RH. For high RH values, the hygroscopic effect should be taken into account since the aerosol forcing efficiency changed from -13W/m2 at dry conditions to -17W/m2 at RH=85%.This work was supported by the Andalusia Regional Government through projects P10-RNM-6299 and P12-RNM-2409; by the Spanish Ministry of Economy and Competitiveness through projects CGL2010-18782, CSD2007-00067, CGL2011-13580-E/CLI and CGL2011-16124-E; and by EU through ACTRIS project (EU INFRA-2010-1.1.16-262254).G. Titos was funded by the program FPI of the Spanish Ministry of Economy and Competitiveness – Secretariat of Science, Innovation and Development under grant BES-2011-043721

Influence of water uptake on the aerosol particle light scattering coefficients of the Central European aerosol

The influence of aerosol water uptake on the aerosol particle light scattering was examined at the regional continental research site Melpitz, Germany. The scattering enhancement factor f(RH), defined as the aerosol particle scattering coefficient at a certain relative humidity (RH) divided by its dry value, was measured using a humidified nephelometer. The chemical composition and other microphysical properties were measured in parallel. f(RH) showed a strong variation, e.g. with values between 1.2 and 3.6 at RH=85% and λ=550 nm. The chemical composition was found to be the main factor determining the magnitude of f(RH), since the magnitude of f(RH) clearly correlated with the inorganic mass fraction measured by an aerosol mass spectrometer (AMS). Hysteresis within the recorded humidograms was observed and explained by long-range transported sea salt. A closure study using Mie theory showed the consistency of the measured parameters

Multi-frequency nonlinear energy transfer from linear oscillators to mdof essentially nonlinear attachments

We report on multi-frequency energy transfer from a two-mode, initially excited linear system to a multi-degree-of-freedom (mdof) essentially nonlinear attachment. This occurs through simultaneous resonance interactions of both linear modes with a set of nonlinear normal modes (NNMs) of the attachment, and is studied utilizing numerical wavelet transforms. The multi-frequency nonlinear energy transfer discussed herein differs from multi-frequency energy transfer caused by resonance capture cascading where sequential energy transfer from a set of linear modes to single-dof nonlinear attachments takes place. (c) 2004 Elsevier Ltd. All rights reserved