929 research outputs found

    Dynamics of a linear beam with an attached local nonlinear energy sink

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    We provide numerical evidence of passive and broadband targeted energy transfer from a linear flexible beam under shock excitation to a local essentially nonlinear lightweight attachment that acts, in essence, as nonlinear energy sink—NES. It is shown that the NES absorbs shock energy in a one-way, irreversible fashion and dissipates this energy locally, without 'spreading' it back to the linear beam. Moreover, we show numerically that an appropriately designed and placed NES can passively absorb and locally dissipate a major portion of the shock energy of the beam, up to an optimal value of 87%. The implementation of the NES concept to the shock isolation of practical engineering structures and to other applications is discussed

    Resonators coupled to voltage-biased Josephson junctions: From linear response to strongly driven nonlinear oscillations

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    Motivated by recent experiments, where a voltage biased Josephson junction is placed in series with a resonator, the classical dynamics of the circuit is studied in various domains of parameter space. This problem can be mapped onto the dissipative motion of a single degree of freedom in a nonlinear time-dependent potential, where in contrast to conventional settings the nonlinearity appears in the driving while the static potential is purely harmonic. For long times the system approaches steady states which are analyzed in the underdamped regime over the full range of driving parameters including the fundamental resonance as well as higher and sub-harmonics. Observables such as the dc-Josephson current and the radiated microwave power give direct information about the underlying dynamics covering phenomena as bifurcations, irregular motion, up- and down conversion. Due to their tunability, present and future set-ups provide versatile platforms to explore the changeover from linear response to strongly nonlinear behavior in driven dissipative systems under well defined conditions.Comment: 12 pages, 11 figure

    Multi-scaled analysis of the damped dynamics of an elastic rod with an essentially nonlinear end attachment

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    We study multi-frequency transitions in the transient dynamics of a viscously damped dispersive finite rod with an essentially nonlinear end attachment. The attachment consists of a small mass connected to the rod by means of an essentially nonlinear stiffness in parallel to a viscous damper. First, the periodic orbits of the underlying hamiltonian system with no damping are computed, and depicted in a frequency–energy plot (FEP). This representation enables one to clearly distinguish between the different types of periodic motions, forming back bone curves and subharmonic tongues. Then the damped dynamics of the system is computed; the rod and attachment responses are initially analyzed by the numerical Morlet wavelet transform (WT), and then by the empirical mode decomposition (EMD) or Hilbert–Huang transform (HTT), whereby, the time series are decomposed in terms of intrinsic mode functions (IMFs) at different characteristic time scales (or, equivalently, frequency scales). Comparisons of the evolutions of the instantaneous frequencies of the IMFs to the WT spectra of the time series enables one to identify the dominant IMFs of the signals, as well as, the time scales at which the dominant dynamics evolve at different time windows of the responses; hence, it is possible to reconstruct complex transient responses as superposition of the dominant IMFs involving different time scales of the dynamical response. Moreover, by superimposing the WT spectra and the instantaneous frequencies of the IMFs to the FEPs of the underlying hamiltonian system, one is able to clearly identify the multi-scaled transitions that occur in the transient damped dynamics, and to interpret them as ‘jumps’ between different branches of periodic orbits of the underlying hamiltonian system. As a result, this work develops a physics-based, multi-scaled framework and provides the necessary computational tools for multi-scaled analysis of complex multi-frequency transitions of essentially nonlinear dynamical systems

    Continuous variable entanglement of phase locked light beams

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    We explore in detail the possibility of intracavity generation of continuous-variable (CV) entangled states of light beams under mode phase-locked conditions. We show that such quantum states can be generated in self-phase locked nondegenerate optical parametric oscillator (NOPO) based on a type-II phase-matched down-conversion combined with linear mixer of two orthogonally polarized modes of the subharmonics in a cavity. A quantum theory of this device, recently realized in the experiment, is developed for both sub-threshold and above-threshold operational regimes. We show that the system providing high level phase coherence between two generated modes, unlike to the ordinary NOPO, also exhibits different types of quantum correlations between photon numbers and phases of these modes. We quantify the CV entanglement as two-mode squeezing and show that the maximal degree of the integral two-mode squeezing(that is 50% relative to the level of vacuum fluctuations) is achieved at the pump field intensity close to the generation threshold of self-phase locked NOPO, provided that the constant of linear coupling between the two polarizations is much less than the mode detunings. The peculiarities of CV entanglement for the case of unitary, non-dissipative dynamics of the system under consideration is also cleared up
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