Rapid non-resonant intermodal targeted energy transfer (IMTET) caused by vibro-impact nonlinearity

Nonlinear Dynamics - This paper describes a rapid and efficient nonlinear non-resonance mechanism for low-to-high-frequency energy scattering, which is referred to as intermodal targeted energy...     

Experimental Study of Nonlinear Resonances and Anti-Resonances in a Forced,Ordered Granular Chain

We experimentally study a one-dimensional uncompressed granular chain composed of a finite number of identical spherical elastic beads with Hertzian interactions. The chain is harmonically excited by an amplitude- and frequency-dependent boundary drive at its left end and has a fixed boundary at its right end. Such ordered granular media represent an interesting new class of nonlinear acoustic metamaterials, since they exhibit essentially nonlinear acoustics and have been designated as “sonic vacua” due to the fact that their corresponding speed of sound (as defined in classical acoustics) is zero. This paves the way for essentially nonlinear and energy-dependent acoustics with no counterparts in linear theory. We experimentally detect time-periodic, strongly nonlinear resonances whereby the particles (beads) of the granular chain respond at integer multiples of the excitation period, and which correspond to local peaks of the maximum transmitted force at the chain’s right, fixed end. In between these resonances we detect a local minimum of the maximum transmitted forces corresponding to an anti-resonance in the stationary-state dynamics. The experimental results of this work confirm previous theoretical predictions, and verify the existence of strongly nonlinear resonance responses in a system with a complete absence of any linear spectrum; as such, the experimentally detected nonlinear resonance spectrum is passively tunable with energy and sensitive to dissipative effects such as internal structural damping in the beads, and friction or plasticity effects. We compare the experimental results with direct numerical simulations of the granular network and deduce satisfactory agreement.     

Nonlinear Parameter Identification of a Mechanical Interface Based on Primary Wave Scattering

We study stress-wave propagation in an impulsively forced split Hopkinson bar system incorporating a threaded interface. We first consider only primary transmission and reflection and reduce the problem to a first-order, strongly nonlinear ordinary differential equation governing the displacement across the interface, called the primary-pulse model. The interface is modeled as an adjusted-Iwan element, which is characterized by matching experimental and numerical eigenfrequencies as well as primary pulse amplitudes. We find that the adjusted-Iwan element parameters are dependent on preload and impact velocity (input force). A high-order finite element model paired with the identified adjusted-Iwan element is used to simulate multiple transmissions and reflections across the interface. We find that the finite element simulation reproduces the experimental results in both the wavelet and Fourier domains, validating the identification method. Our findings demonstrate that the primary-pulse model can be used for experimental parameter identification of nonlinear interfaces in waveguides.     

Periodic orbits, damped transitions and targeted energy transfers in oscillators with vibro-impact attachments

We study complex damped and undamped dynamics and targeted energy transfers (TETs) in systems of coupled oscillators, consisting of single-degree-of-freedom primary linear oscillators (LOs) with vibro-impact attachments, acting, in essence, as vibro-impact nonlinear energy sinks (VI NESs). First, the complicated dynamics of such VI systems is demonstrated by computing the VI periodic orbits of underlying Hamiltonian systems and depicting them in appropriate frequency–energy plots (FEPs). Then, VI damped transitions and distinct ways of passive TETs from the linear oscillators to the VI attachments for various parameter ranges and initial conditions are investigated. As in the case of smooth stiffness nonlinearity [Y. Lee, G. Kerschen, A. Vakakis, P. Panagopoulos, L. Bergman, D.M. McFarland, Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment, Physica D 204 (1–2) (2005) 41–69], both fundamental and subharmonic TET can be realized in the VI systems under consideration. It is found that the most efficient mechanism for VI TET is through the excitation of highly energetic VI impulsive orbits (IOs), i.e., of periodic or quasiperiodic orbits corresponding to zero initial conditions except for the initial velocities of the linear oscillators. In contrast to NESs with smooth essential nonlinearities considered in previous works, VI NESs are capable of passively absorbing and locally dissipating significant portions of the energies of the primary systems to which they are attached, at fast time scale. This renders such devices suitable for applications, like seismic mitigation, where dissipation of vibration energy in the early, highly energetic regime of the motion is a critical requirement.     

Primary pulse transmission in coupled steel granular chains embedded in PDMS matrix: Experiment and modeling

We present an experimental study of primary pulse transmission in coupled ordered steel granular chains embedded in poly-di-methyl-siloxane (PDMS) elastic matrix. Two granular one-dimensional chains are considered (an ‘excited’ and an ‘absorbing’ one), each composed of 11 identical steel beads of 9.5 mm diameter with the centerline of the chain spaced at fixed distances of 0.5, 1.5 or 2.5 mm apart. We directly force one of the chains (the excited one) by a transient pulse and measure, by means of laser vibrometry, the primary transmitted pulses at the end beads of both chains and at the first bead of the absorbing chain. It is well known that the dynamics of this type of ordered granular media is strongly nonlinear due, (i) to Hertzian interactions between adjacent beads, and (ii) to possible bead separations in the absence of compressive forces and ensuing collisions between neighboring beads. Accordingly, we develop a strongly nonlinear theoretical model that takes into account the coupling of the granular chains due to the PDMS matrix, with the aim to model primary pulse transmission in this system. After validating the model with experimental measurements, we employ it in a predictive fashion to estimate energy transfer between chains as a function of the interspatial distance between chains. Furthermore, based on this model we perform predictive matrix design to achieve maximum energy transfer from the excited to the absorbing chain, and provide a theoretical explanation of the nonlinear dynamics governing energy transfer (including energy equi-partition) in this system.     

Dynamic analysis of a unidirectional periodic isolator,consisting of identical masses and intermediate distributed resilient blocks

An analytical procedure for the dynamic analysis of the unidirectional periodic isolator, consisting of n concentrated masses and n intermediate arbitrary blocks is developed. Complex polynomials depending on the four pole parameters of the mounts and on the frequency of excitation are introduced, to express analytical forms for the impedances and transmissibilities of the general system. By means of these polynomials, the frequency equation of the undamped isolator can be derived directly, for free or fixed boundary conditions. Application of the method was made with isolators consisting of masses and distributed elements of rubber with internal damping.     

Complex dynamics of perfect discrete systems under partial follower forces

Equilibrium points, primary and secondary static bifurcation branches, and periodic orbits with their bifurcations of discrete systems under partial follower forces and no initial imperfections are examined. Equilibrium points are computed by solving sets of simultaneous, non-linear algebraic equations, whilst periodic orbits are determined numerically by solving 2- or 4-dimensional non-linear boundary value problems. A specific application is given with Ziegler's 2-DOF cantilever model. Numerous, complicated static bifurcation paths are computed as well as complicated series of periodic orbit bifurcations of relatively large periods. Numerical simulations indicate that chaotic-like transient motions of the system may appear when a forcing parameter increases above the divergence state. At these forcing parameter values, there co-exist numerous branches of bifurcating periodic orbits of the system; it is conjectured that sensitive dependence on initial conditions due to the large number of co-existing periodic orbits causes the chaotic-like transients observed in the numerical simulations.     

Enhanced harmonic conversion efficiency in the self-guided propagation of femtosecond ultraviolet laser pulses in argon

Harmonic generation during the self-guided propagation of femtosecond ultraviolet (UV) laser pulses (248-nm, 450-fs) in argon is investigated. The third (82.7-nm) and fifth (49.6-nm) harmonics are generated in the UV filament. The energy-conversion efficiencies for the harmonics are found to be at least two orders of magnitude higher than those reported in the literature for similar gas pressures. The enhancement is attributed to the quasi-phase matching of the harmonics due to the self-guiding of the driving pulse. PACS 42.25.Bs; 42.65.Jx; 42.65.Re; 42.65.Ky