Localization Of Vibrational Energy Research Articles

A design methodology for nonlinear oscillator chains enabling energy localization tuning and soliton stability enhancement with optimal damping

In this paper, the vibration energy localization in coupled nonlinear oscillators is investigated, based on the creation of standing solitons. The main objective is to establish a design methodology for mechanical lattices using the Nonlinear Schrödinger Equation (NLSE) as a guide strategy, even in the presence of damping. A three-dimensional diagram is used to illustrate stable parameter regions for damped stationary solitons. Moreover, an analysis of the influence of the number of oscillators in the system, and a numerical investigation regarding the stability of solitonic behavior is done. Through numerical analyses, it is observed that the developed algorithm not only has the capability to locate the highest amplitudes in the chain of oscillators, but also to control the intensity at which these amplitudes are located according to design requirements. The outcomes of the proposed methodology elucidate the impact that the coupling stiffness has on the stabilization of the NLSE, as well as the influence of the number of oscillators on the continuity hypothesis. The developed algorithm holds potential for practical applications in mechanical engineering since the NLSE is used as a design line rather than as a consequence of the phenomenon description.

Metamaterial-Based Analog Recurrent Neural Network Toward Machine Intelligence

Wave-based analog computation platforms hold the promise of realizing intelligent information processing with high speed and low computational cost, but current design principles face intractable problems in processing low-frequency wave information end to end at the physical layer. Here we theoretically demonstrate a concept of a metamaterial-based analog recurrent neural network (Meta-RNN) for intelligent classification of physical information carried by mechanical vibrations. With the spatiotemporal recurrence relation induced by coupled local resonators of the simulated metamaterial model, the Meta-RNN is capable of memorizing the internal hidden state in the dynamic displacement field. The trained coupling and synergy of local resonators lead to desirable vibration energy localization with selective frequency extraction capability, which can distinguish the intrinsic characteristics of vibration information. The proposed Meta-RNN provides a foundation for implementing a promising mechanical analog processor for intelligent vibration information processing and classification, and paves the way to efficient machine learning platforms for machine intelligence.

Bandgap widening by optimized disorder in one-dimensional locally resonant piezoelectric metamaterials

Locally resonant piezoelectric metamaterials offer outstanding vibration attenuation properties with the versatility in updating local resonances using either analog or digital electric circuits. The typically narrow bandgap observed in this sort of metamaterial can be enlarged through perturbations (or disorder) on the target frequencies of the resonant attachments, which also induce localization of vibration energy near the excitation source. This paper presents an optimization procedure for locally resonant piezoelectric metamaterial beams that enhances their vibration attenuation performance and avoids energy localization. Differently from the optimizations usually observed in the literature, the proposed one relies on an objective function that also considers the vibration along the whole one-dimensional structure. The large number of design variables given by the number of unit cells in the finite metastructure is tackled by following genetic-algorithm heuristics. The results evidence enhanced vibration attenuation performance due to the non-uniform distribution of target frequencies along a beam with periodic spatial distribution of piezoelements. While the bandgap width of the disordered metastructure is wider than that of a periodic reference case, the vibration localization is avoided. In this sense, the proposed methodology is a promising tool for achieving programmable and wideband electroelastic metastructures.

Transporting and concentrating vibrational energy to promote isomerization.

Visible-light absorption and transport of the resultant electronic excitations to a reaction centre through Förster resonance energy transfer1-3 (FRET) are critical to the operation of biological light-harvesting systems4, and are used in various artificial systems made of synthetic dyes5, polymers6 or nanodots7,8. The fundamental equations describing FRET are similar to those describing vibration-to-vibration (V-V) energy transfer9, and suggest that transport and localization of vibrational energy should, in principle, also be possible. Although it is known that vibrational excitation can promote reactions10-16, transporting and concentrating vibrational energy has not yet been reported. We have recently demonstrated orientational isomerization enabled by vibrational energy pooling in a CO adsorbate layer on a NaCl(100) surface17. Here we build on that work to show that the isomerization reaction proceeds more efficiently with a thick 12C16O overlayer that absorbs more mid-infrared photons and transports the resultant vibrational excitations by V-V energy transfer to a 13C18O-NaCl interface. The vibrational energy density achieved at the interface is 30 times higher than that obtained with direct excitation of the interfacial CO. We anticipate that with careful system design, these concepts could be used to drive other chemical transformations, providing new approaches to condensed phase chemistry.

Nonlinear multimodal electromagnetic device for vibration energy harvesting

A multimodal vibration energy harvesting in a periodic system is proposed. The multimodal approach and the nonlinearity are implemented in order to improve the performances of the studied device. The periodic system, based on electromagnetic transduction, consists of two weakly coupled magnets mechanically guided by two elastic beams. The quasi-periodic system is obtained by varying the mass of one of the moving magnets which leads to the vibration energy localization in regions close to the imperfections. This phenomenon is exploited to maximize the harvested energy. The mechanical nonlinearity is introduced by considering large displacements of the beams. The system is modeled by two coupled forced Duffing equations. The governing equations are solved using finite difference method combined with arc-length method. It is shown that the introduction of the nonlinearity leads to the enlargement of the bandwidth and the increase of the amplitude of the vibration.

Optimization of vibration energy localization in quasi-periodic structures

A mechanical periodic structure in presence of component perturbations can be a seat of a localization of vibration energy. In fact, it is well known that mistuned components have larger response levels than those of perfect components. This results in a localized energy, which can be tapped via harvesting devices. In this study, the dynamic behavior of a quasi-periodic system consisting in weakly connected linear oscillators is investigated. The main objective is to optimize the mistuning parameter, the coupling stiffness and the damping coefficient in order to functionalize the imperfection, which leads to the maximization of the localized vibration energy.

Effect of the localization on the response of a quasi-periodic electromagnetic oscillator array for vibration energy harvesting

Vibration energy harvesting by exploiting the multimodal approach in a quasi-periodic system is proposed. The quasi-periodic system, based on electromagnetic transduction, consists of two weakly coupled magnets mechanically guided by two elastic beams. Mistuning is achieved by varying the mechanical stiffness of one of the beams. These imperfections will lead to the vibration energy localization in regions close to the imperfections which will be exploited to maximize the harvested energy.

Perturbation and asymptotic solutions of energy localization of impurity modes in a one-dimensional anharmonic chain

A 1D anharmonic chain with a single impurity particle is used to study the vibrational energy localization. Numerical and asymptotic solutions for the symmetric anharmonic localized mode are both presented. The numerical results reveal that the energy localization strengthens with decreasing impurity mass or with increasing anharmonicity. In the weak-anharmonicity limit, the energy localization is close to the harmonic results and varies linearly with respect to the anharmonicity parameter. In the strong-anharmonicity limit, the localized structure tends towards a constant value that is independent of anharmonicity, but as a function of impurity mass. We finally analyze the stability of this symmetric impurity mode, and evidence a stable asymmetric mode as the result of a bifurcation from the symmetric mode for the case of the large impurity mass.

Localization of torsion vibrations in a discrete model of alkanes

A simple coarse-grained model of a crystal of normal paraffin (the united-atom model) is considered. By using an original semi-inverse method, it is shown that, alongside with known polymorphic transitions, the model under consideration assumes a dynamic transition, which manifests itself in the localization of vibration energy at a certain threshold value of excitation energy. The prediction of the conditions of this transition requires analytical determination of the spectrum of nonlinear normal modes with arbitrary amplitudes of vibrations because the instability of the mode with the lowest wavenumber is a necessary energy localization condition. The equations obtained make it possible to investigate the resonance interaction between the nonlinear normal modes near the low-frequency edge of the spectrum resulting in capture of the vibration energy by one of the parts of the chain. The conditions of localization of the vibration energy revealed determine the necessary initial data for computer modeling of the predicted dynamic transition in normal paraffins.

Models for blisks with large blends and small mistuning

Small deviations of the structural properties of individual sectors of blisks, referred to as mistuning, can lead to localization of vibration energy and drastically increased forced responses. Similar phenomena are observed in blisks with large damages or repair blends. Such deviations are best studied statistically because they are random. In the absence of cyclic symmetry, the computational cost to predict the vibration behavior of blisks becomes prohibitively high. That has lead to the development of various reduced-order models (ROMs). Existing approaches are either for small mistuning, or are computationally expensive and thus not effective for statistical analysis. This paper discusses a reduced-order modeling method for blisks with both large and small mistuning, which requires low computational effort. This method utilizes the pristine, rogue and interface modal expansion (PRIME) method to model large blends. PRIME uses only sector-level cyclic modes strategically combined together to create a reduction basis which yields ROMs that efficiently and accurately model large mistuning. To model small mistuning, nodal energy weighted transformation (NEWT) is integrated with PRIME, resulting in N-PRIME, which requires only sector-level calculations to create a ROM which captures both small and large mistuning with minimized computational effort.The combined effects of large blends and small mistuning are studied using N-PRIME for a dual flow path system and for a conventional blisk. The accuracy of the N-PRIME method is validated against full-order finite element analyses for both natural and forced response computations, including displacement amplitudes and surface stresses. Results reveal that N-PRIME is capable of accurately predicting the dynamics of a blisk with severely large mistuning, along with small random mistuning throughout each sector. Also, N-PRIME can accurately capture modes with highly localized motions. A statistical analysis is performed to study the effects of random mistuning on both natural frequencies and forced responses and reveals that 1) new clusters of mistuned natural frequencies exist and cannot be treated as small deviations from nominal frequencies, and 2) unexpectedly high amplifications of forced responses exist, showing 3–5 times higher responses compared to the nominal system.

Non-Linear Normal Modes in Dynamics - Discrete Systems

The aim of the paper is to inform about main features of Non-linear Normal Modes (NNM) as a powerful tool for investigation of multi-degree of freedom (MDOF) dynamic systems. In particular, it is shown how this concept can be used to investigate forced resonances of non-linear symmetric systems including non-linear localization of vibrational energy. NNMs can provide a valuable tool for understanding essentially non-linear dynamic phenomena having no counterparts in linear theory and which do not enable analysis using linearized procedures. Discrete MDOF systems are considered in this study. A couple of possible approaches are outlined together with some demonstrations of numerical results.

Mode- and Bond-Selective Chemistry on Metal Surfaces: The Dissociative Chemisorption of CHD3 on Ni(111)

A quantum approach based on an expansion in vibrationally adiabatic eigenstates is used to explore CHD3 dissociation on Ni(111). Symmetric stretch vibrations are shown to have larger efficacies for promoting reaction and bond selectivity than antisymmetric stretches. Mode softening, associated with a localization of vibrational energy on the reacting bond, correlates adiabatically with the symmetric stretch. This lowers the barrier on that vibrationally adiabatic reaction path. At energies below these barriers, reaction occurs via nonadiabatic transitions to lower-energy vibrational states at the avoided crossings. This sudden behavior preserves energy localization on the reactive bond and converts vibrational energy into bond breaking. One of the antisymmetric stretches can typically not couple to the other states due to symmetry, eliminating these pathways. The ν1 stretch has a large efficacy and can give 100% C–H cleavage selectivity. Both CD3 stretches have reasonable efficacies, and both promote C–D ...

Dynamics of nonlinear dissipative systems in the vicinity of resonance

The behavior of nonlinear dissipative 2-DOF mechanical systems in the vicinity of resonance is studied in this paper. Namely, the free resonance vibrations of a spring–mass–pendulum system and the forced resonance vibrations of a 2-DOF dissipative system containing a nonlinear absorber are considered. A reduced system stated with respect to the system energy, the arctangent of the vibration amplitudes ratio, and the phase difference, is obtained and analyzed. The nonlinear normal mode approach is used in this analysis. Conditions for vibration energy localization are discussed.

Forced response characteristics of bladed disks with mistuning non-linear friction

Aimed at the difficulty in revealing the vibration localization mechanism of mistuned bladed disks by using simple non-linear model, a mechanical model of the bladed disk with random mistuning of hysteretic dry friction damping was established. Then, the incremental harmonic balance method was used to analyze the effects of the parameters of bladed disks, such as the mistuning strength of dry friction force, coupled strength, viscous damping ratio and friction strength, on the forced response of the bladed disks. The results show that the vibrational energy localization phenomenon turns up in the tuned bladed disks if the nonlinear friction damping exists, and the random mistuning of the dry friction force intensifies this kind of vibration localization.

Micro‐conformational transitions in L‐alanine single crystals revisited by low wavenumber Raman spectroscopy

AbstractThe properties of the crystalline L‐alanine have been attracting attention for a very long time, and there is much controversy in the results already reported. One of the most interesting problems is that of the localization of vibrational energy and the micro‐transitions (named ‘breathers’ by Barthes et al. [M. Barthes, H. N. Bordallo, F. Dénoyer, J.‐E. Lorenzo, J. Zaccaro, A. Robert, F. Zontone, Eur. Phys. J. 2004, B37, 375]. In the present study, we have addressed this problem once again, having measured the high‐resolution polarized Raman spectra in the temperature range from 4 to 300 K. The wavenumber, bandwidth and intensity of all the modes polarized along the c‐axis (the axis of the head‐to‐tail chains of zwitterion in the structure) show discontinuities at 30–50, 100–120 and 180–220 K. We interpret the observed anomalies of spectral characteristics in terms of micro‐conformational transitions accompanied by the rearrangement of the hydrogen‐bond network and relate them to previously published work. Copyright © 2010 John Wiley & Sons, Ltd.

Mode-dependent enhancement and intramolecular dynamics via vibrationally mediated photodissociation

Vibrationally mediated photodissociation has been shown to control bond cleavage in molecules and probe their dynamics on the ground and excited potential energy surfaces. The application of this method to two seven-atom molecules illustrates surprising vibrational energy localization in methylamine (CH3NH2), a molecule with a torsional degree of freedom and unique information regarding intramolecular vibrational energy redistribution for the C–H methyl stretches of propyne (CH3C ≡ C–H).

Evidence for disorder in l-alanine lattice detected by Pulsed-EPR spectroscopy at cryogenic temperatures

The unusual behavior of lattice dynamics of l-alanine has been assigned to intermolecular dynamics and localization of vibrational energy. Recent heat capacity and Pulsed-EPR measurements support presence of thermally activated dynamic orientational disorder in the l-alanine lattice below 20 K. In the present study, the additional evidence for possible thermally activated disordered behavior of l-alanine lattice have been obtained by investigating dependences of longitudinal relaxation time of first stable l-alanine radical, SAR1, on sample cooling rates for the same low temperature interval. The obtained relaxation time by Pulsed-EPR shows clear dependence on cooling rates and this behavior can be explained within two types of suggested spin-lattice relaxation mechanisms for the paramagnetic centers in the hydrogen-bonded organic crystal.

Low‐wavenumber dynamics of L‐alanine

AbstractL‐Alanine is one of the simplest amino acids, the building block for many polypeptides and proteins. A previous Raman scattering study showed an anomalous temperature dependence of the intensity of the two lowest Raman modes, attributed to dynamic localization of vibrational energy. The present Raman data, collected in the b(cc)b scattering geometry, were aimed at understanding the dynamics of the low‐wavenumber modes in connection with the reported anomalies in other physical properties. Our study shows that the energy and intensity of the observed external modes show unusual behaviour in the temperature range ∼150–250 K. The anomalous temperature dependence of the peak of the NH3+ torsional mode is confirmed. Its wavenumber has a singularity around ∼220 K and its full width at half‐maximum does not increase linearly with temperature. The CH3 torsion and CO2− rock undergo similar discontinuities below ∼250 K. The intensity of the two lowest wavenumbers librons at 42 and 48 cm−1 shows an anomalous temperature dependence and vary in an opposite way from that reported for the c(bb)a scattering geometry. The nature of the subtle symmetry breaking occuring below ∼250 K is discussed. Copyright © 2005 John Wiley & Sons, Ltd.

Study of vibrational energy localization and redistribution in hydrogen peroxide H2O2 at low energy

Vibrational energy localization and/or redistribution in hydrogen peroxide H2O2 is studied at about 4000 cm(-1) above the quantum mechanical ground state using the ab initio potential energy surface of Koput, Carter, and Handy [J. Phys. Chem. A 102, 6325 (1998)]. In this work, the recently derived canonical perturbation procedure for floppy molecules serves two purposes. First, from the quantum mechanical point of view, it is shown that the energies of the lowest 130 states are reproduced with an average error smaller than 1.5 cm(-1) by a two-dimensional Hamiltonian, which is a function of the torsion and OO-stretch coordinates and momenta, while the other four degrees of freedom contribute only through powers of good quantum numbers. Moreover, the canonical perturbation procedure is also used in classical mechanics calculations, in order to define meaningful local modes, for which the ingoing and outgoing energy flows are monitored. Almost all the individual trajectories launched on the ab initio surface display the same behavior, that is, the superposition of (a) rapid (few hundreds of femtoseconds) and quasiperiodic energy exchanges between the two OH stretches and between the torsion and OO-stretch, and (b) slower (few to several picoseconds) but erratic-looking energy flows between all degrees of freedom. When averaging over large numbers of trajectories with the same local mode energies at time t=0, one observes instead a smooth and irreversible energy flow between all degrees of freedom, which usually thermalize in the range of several tens of picoseconds, that is, on time scales larger than the 5 ps period associated with the quantum density of states.

Micro-transitions or breathers in L-alanine?

The lattice dynamics of crystalline L-alanine shows unusual features tentatively assigned to a localization of vibrational energy. However, other properties alternatively suggest the existence of a second order phase transition undetected in previous crystallographic work. In this paper, we present the results of a high resolution X-ray diffraction study down to 10 K, together with new structure determinations at intermediate temperatures. The data rule out the hypothesis of a conventional structural phase transition. No change in the space group symmetry is observed and an anomalous decrease of the lattice parameter c in discrete steps is discovered when heating the crystal from 10 K to room temperature. It could be ascribed to a progressive conformational change of the NH3 + group of the zwitterionic molecule. An analysis of the physical properties of crystalline L-alanine suggests the existence of a strong dynamic Jahn-Teller-like effect owing to the NH3 + charge-lattice coupling. This would explain both the splitting of some vibrational states and properties related to a microscopic lattice instability like the onset of depolarization in the transmitted light below ~250 K.