Coupling Of Vibrational Modes Research Articles

Miniaturized electromechanical devices with multi-vibration modes achieved by orderly stacked structure with piezoelectric strain units

Piezoelectric devices based on a variety of vibration modes are widely utilized in high-tech fields to make a conversion between mechanical and electrical energies. The excitation of single or coupled vibration modes of piezoelectric devices is mainly related to the structure and property of piezoelectric materials. However, for the generally used piezoelectric materials, e.g., lead zirconate titanate ceramics, most of piezoelectric coefficients in the piezoelectric matrix are equal to zero, resulting in many piezoelectric vibration modes cannot be excited, which hinders the design of piezoelectric devices. In this work, an orderly stacked structure with piezoelectric strain units is proposed to achieve all nonzero piezoelectric coefficients, and consequently generate artificially coupled multi-vibration modes with ultrahigh strains. As an example, an orderly stacked structure with two piezoelectric strain units stator, corresponding to 31–36 coupled vibration mode, was designed and fabricated. Based on this orderly stacked structure with two piezoelectric strain units stator, we made a miniature ultrasonic motor (5 mmLength × 1.3 mmHeight × 1.06 mmWidth). Due to the ultrahigh strain of the 31–36 coupled vibration mode, the velocity per volume of the motor reached 4.66 s−1 mm−2. Furthermore, its moving resolution is around 3 nm, which is two orders higher than that of other piezoelectric motors. This work sheds a light on optimizing the performance of state-of-the-art electromechanical devices and may inspire new devices based on multi-vibration modes.

A Proof-of-Concept Study on an Internal-Resonance-Based Piezoelectric Energy Harvester With Coupled Three-Dimensional Bending-Torsion Motions

Abstract By exchanging the internal energy between coupled vibration modes, internal-resonance-based energy harvesters may provide an effective solution to broadening and enhancing bandwidth and power performance in dealing with natural vibration sources. With the development of piezoelectric-based transducers, thickness and face shear coefficients in proper piezoelectric elements can also generate power output from shear deformation on the core vibrating elements. However, in most cantilever-based energy harvesters that focused on bending modes, the shear responses were neglected. In this paper, we present an internal-resonance-based piezoelectric energy harvester with three-dimensional coupled bending and torsional modes, for the first time. The fine-tuned system leverages a two-to-one internal resonance between its first torsion and second bending modes to enhance the power output with piezoelectric effects. The dynamic behavior implies the coexistence of in-plane and out-of-plane motions under a single excitation frequency, and the corresponding strain changes in the bending and shear directions are captured by bonded piezoelectric transducers. Dependence between excitation levels and the internal-resonance phenomenon is justified as a critical system parameter study; the results also indicate that an intriguing non-periodic region exists near the center frequency. The outcomes of this study feature a multi-directional and multi-modal energy harvester that displays rich dynamic behaviors. The operational bandwidth is promising for broadband energy harvesting, and the output voltage is enhanced by capturing both in-plane and out-of-plane motions at the same time.

Complex wave loads and hydroelastic responses of a very large tourism floating platform ‘Ocean Diamond'

Potential fluid In order to meet the needs of tourism development in the South China Sea, this paper designs a heart-shaped very large floating tourism platform, which integrates the comprehensive functions of cruise ship docking and entertainment. The platform has the characteristics of low flexibility, discontinuous multi-free-surface water and complex phenomena such as water resonance. Firstly, the three-dimensional finite element model of the platform is established, and the complex vibration modes in vacuum are analyzed. It is found that the heart-shaped platform has complex vertical and torsional coupled vibration modes. Secondly, the irregular frequency and water resonance of the elastic structure of the platform are studied by using the three-dimensional frequency domain hydroelastic method based on the extended boundary integral method. The irregular frequencies of the floating body are removed through one rigid lid effectively, and the resonant points of internal free water is clearly revealed. Then, the laws of motions, elastic deformation responses and structural sectional loads are analyzed, and the effects of water resonance point and structural elastic resonance point on motions, structural deformation responses and sectional loads are investigated. Finally, the extreme load prediction is carried out, and the dangerous load conditions and dangerous structural areas are identified.

Review on single-phase driven ultrasonic motors

In recent decades, various single-phase drive ultrasonic motors have emerged, and only a single excitation signal is used in their working states. Single-phase driven ultrasonic motors have the benefits of most ultrasonic motors, as well as the advantages of a simple driving circuit construction, low cost, high design flexibility, and high reliability, among others. According to the working principles, they are divided into three types: the vibration mode alternating type, the vibration mode coupling type, the vibration mode converting type. This paper summarizes various types of single-phase ultrasonic motors. The three types of the working principles and its representative structures are explained; output performances of the single-phase ultrasonic motors are described; then, practical and potential applications of the single-phase ultrasonic motors are introduced; finally, the research of single-phase ultrasonic motors are reviewed, and its development prospect is prospected. This review is helpful for a comprehensive understanding of single-phase drive ultrasonic motors. This paper offers the groundwork for the development of a novel single-phase driven ultrasonic motor with improved mechanical output.

Meso-scale method of asymptotic analysis of elastic vibrations in periodic and non-periodic multi-structures

Summary The method of meso-scale asymptotic approximations has proved to be very effective for the analysis of models of solids containing large clusters of defects, such as small inclusions or voids. Here, we present a new avenue where the method is extended to elastic multi-structures. Geometrically, a multi-structure makes a step up in the context of overall dimensions, compared to the dimensions of its individual constituents. The main mathematical challenge comes from the analysis of the junction regions assigned to the multi-structure itself. Attention is given to problems of vibration and on the coupling of vibration modes corresponding to displacements of different orientations. The method is demonstrated through the dynamic analysis of infinite or finite multi-scale asymmetric flexural systems consisting of a heavy beam connected to a non-periodic array of massless flexural resonators within some interval. In modelling the interaction between the beam and the resonators, we derive a vectorial system of partial differential equations through which the axial and flexural motions of the heavy beam are coupled. The solution of these equations is written explicitly in terms of Green’s functions having intensities determined from a linear algebraic system. The influence of the resonators on the heavy beam is investigated within the framework of scattering and eigenvalue problems. For large collections of resonators, dynamic homogenization approximations for the medium within the location of the resonant array are derived, leading to (i) the classical Rayleigh beam for symmetric systems and (ii) a generalized Rayleigh beam for asymmetric structures that support flexural–longitudinal wave coupling. Independent numerical simulations are also presented that demonstrate the accuracy of the analytical results.

Localized and non-localized nonlinear normal modes in a system of two coupled pendulums under a magnetic field

The dynamics of two coupled pendulums under a magnetic field are considered. Inertial components of the pendulums are essentially different, and a ratio of masses is chosen as a small parameter. Padé approximations are used to describe magnetic excitation with good accuracy. The small parameter method is used to construct two nonlinear normal modes (NNMs) one of them is the coupled vibration mode, and the second is the localized one. The influence of the masses ratio and other system parameters to the NNMs for small and not small initial angles of the pendulums is studied.

Noise-Tolerant Optomechanical Entanglement via Synthetic Magnetism.

Entanglement of light and multiple vibrations is a key resource for multichannel quantum information processing and memory. However, entanglement generation is generally suppressed, or even fully destroyed, by the dark-mode (DM) effect induced by the coupling of multiple degenerate or near-degenerate vibrational modes to a common optical mode. Here we propose how to generate optomechanical entanglement via DM breaking induced by synthetic magnetism. We find that at nonzero temperature, light and vibrations are separable in the DM-unbreaking regime but entangled in the DM-breaking regime. Remarkably, the threshold thermal phonon number for preserving entanglement in our simulations has been observed to be up to 3 orders of magnitude stronger than that in the DM-unbreaking regime. The application of the DM-breaking mechanism to optomechanical networks can make noise-tolerant entanglement networks feasible. These results are quite general and can initiate advances in quantum resources with immunity against both dark modes and thermal noise.

Combination resonances of rotor systems with asymmetric residual preloads in bolted joints

For highly-loaded rotor systems of aero-engines, residual preloads in the same row of bolts are generally asymmetric after multiple operational cycles. The asymmetry in residual bolt preloads could lead to time-varying stiffness of rotors, which become parametrically excited systems. This paper investigates the combination resonances of bolted rotor systems with asymmetric preloads under multi-frequency excitation. A new breathing model induced by asymmetric bolt preloads is proposed, which takes the rotor whirling position into account, instead of using the assumption of weight dominance. Theoretical studies are conducted on a Jeffcott rotor with asymmetric bolt preloads under two-frequency excitation, whose approximate analytical solution is obtained through the Harmonic Balance Method. Results show that combination tones arise in the vibration spectra, whose frequencies are the combinations of two excitation frequencies. The amplitude of a combination tone reaches the maximum value when its frequency is in the vicinity of natural frequencies, which correspond to the combination resonance. To extend these results to practical rotors with more complex structures, the finite element modeling method of bolted joints with asymmetric preloads is presented based on the Euler-Bernoulli beam theory. Experimental validations are performed on a practical aero-engine dual rotor system with an inter-shaft bearing. Good agreement is shown in the comparison between numerical and experimental results, which indicate that combination resonances of practical dual rotor systems could occur in the vicinity of dual-rotor coupled vibration mode.

Tracking Energy Transfer across a Platinum Center.

Rigid, conjugated alkyne bridges serve as important components in various transition-metal complexes used for energy conversion, charge separation, sensing, and molecular electronics. Alkyne stretching modes have potential for modulating charge separation in donor–bridge–acceptor compounds. Understanding the rules of energy relaxation and energy transfer across the metal center in such compounds can help optimize their electron transfer switching properties. We used relaxation-assisted two-dimensional infrared spectroscopy to track energy transfer across metal centers in platinum complexes featuring a triazole-terminated alkyne ligand of two or six carbons, a perfluorophenyl ligand, and two tri(p-tolyl)phosphine ligands. Comprehensive analyses of waiting-time dynamics for numerous cross and diagonal peaks were performed, focusing on coherent oscillation, energy transfer, and cooling parameters. These observables augmented with density functional theory computations of vibrational frequencies and anharmonic force constants enabled identification of different functional groups of the compounds. Computations of vibrational relaxation pathways and mode couplings were performed, and two regimes of intramolecular energy redistribution are described. One involves energy transfer between ligands via high-frequency modes; the transfer is efficient only if the modes involved are delocalized over both ligands. The energy transport pathways between the ligands are identified. Another regime involves redistribution via low-frequency delocalized modes, which does not lead to interligand energy transport.

Quantum Anharmonic Calculations of Vibrational Spectra for Water Adsorbed on Titania Anatase(101) Surface: Dissociative versus Molecular Adsorption.

The interaction of water molecules and hydroxyl groups with titanium dioxide (TiO2) surfaces is ubiquitous and very important in anatase nanoparticle photocatalytic processes. Infrared spectroscopy, assisted by ab initio calculations of vibrational frequencies, can be a powerful tool to elucidate the mechanisms behind water adsorption. However, a straightforward comparison between measurements and calculations remains a challenging task because of the complexity of the physical phenomena occurring on nanoparticle surfaces. Consequently, severe computational approximations, such as harmonic vibrational ones, are usually employed. In the present work we partially address this complexity issue by overcoming some of the standard approximations used in theoretical simulations and employ the Divide and Conquer Semiclassical Initial Value Representation (DC-SCIVR) molecular dynamics. This method allows to perform simulations of vibrational spectra of large dimensional systems accounting not only for anharmonicities, but also for nuclear quantum effects. We apply this computational method to water and deuterated water adsorbed on the ideal TiO2 anatase(101) surface, contemplating both the molecular and the dissociated adsorption processes. The results highlight not only the presence of an anharmonic shift of the frequencies in agreement with the experiments, but also complex quantum mechanical spectral signatures induced by the coupling of molecular vibrational modes with the surface ones, which are different in the hydrogenated case from the deuterated one. These couplings are further analyzed by exploiting the mode subdivision performed during the divide and conquer procedure.

A Linear Piezoelectric Actuator Based on Working Principle of Three-Petal Mouth of a Rabbit

A ring-shaped linear piezoelectric actuator with three driving teeth is proposed and designed based on an axial-radial bending coupling vibration mode. The coupling vibration mode is neither pure axial bending mode nor pure radial bending mode, but an axial-radial bending hybrid one, which is generated by only one group of PZT elements and one exciting signal under an asymmetrical fixed boundary condition. The working principle of the proposed actuator is similar to the opening and closing actions of the three-petal mouth of a rabbit, which is analyzed by the finite element method. Then, the coupling vibration mode is verified by a scanning laser Doppler vibrometer after the fabrication of a prototype. Experimental results show that the prototype can achieve a maximum velocity of 60.46 mm/s and a displacement resolution of 0.5 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> m, and the velocity of the linear actuator can be smoothly adjusted in a wide range of 0.005–60.46 mm/s. In addition, the actuator can drive a hollow cylinder mover along different slopes without other auxiliary structures. The simulated and experimental results confirm that the proposed ring-shaped actuator is feasible without any guiding structure, which has great potential to realize further miniaturization of linear piezoelectric actuators.

Multi-mode coupled vibration performance analysis of a radial-longitudinal (R-L) ultrasonic transducer.

A radial-longitudinal (R-L) ultrasonic transducer is designed by compounding a piezoelectric ceramic and an outer metal ring on the central coupling cylinder of a longitudinal cascade transducer. This design is used to realize multi-mode vibration and increase the radiation range. By applying longitudinal and radial double excitation, three coupled vibration modes of the transducer are generated in the frequency range of 15-65 kHz. The coupled vibration dominated by radial vibration is regarded as the best vibration mode of this transducer. The electromechanical equivalent circuit and the resonance frequency equation of the transducer's coupled vibration are derived by using the equivalent elastic method and one-dimensional vibration theory and verified by the finite element method and experimental method. The results show that the electrical impedance frequency curves of the transducer from the three methods are consistent. The transducer is expected to be used in ultrasonic cleaning and liquid processing applications.

Coupling of molecular vibration and metasurface modes for efficient mid-infrared emission

We demonstrate extraordinarily spectrally selective narrowband mid-infrared radiationviacoupling of plasmon resonance and molecular vibration. Absorbance and thermal emittance with resonant peak FWHM ≤ 124 nm atλ= 5.73 μm, corresponding to aQ-factor of ∼92.3 were obtained.

Integrated Molecular Optomechanics with Hybrid Dielectric-Metallic Resonators.

Molecular optomechanics describes surface-enhanced Raman scattering using the formalism of cavity optomechanics as a parametric coupling of the molecule’s vibrational modes to the plasmonic resonance. Most of the predicted applications require intense electric field hotspots but spectrally narrow resonances, out of reach of standard plasmonic resonances. The Fano lineshapes resulting from the hybridization of dielectric–plasmonic resonators with a broad-band plasmon and narrow-band cavity mode allow reaching strong Raman enhancement with high-Q resonances, paving the way for sideband resolved molecular optomechanics. We extend the molecular optomechanics formalism to describe hybrid dielectric–plasmonic resonators with multiple optical resonances and with both free-space and waveguide addressing. We demonstrate how the Raman enhancement depends on the complex response functions of the hybrid system, and we retrieve the expression of Raman enhancement as a product of pump enhancement and the local density of states. The model allows prediction of the Raman emission ratio into different output ports and enables demonstrating a fully integrated high-Q Raman resonator exploiting multiple cavity modes coupled to the same waveguide.

Accessing the Exceptional Points in a Graphene Plasmon–Vibrational Mode Coupled System

The coupling of plasmons and vibrational modes has been routinely observed in graphene and other 2D systems in both near-field and far-field spectroscopy. However, the relation between coupling strength and modal losses, and exceptional point physics has not been discussed. Here we apply a non-Hermitian framework to a model system of molecular layers on graphene and show that the transition point between strong and weak coupling regimes coincides with the exceptional point of non-Hermitian physics. We further show that the exceptional point can be conveniently located by changing the incident angle of the light and the graphene Fermi energy. Finally, we show that enhanced spectral sensitivity is obtained from small changes in molecular film thickness when the system is tuned to the exceptional point.

Dynamic characteristics of electromechanical coupling of wind turbine drive system under multi‐source excitation

AbstractWith the rapid development of wind turbine, the operational reliability of the main drive systems of wind turbine has received extensive attention. The wind turbine drive system is affected not only by random wind loads for a long time but also by the electromagnetic torque of the generator. Exploring the coupling behavior and mechanism is particularly important for optimizing the design of the drive system and improving the operational reliability of the main drive system. This study establishes a mechanical–electrical coupling model, which includes a translational–torsional dynamic model of a gear transmission system that can be used for variable speed and variable‐load conditions, a finite element model of the generator, and voltage vector control. This model takes into account nonlinear factors such as the time‐varying meshing stiffness of the gear system and the magnetic characteristics of the generator. The speed sweep analysis method was used to identify the resonance speed and dangerous components of the system. Under different external excitation conditions, the dynamic characteristics of the system were compared with and without considering electromagnetic characteristics. The generator speed of 1030 r/min and 651 r/min is the potential resonance speed of the system. The gear system and generator system have strong coupling characteristics. In the vibration signal of the gear system, there will be electrical system frequency components dominated by 6kfe and (h − 1)fe. In the current signal, not only appeared the excitation frequency in the gear system, but also the modulation signal with the excitation frequency in the gear system as the carrier frequency and the electric frequency as the fundamental frequency ((6k ± 1) ⋅ fe ± n ⋅fm) appeared. Under the gust wind, the transient response of the system will excite the gear‐generator coupling vibration mode. The electromagnetic characteristic of generator can suppress the vibration of mechanical system.

Review on Vibration Analysis of Cracked Cantilever Beam

Abstract: A unique feature of fiber-reinforced composite materials is that it allows structural tailoring for favorable dynamic performance, due to the directional nature of composite materials. Because of the directed character, material coupling occurs, resulting in coupled vibration modes and complicating dynamic analysis. A transverse triangular force impulse modulated by a harmonic motion excites the beam. For the substance of the beam, the Kelvin–Voigt model is employed. The fractured beam is represented by two sub-beams linked by a massless elastic rotating spring. The beams are designed to function in wet environments, which cause rusting. Corrosion causes cracks to form in beams, altering their inherent frequency and mode shape. The present paper examines the different investigations that have been done to investigate the impact of fracture on the dynamic properties of beams. The researchers provided a comprehensive evaluation of the impact of crack design factors (crack depth, crack location) on cantilever beam transverse and torsional frequencies. It is also given the analytical approach, numerical method, and experimental methods for studying the impact of fracture on vibration characteristics. Keywords: Cantilever Beam, Crack dimensions, Damage, Kelvin–Voigt model.

Thermal transport of amorphous phase change memory materials using population-coherence theory: a first-principles study

Thermal conduction plays a vital role in applications of phase change memory (PCM) materials. Phonon-based theory and the Wiedemann–Franz–Lorenz rule have been widely utilized to describe the thermal transport in crystalline PCM materials, while the understanding of heat conduction in the amorphous phase remains insufficient. Here, we quantify the contributions of the coherences (coupling of vibrational modes) and populations (phonon-like) to the thermal conduction of amorphous Ge2Sb2Te5 (GST) and GeTe4, two kinds of typical PCM materials. The contributions of the coherences and populations are calculated using the theory proposed by Allen and Feldman (AF theory) and the single-mode relaxation time approximation of the Boltzmann transport equation based on first-principles calculations. Our results demonstrate that coherences contribute more than 97% of the total thermal conductivities for both amorphous GST and GeTe4 above Debye temperature, while the populations’ contribution is negligible. Besides, the temperature dependence of the thermal conductivities is predicted and analyzed, allowed by the AF theory with the mode linewidths-dependent broadening method introduced in this paper. The predicted positive temperature dependence of amorphous GeTe4 above Debye temperature, in good agreement with the experimental results, is due to the unique nature of coherences, i.e. larger contribution to heat conduction from stronger couplings between different normal modes at a higher temperature. Our calculation provides new insight into thermal transport in amorphous PCM materials and reveals the physical mechanisms of temperature-dependent thermal conductivities above Debye temperature, and the calculation framework can also be extended to other disordered systems.

Coupling of Vibrational Modes to the Electron-Hole Continuum in Doped Single-Wall Carbon Nanotubes

Electron-phonon coupling is at the heart of many physical phenomena like superconductivity, charge transport and the Raman effect (Ferrari2007). Previously, it has been shown that a coupling of vibrational modes to the low-energy electronic continuum absorption in graphene and carbon nanotubes results in transparency windows in the mid-infrared spectral region (Lapointe2012, Lapointe2017). The reduced absorption at the vibrational energies can be attributed to so-called Fano (anti-)resonances (Fano1961).Here, we present a systematic study of the infrared continuum absorption and such antiresonances in purely semiconducting, monochiral carbon nanotube (CNT) thin-films. We observe strong antiresonances for the Raman active D- and G-phonons, which acquire oscillator strength via coupling to the bright Drude-like intraband continuum in doped CNTs. Both the spectrum of the continuum absorption and the amplitude of the Fano resonances critically depend on the doping level. With increasing carrier concentration, we find a redshift of the Drude peak accompanied with a non-monotonic doping level dependence of the antiresonance intensity. Our observations show that carrier localization and delocalization as well as disorder induced by defects play a critical role for both charge transport and electron-phonon coupling as evidenced by the Fano resonances. We suggest that our findings also have implications for other low-dimensional systems with a low-energy electronic continuum absorption.C. Ferrari, Solid State Commun. 2007, 143, 47-57.Lapointe et al., Phys. Rev. Lett. 2012, 109, 097402.Lapointe et al., J. Phys. Chem. C 2017, 121, 9053-9062.Fano, Phys. Rev. 1961, 124, 1866-1878.

Theoretical analysis of transverse and planar vibrations for the piezoceramic disk based on Mindlin plate theory

In this paper, the out-of-plane and in-plane displacements coupled behavior of the transverse and planar vibration characteristics for piezoceramic disks under fully-clamped and traction-free boundary conditions are investigated theoretically base on the Mindlin's and Kirchhoff's plate models. By varying the radius-to-thickness ratios, the piezoceramic disks with moderate and thin thickness are considered in the analysis. It is verified that Mindlin's plate theory with first-order shear deformation hypothesis provides sufficient accuracy for transverse vibration analysis in comparison with Kirchhoff's model; however, this circumstance does not occur for planar vibration analysis. With the aid of theoretical analysis, both the resonant frequency and the corresponding mode shape are obtained for piezoceramic disks with various radius-to-thickness ratios. In addition, maximum normalized displacement components in three directions are also explored to identify the coupled vibration modes. Numerical calculations using the finite element method (FEM) are performed and the results are compared with the theoretical analysis. Excellent consistence between the theoretical and numerical results are found for the three-dimensional coupled vibration characteristics of piezoceramic disks.