Vibrational Coupling Research Articles

Piezoelectric Transducers: Complete Electromechanical Model with Parameter Extraction.

This paper presents a complete electromechanical (EM) model of piezoelectric transducers (PTs) independent of high or low coupling assumptions, vibration conditions, and geometry. The PT's spring stiffness is modeled as part of the domain coupling transformer, and the piezoelectric EM coupling coefficient is modeled explicitly as a split inductor transformer. This separates the coupling coefficient from the coefficient used for conversion between mechanical and electrical domains, providing a more insightful understanding of the energy transfers occurring within a PT and allowing for analysis not previously possible. This also illustrates the role the PT's spring plays in EM energy conversion. The model is analyzed and discussed from a circuits and energy harvesting perspective. Coupling between domains and how loading affects coupled energy are examined. Moreover, simple methods for experimentally extracting model parameters, including the coupling coefficient, are provided to empower engineers to quickly and easily integrate PTs in SPICE simulations for the rapid and improved development of PT interface circuits. The model and parameter extractions are validated by comparing them to the measured response of a physical cantilever-style PT excited by regular and irregular vibrations. In most cases, less than a 5-10% error between measured and simulated responses is observed.

Environmental damping and vibrational coupling of confined fluids within isolated carbon nanotubes

Because of their large surface areas, nanotubes and nanowires demonstrate exquisite mechanical coupling to their surroundings, promising advanced sensors and nanomechanical devices. However, this environmental sensitivity has resulted in several ambiguous observations of vibrational coupling across various experiments. Herein, we demonstrate a temperature-dependent Radial Breathing Mode (RBM) frequency in free-standing, electron-diffraction-assigned Double-Walled Carbon Nanotubes (DWNTs) that shows an unexpected and thermally reversible frequency downshift of 10 to 15%, for systems isolated in vacuum. An analysis based on a harmonic oscillator model assigns the distinctive frequency cusp, produced over 93 scans of 3 distinct DWNTs, along with the hyperbolic trajectory, to a reversible increase in damping from graphitic ribbons on the exterior surface. Strain-dependent coupling from self-tensioned, suspended DWNTs maintains the ratio of spring-to-damping frequencies, producing a stable saturation of RBM in the low-tension limit. In contrast, when the interior of DWNTs is subjected to a water-filling process, the RBM thermal trajectory is altered to that of a Langmuir isobar and elliptical trajectories, allowing measurement of the enthalpy of confined fluid phase change. These mechanisms and quantitative theory provide new insights into the environmental coupling of nanomechanical systems and the implications for devices and nanofluidic conduits.

Coupled nonlinear vibration characteristics of quasi-zero-stiffness Gough-Stewart isolation platform

The quasi-zero-stiffness (QZS) Gough-Stewart vibration isolation platform is designed for six degrees-of-freedom (DOFs) low-frequency vibration isolation. Lots of studies regarding the amplitude-frequency relationship of the platform are based on the assumption that interference with the platform in one direction only provokes a response in that direction. This assumption artificially decouples a six DOFs coupling model into six single DOF equations, ignoring the coupling relationship between each DOFs, making the analysis results inaccurate. Therefore, without simplifying the nonlinear terms and taking the coupling effect into consideration, the improved Incremental Harmonic Balance Method (IHBM) is employed to discuss the coupling relationship between different DOFs of the QZS Gough-Stewart vibration isolation platform. The results show that the platform has multiple equilibrium positions. When the platform is excited from different directions, it will vibrate at different equilibrium positions, and the closer these positions are to the zero-stiffness position, the more likely the system is to exhibit jump phenomenon and sudden increases in response. The platform exhibits a single-directional response only when excited from the z-direction. Through comparative study, it is found that the cubic configuration can weaken the coupling effect between each DOFs compared with the general configuration.

Resonance theory of vibrational strong coupling enhanced polariton chemistry and the role of photonic mode lifetime

Recent experiments demonstrate polaritons under the vibrational strong coupling (VSC) regime can modify chemical reactivity. Here, we present a complete theory of VSC-modified rate constants when coupling a single molecule to an optical cavity, where the role of photonic mode lifetime is understood. The analytic expression exhibits a sharp resonance behavior, where the maximum rate constant is reached when the cavity frequency matches the vibration frequency. The theory explains why VSC rate constant modification closely resembles the optical spectra of the vibration outside the cavity. Further, we discussed the temperature dependence of the VSC-modified rate constants. The analytic theory agrees well with the numerically exact hierarchical equations of motion (HEOM) simulations for all explored regimes. Finally, we discussed the resonance condition at the normal incidence when considering in-plane momentum inside a Fabry-Pérot cavity.

The Influence of Large Variations in Fluid Density and Viscosity on the Resonance Characteristics of Tuning Forks Simulated by Finite Element Method

The use of tuning forks to measure fluid density and viscosity is widely employed in fields such as food, medicine, textiles, automobiles, petrochemicals, and deep drilling. The explicit analytical model based on the Euler–Bernoulli cantilever-beam theory for the relationship between tuning-fork resonance characteristics and the density and viscosity of fluid is only applicable to the situation where the fluid viscous effect is very small. In this paper, the finite element method is used to simulate the influence of large variations in fluid density and viscosity on the resonance characteristic parameters (resonant frequency and quality factor) of the tuning fork. The numerical simulation results are compared with the analytical analysis results and experimental measurement results. Then, the sensitivity of tuning-fork resonance characteristic parameters to fluid density and viscosity is studied. The results show that compared with the analytical results, the numerical simulation results have a higher degree of agreement with the experimental measurement results. The relative difference in resonant frequency is less than 2%, and the relative difference in quality factor is less than 4%. This indicates that the finite element method includes the influence of fluid viscosity on tuning-fork resonance parameters, which is more in line with the actual conditions than the analytical model. Simulating and analyzing the sensitivity of the tuning fork to fluid density and viscosity by the finite element method, it is possible to consider the situation where fluid density and viscosity vary over a large range. Compared with experimental measurements, this method has higher efficiency and can significantly save time and economic costs. This study can overcome the limitation of existing explicit analytical models, which are only applicable when the viscous effects of the fluid are very small. It enables a more accurate simulation of the coupling vibration between tuning forks and fluids, thereby providing theoretical references for further optimizing tuning-fork structural parameters to enhance the accuracy of measuring fluid characteristic parameters.

A time-averaged method to analyze slender rods moving in tubes

The motion of slender rods in narrow tubes involves the coupling of axial movements and transverse vibrations, in which the transverse vibration exhibits high frequency and chaotic characteristics. These characteristics render the computational cost of the time integration to the motions of rods and tubes expensive. To solve this problem, this paper proposes a novel time-averaged method, which contains two innovations: 1) By time averaging the traditional dynamic equations, the time-averaged dynamic equations describing the rod-tube system are established based on the time-averaged concept used in turbulence problems; 2) Two time-averaged contact models are developed, by fitting the time-averaged sample set using the polishing function and the machine learning, respectively, to construct the relationship between the time-averaged contact gaps and the time-averaged contact forces. The time-averaged method can use a large time step, which is far larger than that required for the time integration of traditional methods, thus reducing the computational cost. Inclined and rolling experiments of the rod-tube system, as well as numerical experiments of the control rod drop in a nuclear reactor, are conducted to validate the accuracy of the time-averaged method. Comparative analyses are carried out between the time-averaged method and six continuous contact models, demonstrating the high computational efficiency of the proposed method. Moreover, the experimental results can provide benchmark data for algorithm verification for scholars studying dynamic contact algorithms.

Mesoscale Molecular Simulations of Fabry-Pérot Vibrational Strong Coupling.

Developing theoretical frameworks for vibrational strong coupling (VSC) beyond the single-mode approximation is crucial for a comprehensive understanding of experiments with planar Fabry-Pérot cavities. Herein, a generalized cavity molecular dynamics (CavMD) scheme is developed to simulate VSC of a large ensemble of realistic molecules coupled to an arbitrary 1D or 2D photonic environment. This approach is built upon the Power-Zienau-Woolley Hamiltonian in the normal mode basis and uses a grid representation of the molecular ensembles to reduce the computational cost. When simulating the polariton dispersion relation for a homogeneous distribution of molecules in planar Fabry-Pérot cavities, our data highlight the importance of preserving the in-plane translational symmetry of the molecular distribution. In this homogeneous limit, CavMD yields the consistent polariton dispersion relation as an analytic theory, i.e., incorporating many cavity modes with varying in-plane wave vectors (k∥) produces the same spectrum as the system with a single cavity mode. Furthermore, CavMD reveals that the validity of the single-mode approximation is challenged when nonequilibrium polariton dynamics are considered, as polariton-polariton scattering occurs between modes with the nearest neighbor k∥. The procedure for numerically approaching the macroscopic limit is also demonstrated with CavMD by increasing the system size. Looking forward, our generalized CavMD approach may facilitate understanding vibrational polariton transport and condensation.

Effect of Filling Material Properties on 1-3 Piezoelectric Composite Performance.

The 1-3 piezoelectric composite is the key component of the acoustic transducer, which is widely used in detection, due to the high energy conversion efficiency, cheap raw material, and low aging. To reveal the influence of epoxy mixture, used to connect the piezoelectric column, on the composite performance, a 1-3 piezoelectric composite model was built. The effects of mixture properties on the impedance curves, vibration mode, and deformation displacement of the composite were determined. Six 1-3 piezoelectric composites with different filling mixture properties, by changing the glass microspheres' mass ratio in the epoxy, were prepared and measured to validate the model. The results showed that with the increase in the proportion of the glass microsphere in the epoxy mixture, the vibration coupling of the piezoelectric composites was gradually eliminated. The acoustic impedance was reduced by 12%. The electromechanical coupling coefficient and effective electromechanical coupling coefficient were increased by 5.4% and 8.3%, respectively. The density and Young's modulus decrease in filling mixture can significantly improve piezoelectric composite performance.

Tunable Phonon Polariton Hybridization in a Van der Waals Hetero-Bicrystal.

Phonon polaritons, the hybrid quasiparticles resulting from the coupling of photons and lattice vibrations, have gained significant attention in the field of layered van der Waals heterostructures. Particular interest has been paid to hetero-bicrystals composed of molybdenum oxide (MoO3) and hexagonal boron nitride (hBN), which feature polariton dispersion tailorable via avoided polariton mode crossings. In this work, the polariton eigenmodes in MoO3-hBN hetero-bicrystals self-assembled on ultrasmooth gold are systematically studied using synchrotron infrared nanospectroscopy. It is experimentally demonstrated that the spectral gap in bicrystal dispersion and corresponding regimes of negative refraction can be tuned by material layer thickness, and these results are quantitatively matched with a simple analytic model. Polaritonic cavity modes and polariton propagation along "forbidden" directions are also investigated in microscale bicrystals, which arise from the finite in-plane dimension of the synthesized MoO3 micro-ribbons. The findings shed light on the unique dispersion properties of polaritons in van der Waals heterostructures and pave the way for applications leveraging deeply sub-wavelength mid-infrared light-matter interactions.

Spatially Resolved Near Field Spectroscopy of Vibrational Polaritons at the Small N Limit.

Vibrational polaritons, which have been primarily studied in Fabry-Pérot cavities with a large number of molecules (N ∼ 106-1010) coupled to the resonator mode, exhibit various experimentally observed effects on chemical reactions. However, the exact mechanism is elusively understood from the theoretical side, as the large number of molecules involved in an experimental strong coupling condition cannot be represented completely in simulations. This discrepancy between theory and experiment arises from computational descriptions of polariton systems typically being limited to only a few molecules, thus failing to represent the experimental conditions adequately. To address this mismatch, we used surface phonon polariton (SPhP) resonators as an alternative platform for vibrational strong coupling. SPhPs exhibit strong electromagnetic confinement on the surface and thus allow for coupling to a small number of molecules. As a result, this platform can enhance nonlinearity and slow down relaxation to the dark modes. In this study, we fabricated a pillar-shaped quartz resonator and then coated it with a thin layer of cobalt phthalocyanine (CoPc). By employing scattering-type scanning near-field optical microscopy (s-SNOM), we spatially investigated the dependency of vibrational strong coupling on the spatially varying electromagnetic field strength and demonstrated strong coupling with 38,000 molecules only-reaching to the small N limit. Through s-SNOM analysis, we found that strong coupling was observed primarily on the edge of the quartz pillar and the apex of the s-SNOM tip, where the maximum field enhancement occurs. In contrast, a weak resonance signal and lack of coupling were observed closer to the center of the pillar. This work demonstrates the importance of spatially resolved polariton systems in nanophotonic platforms and lays a foundation to explore polariton chemistry and chemical dynamics at the small N limit-one step closer to reconcile with high-level quantum calculations.

Coupled Vibration of a Vehicle Group–Bridge System and Its Application in the Optimal Strategy for Bridge Health Monitoring

The accuracy of bridge performance monitoring and evaluation is easily affected by unfavorable factors such as vehicle coupling and test noise. In order to accurately evaluate the dynamic response and health monitoring threshold of the bridge under different operating conditions, a time-varying dynamic vehicle group model including the main uniform mass and the coupling mass was established, and the influence of road roughness was considered in the coupling equation. A bridge monitoring strategy considering signal noise ratio and vehicle–bridge interaction was proposed, and the effectiveness of the monitoring strategy was verified by taking a simple supported beam as an example. The results showed that the proposed time-varying dynamic vehicle group model could accurately consider the influence of road roughness and estimate the threshold of health monitoring, and the proposed bridge monitoring strategy could filter out a large amount of low signal-to-noise ratio or meaningless data, thus saving computing resources and realizing the lightweight safety monitoring of bridges.

The Structure-Dependent Dynamic Performance of a Twin-Ball-Screw Drive Mechanism via a Receptance Coupling Approach

The drive at the center of gravity (DCG) concept-based twin-ball-screw drive mechanism (TBSDM) is vital in automated factories for its robustness and reliability. However, changes in the worktable mass or position result in changes in the center of gravity (CG), significantly affecting the system’s dynamic properties. In this regard, this paper introduces a novel analytical model using improved receptance coupling to analyze vibrations in four modes. A mathematical framework for the twin TBSDM is generated, and the effect of changing the worktable position–mass on each mode is examined. The applicability of the proposed method is verified based on dynamic experiments that were carried out on a TBSDM of a CNC grinding wheel machine tool. After thoroughly analyzing the experimental and theoretical results, it is revealed that changing the worktable position primarily influences the rotational and axial vibrations of the twin ball screw (TBS). Furthermore, changes in the worktable mass significantly affect the coupling vibration among the TBSs and rotors or bearings. Moreover, in terms of performance, the variances between the theoretical and experimental natural frequencies are consistently below 5%. Thus, the proposed method is promising for the improvement of the modeling and analysis of the TBSDM.

Multi-field coupling vibration patterns of the multiphase sink vortex and distortion recognition method

Fluid-induced vibration sensing technology plays an essential role in the safety and stable operation of fluid control equipment. The sensing works oriented to the multiphase sink vortex-induced vibration (MSVIV) face significant challenges in state recognition, such as the aero-engine oil pipe, metallurgical casting ladle, and microfluidic equipment. This paper presents a multi-field coupling vibration modelling and solving strategy to investigate the MSVIV transition patterns. Based on the volume of fluid and level set method, an efficient volume-correction strategy is presented to consider the mass variation and keep velocity fields without divergence. Then, a fluid–structure-acoustic dynamic model is conducted to explore multiphase vortex transport regularities. Considering the solution singularity of the fluid–solid-acoustic coupling system, a residue theorem-based solution strategy is presented to obtain the MSVIV evolution behaviors. Finally, a multichannel sensing MSVIV water-model experiment (MSVIV-WME) platform is conducted to verify the above results, and a wavelet transform-based processing approach can be utilized to obtain mutation energy features. Research results illustrate that the proposed strategy has revealed the MSVIV transition behaviors. The MSVIV process in critical states dominates nonlinear vibration patterns. The self-development sensing platform can monitor the MSVIV evolution process in real-time, and the wavelet transform-based sensing attribute with the dw3 frequency band can identify distortion characteristics. Relevant results can offer useful references for MSVIV state recognition and offer technical solving strategies for microfluidics monitoring equipment.

Fatigue Evaluation of CFST Arch Bridge Based on Vehicle–Bridge Coupling Vibration Analysis

Fatigue Evaluation of CFST Arch Bridge Based on Vehicle–Bridge Coupling Vibration Analysis

Digital Simulation of Coupled Dynamic Characteristics of Open Rotor and Dynamic Balancing Test Research

An aero engine, as the core power equipment of the aircraft, enables safe and stable operation with a very high reliability index, and is an important guarantee in flight. The open rotor turbine engines (contra-rotating propeller) have stood out as a research hotspot for aviation power equipment in recent years due to their outstanding advantages of low fuel consumption, high airspeed, and strong propulsion efficiency. Aiming at the problems of vibration exceeding the standard generated by imbalance during the operation of the dual-rotor system of aircraft development, the difficulty of identifying the coupled vibration under the micro-differential speed condition, and the complexity of the dynamic characteristic law, a kind of numerical simulation of the dynamics based on the finite element technology is proposed, together with an experimental research method for the fast and accurate identification of the coupled vibration of the dual-rotor system. Based on the existing open rotor engine structure design to build a simulation test bed, establish a double rotor finite element simulation digital twin model, and analyze and calculate the typical working conditions of the dynamic characteristics of parameters. The advanced algorithm of double rotor coupling vibration signal identification is utilized to carry out decoupling and dynamic balancing experimental tests, comparing the simulation results with the measured data to verify the accuracy of the technical means. The results of the study show that the vibration suppression rate of the finite element calculation simulation test carried out for the simulated double rotor is 98%, and the average vibration reduction ratio of the actual field test at 850 rpm, 1000 rpm, and 3000 rpm is over 50%, which achieves a good dynamic balancing effect, and has the merit of practical engineering application.

Analysis of Shafting System Vibration Characteristics for Mixed-Flow Hydropower Units Considering Sand Wear on Turbine Blades

Addressing the issue of increased shaft-system vibration in high-altitude mixed-flow hydropower generating units due to sand wear on turbine blades, a three-dimensional model of a specific mixed-flow water turbine was constructed. CFD numerical simulations were employed to analyze the fluid exciting force acting on the turbine runner under varying degrees of blade wear. An approximate analytical model was then established for the variation of fluid exciting force in the turbine runner system using the Fourier harmonic analysis method. A multi-degree-of-freedom mathematical model of flexural and inclined coupling vibration of a hydropower unit’s shafting, considering blade wear, was constructed. The nonlinear dynamic model was numerically calculated by the Runge–Kutta method. The vibration responses of the shafting of hydropower units under different wear degrees were obtained by means of a time-domain diagram, frequency-domain diagram, axis-locus diagram, phase-locus diagram, and Poincare mapping. Based on the formula for calculating the wear amount of the blade material, the runner amplitude degradation trajectory model was established, and the pseudo-failure time of turbine blades was determined according to the allowable value of amplitude.

Study on the coupling vibration characteristics of vertical unit and plant of large underground pumping station for water transfer project

Abstract To investigate the coupled vibration characteristics of vertical pumping unit and plant structure of large underground pumping station for water transfer project, the coupled vibration differential equations are established. The structure nodes of are simplified from horizontal direction and vertical direction respectively by force. The structural parameters and load parameters of the model are analyzed and calculated, and the vibration response of each node are calculated by solving the vibration differential equations. A spectral analysis of white noise is applied to the coupled model, and the natural frequencies and vibration structures of dominant vibration modals are obtained. Research indicates that the vertical vibration modes of the system exhibit a relatively low coupling degree with the plant structure. The shaft system and the plant structure mainly display combined vertical vibrations, while the plant structure predominantly exhibits independent vertical vibrations. This implies that vertical vibrations are jointly influenced by shaft system stiffness and plant structure properties. In horizontal vibration modes, a strong coupling characteristic is observed between the upper structure of the pump station unit and the plant structure. This is primarily manifested as coupled vibrations between the support and the plant structure, which are collectively influenced by support constraints, shaft system stiffness, and plant structural properties.

Experimental study on the influence of welding structure details of TC4 titanium alloy under thermo-vibration coupling environment on vibration fatigue life

The widespread application of titanium alloy materials in aerospace structural design makes them susceptible to thermo-vibration coupling fatigue failure in harsh vibration and thermal environments. Vibration fatigue issues significantly affect the safety and operational reliability of aircraft. In order to obtain optimal design details for titanium alloy welding structures under thermo-vibration coupling conditions, experimental specimens with different structural details of TC4 titanium alloy welding structures were designed to simulate actual structural designs. The structural details included skin with U-shaped supports at different angles, skin with L-shaped supports, and skin with T-shaped supports. A thermo-vibration coupling vibration fatigue test system was established, and vibration fatigue tests were conducted at a temperature of 150°C. All structural fatigue crack failures occurred at the welds. The experimental results were statistically analysed, and using the Chauvinet criterion, abnormal data points were removed. The influence of structural details on vibration fatigue life was determined through F-tests. It was found that for the skin with a U-shaped support structure, a support angle of 90° resulted in a longer vibration fatigue life. When comparing skin with T-shaped support and skin with L-shaped support structures, the T-shaped support structure exhibited a longer vibration fatigue life. Among the three structural types, the skin with a T-shaped support structure has the longest vibration fatigue life. These experimental conclusions serve as important references for the design of thin-walled structures in aircraft structural design.

Damage resistance of calcium sulfoaluminate cement-based engineered cementitious composite (CSA–ECC) under vehicle-bridge coupling vibration

Damage resistance of calcium sulfoaluminate cement-based engineered cementitious composite (CSA–ECC) under vehicle-bridge coupling vibration

Coupled vibration analysis of the spacecraft with the flexible shaft and solar panels assembly

Dynamical characteristics of the spacecraft with flexible components are investigated in this paper. The component consists of a flexible shaft and solar panels, where solar panels are completely fixed on the shaft. A novel power series multiplier polynomial method is proposed to describe the connecting condition between the shaft and solar panels. The deformation and force matching conditions between the one dimensional shaft and two dimensional panels are established, which is the major contribution about the multidimensional combined structure of this study. According to constraining boundary conditions of the shaft and solar panels, the bending-torsion coupled deformation of the component is expressed. The attitude maneuvering of the central platform and the elastic vibration of the component cause the rigid-flexible coupled effect. Then the discrete dynamical equation of the spacecraft is obtained by using the rigid-flexible coupled modal shapes. The correctness of the proposed method is verified by comparing the natural characteristics with that of the finite element model. The relative error of the higher order frequency is not more than 4%. Numerical results show that the degree of the bending angle polynomial should be at least quadratic to ensure the accuracy of the calculation. The proposed power series multiplier polynomial breaks through the barriers that the traditional Lagrange multiplier cannot express the continuous constraint. It is an effective method to fit the constrained boundary by the polynomial rather than by the discrete multipoint method.