Modal Coupling Research Articles

Milling stability considering multiple effects and variable rotational speed milling chatter control

One of the most frequent barriers to decreasing the surface quality of workpieces during milling machining is chatter, and the accuracy of chatter prediction is directly impacted by the number of effects that are considered during the modeling of the milling process. Previous researchers have studied the impact of chatter suppression on the spindle variable rotational speed method in the milling model while considering various effects. The variable rotational speed waveforms primarily focus on the fundamental waveform or a composite of sine waveforms. The study presents a novel method for variable speed control, utilizing a waveform that combines sine and triangular waveforms. The effect of this method on chatter suppression is investigated in a milling dynamics model that considers regenerative, modal coupling, and process damping effects. This novel method overall improves milling stability significantly. The accuracy of the novel method is verified by simulation and experiment. Next, the analysis focuses on the influence of immersion rate, spindle modulation coefficients, and phase difference on stability, based on stability prediction. The choice of these parameters has a direct influence on the ability to suppress chatter.

Chiroptical response of an array of isotropic plasmonic particles having a chiral arrangement under coherent interaction.

The chirality and chiroptical response of materials have attracted significant attention for their potential to introduce the new science of light-matter interactions. We demonstrate that collective mode formation under modal coupling between localized surface plasmon resonances (LSPRs) with a chiral arrangement and Fabry-Pérot (FP) nanocavity modes can induce chiroptical responses. We fabricated a cluster of isotropic gold nanodisks with a chiral arrangement (gold nano-windmills, Au-NWs) on the FP nanocavities of TiO2 and Au film. The differential absorption of the Au-NWs coupled with the FP nanocavities under left- and right-handed circularly polarized light irradiations in the far field was significantly enhanced compared with the differential absorption without the FP nanocavities. Far- and near-field analyses by numerical simulation revealed that the Au-NWs coupled with the FP nanocavities formed a collective mode in the near field, and the collective mode represented the chiroptical response in the far field. The light field with the large helicity, can be used in chiral light-matter interactions. The concept of collective mode formation using isotropic metal nanodisks coupled with FP nanocavities provides a platform for controlling complex light fields.

Effects of modal coupling on the nonlinear dynamics of hyperelastic circular cylindrical shells

The nonlinear dynamics of a simply supported circular cylindrical shell is analyzed using an analytical model that considers both physical and geometric nonlinearities. The material that composes the shell is assumed as homogeneous, isotropic, hyperelastic and incompressible, being described by the Mooney-Rivlin hyperelastic constitutive law. The geometric nonlinearity is introduced into the analytical model by applying the Sanders-Koiter’s nonlinear shell theory. The Rayleigh-Ritz method and Hamilton's principle are employed to obtain the nonlinear equilibrium equations. For that, the energy density function is expanded in Taylor series up to the fourth order and the transversal displacement field is described in Fourier series that considers both asymmetric and axisymmetric modes. This works focusses on evaluating the influence of the asymmetric and axisymmetric modes, selected in the modal solution of the transversal displacement field, on the frequency-amplitude relationships of the shell and resonance curves. It can be observed that the asymmetric modes provoke nonlinear hardening behavior of the hyperelastic shell. On the other hand, when the axisymmetric modes are added, there is a significant change in the nonlinear behavior of the hyperelastic shell - which indicates the importance of this modal coupling in the nonlinear dynamic analysis.

Optimal placement of thin piezoelectric patches for maximum modal coupling

The aim of this paper is to present an innovative approach for optimal placement of piezoelectric patches in the context of vibration control or energy harvesting applications. Targeting a specific mode shape and assuming that the addition of thin surface-bonded piezoelectric layers has a sufficiently weak influence, the analysis of the stress or strain fields over the bare structure directly provides the best areas for maximized piezoelectric coupling. The area extension of a patch is then optimized based on the modal electromechanical coupling factor. The whole process only requires a standard finite element model, without the need of any piezoelectric elements. Three criteria of increasing complexity are proposed and numerically validated on a benchmark structure which offers a non-standard geometry. Such criteria and methods may have a strong interest in an industrial context where coupled models or specific expertise in piezoelectric coupling are not always available.

Controlling harmful milling vibration for robotic milling system based on the optimization of milling posture and spindle speed

Harmful machining vibration including milling chatter and resonance are easily generated during robotic milling process, and it seriously restrict the machining ability of the robot. To address this problem, a harmful machining vibration-controlled method based on the combined optimization of milling posture and spindle speed is proposed for robotic milling system in this paper. With this context, firstly, the robot stiffness model is established based on the theory of the multi-body with small-deformation, and the stiffness ellipsoid at the tool cutting point is used to optimize the milling posture, so that the structure stiffness of the robot can be enhanced; Then, the robot chatter stability model is constructed considering the modal coupling effect, and the spindle speed is optimized to restrain the milling chatter and resonance. Finally, with the optimized milling posture and spindle speed, the milling process is planned and performed with a Staubli TX-200 robot, and two experiments for workpiece with steel and aluminum are implemented to verify the proposed method. The experiment results demonstrate that the comprehensive optimization of milling posture and spindle speed can efficiently control the harmful machining vibration for the robotic milling system, thus, the machining quality of the workpiece can be improved.

Plasma-Fluid Energy Transfers in Plasma Assisted Ignition

ABSTRACT A three-dimensional model of plasma-fluid coupling is developed, including the Navier-Stokes, the drift-diffusion, and the radiative transfer equations, to investigate the energy transfers between plasma and fluid in repetitive-pulsed discharge ignition. A modal decomposition of the energy transfer is performed to determine the contributions of plasma to the mechanical coupling and pressure losses during ignition. The detailed model is validated against experiments and compared against a well-known empirical approximation. The main findings are that the modal coupling is dependent on the geometry of the electrodes and flat electrodes provide the strongest mechanical transfer into the acoustic modes. Uniform flow conditions decrease the extent of the mechanical coupling due to the decreased pressure velocity correlations in shear flows. Water vapor production reduces the entropic mode of the energy coupling.

Nonlinear normal modes and response to random inputs of systems with bilinear stiffness

This work seeks to provide a comprehensive review of the effects that stiffness bilinearity can have on the nonlinear modes of a system, its response in a random vibration environment, and the connection between the two. Stiffness bilinearity here refers to a continuous piecewise linear force vs displacement function that is composed of two linear regions. This work focuses on a bilinear stiffness function that is regularized so there is a smooth transition at the point where the two linear regions meet. A single-degree-of-freedom system (SDOF) and a two-degree-of-freedom (2DOF) system are explored and several interesting behaviors are shown. The SDOF bilinear spring model is characterized by four parameters: the low amplitude frequency, the ratio of the linear stiffnesses on either side of the transition, the displacement at which the transition occurs, and the rate or sharpness of the transition. The effect of each parameter on the shape of the NNM is described. In a 2DOF system, these parameters have similar effects, but modal coupling is found to play a significant role. When a bilinear system is subjected to random excitation, many harmonics appear in the response for both the SDOF and 2DOF cases. The root-mean-square (RMS) response of the bilinear system can be larger or smaller than the corresponding linear case depending on the values of the parameters and the type of forcing (broadband, bandlimited, in the shape of a vibration mode, etc.). However, many cases were observed in which the RMS response of the bilinear system was almost the same as that of a linear system, and hence the response could be predicted well using linear analysis. It is hoped that the results presented herein can assist engineers in helping to determine when linear analysis would be adequate to predict the failure of a system, when a rigorous nonlinear analysis is required, and what phenomena are likely to be observed in the latter case.

Modal Analysis and Optimization of Fluid-Structure Coupling for Rotor and Inner Cylinder of Vertical Condensate Pump

Background: Low-frequency resonance is one of the common issues encountered during the variable-frequency operation of condensate water pumps. There have been numerous patents and papers proposing solutions to address the low-frequency resonance problem in condensate water pumps. However, the solutions for resonance problems often need to be tailored to specific circumstances. Methods: Based on the acoustic method, the dynamic model of the rotor and inner cylinder of Jiangsu Guohua Chenjiagang Power Plant 2B condensate pump is established to compare the difference between dry modal and fluid-structure coupling modal, the influence of perpendicularity, concentricity and bearing wear on the natural frequency of rotor is studied. Results: The rotor is rigid under normal conditions. When the bearing is worn, the frequency of the rotor will be greatly reduced and may fall into the frequency conversion operation range to excite resonance. The deviation of perpendicularity and concentricity will not directly lead to the decrease of rotor modal but will lead to the increase of bearing stress, aggravate bearing wear, and then affect the rotor modal. As the inner cylinder only relies on the fixed support at the top, the structure stiffness is low, which may lead to low-frequency resonance. By adding two support structures at the guide vane, the first-order modal frequency of the inner cylinder can be increased from 3.29 Hz to 28.88 Hz, effectively avoiding the operating frequency range of the system. Conclusion: This study can guide the optimization of similar pump structures.

Attachment detection on the inner wall of gas-liquid two phase flow pipe based on ultrasonic guided waves

Gas-liquid two-phase flow pipelines are commonly found in building thermal systems. However, the attachment on the inner wall of the pipeline brings great safety hazards to the system. At present, ultrasonic guided wave technology has been widely used for the structural inspection of pipelines. The boundary conditions significantly affect the propagation characteristics of ultrasonic guided waves and the detection accuracy. Therefore, this paper investigates the influence of the flow pattern on the propagation characteristics of guided waves using semi-analytical finite element method and proposes an excitation frequency selection method independent of the flow pattern to improve the accuracy of the detection of attachments in gas-liquid two-phase flow pipelines. The relationship between the attachment size and the reflection echo characteristics is analyzed. Numerical simulation and experimental results show that the flow pattern leads to the modal coupling phenomenon of the L(0,1) guided wave, and the modes vary with the spatial distribution of the gas plug. The attachment echo contains not only the attachment information but also the position of the gas plug in the fluid. Finally, the maximum error of the attachment position accuracy in two-phase flow pipes with different flow patterns is no more than 3 %. An innovative dispersive surface result reflecting the changes in the propagation characteristics of UGWs along a pipe with changing cross-section (plug flow) is established.

Integrated analytical, experimental, and numerical study of the effect of hydro-static loading on the vibrational response of clamped circular plates

This paper presents a comprehensive investigation, comprised of analytical, experimental and numerical approaches, into the interaction between a water cavity of varying fluid cavity height and the vibration of a thin circular plate subjected to its hydro-static pressure. We extend the application of the strong modal coupling method to derive a solution for this unexplored physical problem by utilising classic plate theory, Fourier-Bessel series formulation and the uncoupled solution of a thin clamped circular plate with uniform radial tension. Using a set of geometric and physical properties for the system, the resonance frequencies, response functions and non-dimensionalised added virtual mass incremental (NAVMI) factors are calculated and investigated as a function of hydro-static pressure and fluid cavity height, providing novel fundamental insights into the physical system. We construct an experimental rig to embody the conditions of the analytical investigation for the purpose of validation and to uncover experimental insights into the physical problem. Finite element analysis (FEA), employing modal analysis and transient dynamic analysis, is used to further validate and extend the analytical insights while more accurately mirroring the experimental conditions. The response functions, resonance frequencies and NAVMI factors and their dependence on the cavity pressure were experimentally measured and numerically simulated, with direct comparisons made with the analytical model. A high degree of accuracy for the analytical model is validated, along with its ability to describe the underlying physical phenomena. The validated analytical model is then leveraged to perform fundamental explorations into the modal compositions of the coupled system modes as a function of cavity height and hydro-pressure, the deformation of the coupled system mode shapes and a parametric sensitivity analysis on the effects of plate radii and plate thickness on the coupled system resonance frequencies and NAVMI factors. In totality, this study provides detailed modelling and prediction of the frequency response, resonance frequencies, added mass factors, modal contributions, and deformation of the coupled mode shapes, offering comprehensive insights with wide applicability.

Mie Magnetic Structural Colors from Short Chains of TiO2 Nanospheres.

We demonstrate distinctive structural colors within a small footprint by using a short chain of nanospheres. Rather than using high-index materials like Si (n ∼ 4), which ensure strong modal confinement, TiO2 is employed. TiO2 has an intermediate index (n ∼ 2), promoting stronger modal coupling between the magnetic dipoles of each particle. This approach enables selective engineering of the magnetic response and yields larger spectral changes compared to that of Si. Despite the lower refractive index, the absence of absorption in TiO2 also produces higher scattering intensities than Si. We develop a quasistatic analytical model that describes the dipolar modal coupling in a trimer and use it to reveal distinct magnetic field strengths in the outer or central particle depending on the polarization of incident light. These results suggest pathways to manipulate the magnetic field in chains of particles and create vibrant structural colors with simple configurations.

Continuation of nonlinear normal modes using reduced-order models based on generalized characteristic value decomposition

Over the past two decades, data-driven reduced-order modeling (ROM) strategies have gained significant traction in the nonlinear dynamics community. Currently, several challenges in physical interpretation and data availability remain overlooked in current methodologies. This work proposes a novel ROM methodology based on a newly proposed generalized characteristic value decomposition (GCVD) to address these obstacles. The GCVD-ROM approach proposes a new perspective toward data-driven ROMs via characterization of the dynamics before any ROM considerations are made. In doing so, a significant degree of versatility is inherited in the GCVD-ROM strategy, allowing our models to reproduce the full-scale dynamics in different regions of the parameter space at the cost of a single training data set. Our approach utilizes computationally efficient free-decay data sets alongside a windowed-decomposition scheme, allowing us to extract energy-dependent modal structures for use in model-order reduction. This is accomplished using the physically insightful characteristic values provided by the GCVD, which are shown to be directly related to the system poles at a particular response amplitude. This natural metric, paired with a resonance tracking scheme, allows us to address the difficulties associated with physical interpretation and data availability without sacrificing the convenient aspects of linear projection-based model order reduction. A computational framework for the continuation and bifurcation analysis using linear projection-based ROMs is also presented, permitting us to deploy rigorous analysis and bifurcation studies to verify that our ROMs reproduce the intrinsic complexity of full-scale systems. A detailed walk-through of the GCVD-ROM approach is demonstrated on a simple system where important practical considerations and implementation details are discussed using a concrete example. The discretized von Kármán beam and shallow arch partial differential equations are also used to explore complicated scenarios involving modal coupling across disparate time scales and internal resonances.

Systematic Experimental Evaluation of Aeroelastic Characteristics of a Highly Flexible Wing Demonstrator

This paper presents a comprehensive experimental analysis of the evolutionary modal characteristics of a highly flexible wing that exhibits bending–torsion coupling-driven instability. By implementing operational modal analysis on responses triggered by a combination of an external pulse-like stimulation and turbulence within the flow, this paper presents the airspeed-driven variations of the modal frequencies, damping ratios, and the underlying modal coupling behavior, leading to instability. This analysis is extended to varying the wing root pitch angles through which the effects of geometrical nonlinearity are exercised. Their effects are particularly noted on the hump feature of the airspeed-driven damping ratio locus of the mode responsible for instability. The decreasing critical damping ratio is shown to result in amplified turbulence-driven responses, which pose significant challenges to identification procedures by masking the visibility of other modes. Furthermore, through a novel technique used to analyze the modal coupling, the relative phase and magnitude properties of the coupled bending–torsion composition of the critical mode before and at flutter onset are evidenced experimentally. It is demonstrated that these relative participation measures provide a strong indication of the response content of the limit cycle oscillations that emerge after the flutter speed.

A distributed parameter model of the cavity-loaded piston transducer

Abstract Adding a cylindrical liquid cavity at the radiation surface of a piston transducer can introduce the liquid cavity resonance into the vibration system, thereby extending the operating bandwidth of the transducer. However, recent studies have shown that effective coupling of the liquid cavity resonance with the self-resonance of the piston transducer presents difficulties, resulting in significant fluctuations in the transmitting voltage response (TVR) within the operating frequency band. The physical mechanism behind this phenomenon remains unclear to date. In this paper, a distributed parameter model (DPM) for the cavity-loaded piston transducer is proposed. The admittance, amplitude and phase of the vibration velocity and TVR of the transducer are calculated using both DPM and finite element method (FEM). The results from DPM and FEM exhibit good agreement, indicating that the DPM can accurately describe the vibration characteristics of the transducer. Finally, two physical analogies of the transducer are proposed and explanations for the large fluctuations in TVR are given. This study reveals the modal coupling mechanism of the cavity-loaded piston transducer, and provides theoretical support for the analysis and designs of such transducers.

Ultrasonic scalpel based on fusiform phononic crystal structure

Abstract In response to the ultrasonic scalpels with the vibrational modal coupling which leads to a decrease in efficiency, an ultrasonic scalpel based on fusiform phononic crystals (PnCs) is proposed. An accurate theoretical model is constructed, which is mainly composed of electromechanical equivalent circuit models to analyze the frequency response function and the frequency response curves of the admittance. Bragg band gaps exist in the fusiform PnCs owing to the periodic constraint, which can suppress the corresponding vibrational modes. The vibration characteristics (vibration mode, frequency, and displacement distribution) of the ultrasonic scalpel are analyzed, and the validity of the electromechanical equivalent circuit method is verified. The results indicate that other vibration modes near the working frequency can be isolated. In addition, blades based on fusiform PnCs have a function akin to that of the horn, which enables displacement amplification.

Investigation on vortex-induced vibrations of square-sectioned high-rise buildings with various structural eccentricities

Structural eccentricities in a high-rise building can induce strong modal coupling, which therefore influences vortex-induced vibration (VIV) responses of the building and consequently affects human comfort within the building. This study investigates the VIV behaviour of square-sectioned high-rise buildings with different structural eccentricities, using both wind tunnel test and computational fluid dynamics (CFD) technique. Firstly, a novel method for constructing the multi-degree-of-freedom (MDOF) aeroelastic model of a high-rise building with specified structural eccentricities is introduced in detail. Seven MDOF aeroelastic models with different structural eccentricities are constructed. Wind tunnel test is then conducted to examine VIV responses of these high-rise building models. Effects of eccentricity ratio and direction on the models’ VIV responses are comprehensively investigated. In addition, CFD simulation is conducted to elucidate the aerodynamic mechanism of VIV responses of high-rise buildings with structural eccentricities. Results reveal that the direction of structural eccentricity influences the reattachment of vortex shedding over the building, which in turn affects the lift and, consequently, the building’ VIV responses. The maximum VIV response of the building models exhibits a negative correlation with the windward eccentricity ratio, while a positive correlation with the leeward eccentricity ratio. Results from CFD simulation demonstrate that the structural eccentricity tends to broaden the wake downstream, resulting in a reduction in the building’s vortex shedding frequency and, consequently, the Strouhal number. Findings of the present study can enhance the understanding of VIV behaviours of high-rise buildings with structural eccentricities, providing valuable insights for the wind design of such structures.

Multi-modal control and position optimization of solar panels

This paper investigates the impact of the position of piezoelectric actuators on the vibration control effect of the membrane plane composed of solar sail materials with a given unit area. Firstly, the nonlinear vibration equation of the membrane structure is perfected based on the system equation established by Yifan Lu et al. Then, the modal coupling effect pointed out by Liu Xiang is considered, and the fourth-order modal displacement generated by the piezoelectric actuator in vibration control is derived. Subsequently, the sliding mode controller used in vibration control is designed based on Lyapunov stability theory, and its effectiveness is verified through Simulink simulation. The sliding mode controller is used to calculate the required excitation signal and apply it to the piezoelectric patches. The reverse force is generated through the inverse piezoelectric effect of the patches to actively suppress the vibration of the solar sail. By changing the position and size of each piezoelectric actuator on the solar sail plane, this paper compares the impact of different layout positions on vibration control, and proposes an optimal layout scheme for the position of the piezoelectric patches in terms of control effectiveness.

A forecasting method for corrected numerical weather prediction precipitation based on modal decomposition and coupling of multiple intelligent algorithms

A forecasting method for corrected numerical weather prediction precipitation based on modal decomposition and coupling of multiple intelligent algorithms

Asymmetric modal coupling in a passive resonator towards integrated isolators

Asymmetric modal coupling in a passive resonator towards integrated isolators

Optical steelyard: high-resolution and wide-range refractive index sensing by synergizing Fabry–Perot interferometer with metafibers

Refractive index (RI) sensors play an important role in various applications including biomedical analysis and food processing industries. However, developing RI sensors with both high resolution and wide linear range remains a great challenge due to the tradeoff between quality (Q) factor and free spectral range (FSR) of resonance mode. Herein, the optical steelyard principle is presented to address this challenge by synergizing resonances from the Fabry–Perot (FP) cavity and metasurface, integrated in a hybrid configuration form on the end facet of optical fibers. Specifically, the FP resonance acting like the scale beam, offers high resolution while the plasmonic resonance acting like the weight, provides a wide linear range. Featuring asymmetric Fano spectrum due to modal coupling between these two resonances, a high Q value (~ 3829 in liquid) and a sensing resolution (figure of merit) of 2664 RIU−1 are experimentally demonstrated. Meanwhile, a wide RI sensing range (1.330–1.430 in the simulation and 1.3403–1.3757 in the experiment) is realized, corresponding to a spectral shift across several FSRs (four and two FSRs in the simulation and experiment, respectively). The proposed steelyard RI sensing strategy is promising in versatile monitoring applications, e.g., water salinity/turbidity and biomedical reaction process, and could be extended to other types of sensors calling for both high resolution and wide linear range.