Excitation Force Research Articles

An analytical dynamic stiffness method for efficient broadband vibro-acoustic analysis of complex built-up structures

An analytical modelling technique is presented, combining the dynamic stiffness method (DSM) with the spectral DSM (SDSM) for the broadband vibro-acoustic analysis of complex built-up structures. In particular, the structures are modelled exactly by the DSM based on particular solutions tailored for general acoustic or distributed force excitations; whereas the acoustic cavities are modelled by the SDSM where the boundary conditions are described by modified Fourier series with a rapid convergence rate. The vibro-acoustic coupling along the interfaces between the structures and the cavities is achieved by applying the normal velocity continuity condition, leading to a coupling matrix in an analytical manner. Both structural and acoustic cavity elements are assembled directly to model complex vibro-acoustic systems and no extra element discretization is required for both structural and acoustic domains. Consequently, the proposed method uses very few degrees of freedom (DoFs) but describes the broadband vibro-acoustic behaviour highly accurately. It is demonstrated that the proposed method exhibits a predominant advantage over the finite element package COMSOL in terms of accuracy and computational efficiency. This approach also has the potential to serve as the benchmark for a wide range of vibro-acoustic problems.

Analysis of the influence of nonlinear energy sink parameters applicable to helicopter main reduction systems

Abstract In response to the vibration problem of helicopter fuselage caused by continuous rotor periodic excitation force, a nonlinear energy sink is considered to be installed on the main reduction transmission channel to reduce the vibration level of the fuselage. This article conducts an analysis of the influence of nonlinear energy sink structure parameters under harmonic excitation force, establishes a coupled dynamic model of helicopter main reduction/absorber/fuselage, and uses harmonic balance method and stability analysis theory to analyze the periodic solution and stability of the system. Using the vibration amplitude of the system as the evaluation criterion, the influence of damping, stiffness, and mass ratio on the vibration suppression effect of the nonlinear energy sink was explored. The results showed that as the damping of the nonlinear energy sink increased, the resonance frequency of the coupled system shifted to the left, and the vibration amplitude of the main reduction system increased; As the stiffness of the nonlinear energy sink increases, the vibration amplitude of the coupled system will first decrease and then increase, gradually approaching the vibration amplitude of the system without coupled dampers; The influence of mass ratio on system amplitude follows the same trend as the influence of stiffness. By optimizing, the structural parameters of the nonlinear absorber with good vibration suppression effect are ultimately obtained.

Influence of collapsible shape of Loess Foundation on high-speed railway subgrade under train vibration loading

Collapsible loess has special sensitivity to water, and its engineering mechanical properties deteriorate significantly after immersion in water, causing the foundation to sink, which seriously threatens the safety and stability of the high-speed railway subgrade under train vibration loading. Studying this effect is essential to prevent and control the disasters of high-speed railway subgrades. In this study, a model with the function of simulating foundation settlement is established to conduct disaster testing of high railway subgrade under train vibration loading. The results indicate that when different foundation shapes are settled, the surface of the subgrade under static load is gradually settled in a short time, and the settlement value of the track surface is lower than that of the corresponding subgrade surface. Under train vibration load, the maximum dynamic settlement occurs at the middle of the subgrade slope, which is smaller than the corresponding settlement under static load. The number of stabilization times required from different monitoring positions on the subgrade surface is different under different excitation forces, and the number of stabilization times required is more in the middle of the subgrade slope and the slope shoulder. The influence of train speed on subgrade has a critical respond speed that increases with increasing vibration times. There are horizontal, vertical and 45° angle cracks in the middle of subgrade slope. It is qualitatively assessed that the slope of the high-speed railway subgrade in the collapsible loess area is unstable under the effect of train load. The data and rules provided in this document provide some reference values for the construction of a high-speed railway in the collapsible loess area.

Synchronization analysis of a four-motor excitation with torsion spring coupling vibrating system

In oil drilling processes, vibrating screen is a crucial solid control equipment for separating harmful solid-phase particles. However, the conventional utilization of either dual-motor or triple-motor is inadequate demanding the excitation force of large vibrating equipment. Moreover, self-synchronization in zero phase is difficult to achieve in multiple motors system. To avoid cancellation of the excitation force caused by the phase inconsistency of multiple motors, the adoption of a four-motor excitation with torsion spring coupling system is proposed this work. Initially, the mathematical model of the vibrating system is formulated through the Lagrange's equation. Subsequently, the steady-state solution is determined using Laplace transform. Then the conditions and characteristics in stable equilibrium state are elucidated employing the small parameter averaging method. Ultimately, the reliability and applicability of the theoretical results are substantiated through numerical simulations. The findings reveal that with the increase of the torsion spring stiffness, the phase difference between the motors connected by torsion springs (MCTSs) is exponentially decreased, and desired zero-phase synchronization in engineering is eventually achieved. Furthermore, the present study uncovers two distinct synchronization mechanisms in the torsion spring coupling system: mechanical controlled synchronization between MCTSs is inevitably achieved, while the self-synchronization between motors unconnected by torsion springs (MUTSs) is limited by the synchronization conditions. The study provides valuable insights for designing mechanical controlled synchronization and self-synchronization vibrating machines.

Chaotic dynamics of flexible graphene electronic membranes with variable density in motion

With advancements in artificial intelligence and wearable technology, flexible electronic devices characterized by their flexibility and extensibility have found widespread applications in fields such as information technology, healthcare, and military. Printing technology can accurately print a circuit diagram onto a flexible membrane substrate by the pressure transfer of a conductive ink, which makes the large-scale printing of flexible graphene electronic membranes possible. However, during the roll-to-roll printing process used to prepare flexible graphene electron membranes, the density of electron membranes is variable due to the uneven distribution of inkjet-printed circuits, which limits the printing speed of flexible graphene electron membranes. Hence, investigating the dynamic properties of flexible graphene electron materials with different densities is of paramount importance to improve the production efficiency and quality of flexible graphene electron membranes. This paper takes roll-to-roll intelligent graphene electronic membranes as the research object. According to Hamilton’s principle, nonlinear vibration partial differential equations for the motion of flexible graphene electron membranes with varying densities were established and subsequently discretized using the assumed displacement function and the Bubnov–Galerkin method. Through numerical calculations, the simulation results obtained based on the fourth-order Runge–Kutta method and the multiscale algorithm were compared, and the multiscale algorithm was verified to be more correct and effective. The primary resonance amplitude–parameter characteristic curve, along with phase-plane portraits, Poincaré maps, power spectrum, time history plots, and bifurcation diagrams, for the nonlinear behavior of the membrane was obtained. The impacts of the density coefficient, velocity, damping ratio, excitation force, and detuning parameters on the nonlinear primary resonance and chaotic behavior of the moving graphene electron membrane were determined, and the stable operational region was identified, laying a theoretical foundation for the development of flexible graphene electronic membranes.

A study of the effects of housing tongue design on radial turbine performance

The nozzleless volute housings can generate non-uniform flow distributions to the downstream radial turbine rotors, which not only affects turbine aerodynamic performance but also poses a threat to the fatigue life of the rotors. It is believed that the housing tongue is the main factor in generating this non-uniformity. Tongue design is based on experience and the geometric parameters of tongue, such as the distance between the tongue and rotor, the thickness of the tongue, and tongue shape are to be specified in the design. A few studies on housing tongue can be found in the literature, but in these investigations of the influences of tongue geometric parameters, factors such as mass flow rate and volute A/R distribution were not kept constant, thus introducing additional factors and reducing the persuasiveness of the results. Therefore, three new housings with different tongue-rotor distances are designed with a two-dimensional method for comparative CFD studies. The results indicate that when the mass flow of the turbines is kept, the distance between the tongue and the rotor has little impact on the turbine efficiency (about 0.1%), while the blade excitation forces from the housing increase with the decrease of the distance by more than 50%. Two further new housings are then created by modifying the housing inlet pipe to minimize tongue thickness, one of the housings is more practical with a short and thin tongue. CFD results indicate 0.2%∼0.4% improvement of turbine efficiency and reduction of housing excitation forces by more than 50% using these two thin tongue housings.

Exciting DeePMD: Learning excited-state energies, forces, and non-adiabatic couplings.

We extend the DeePMD neural network architecture to predict electronic structure properties necessary to perform non-adiabatic dynamics simulations. While learning the excited state energies and forces follows a straightforward extension of the DeePMD approach for ground-state energies and forces, how to learn the map between the non-adiabatic coupling vectors (NACV) and the local chemical environment descriptors of DeePMD is less trivial. Most implementations of machine-learning-based non-adiabatic dynamics inherently approximate the NACVs, with an underlying assumption that the energy-difference-scaled NACVs are conservative fields. We overcome this approximation, implementing the method recently introduced by Richardson [J. Chem. Phys. 158, 011102 (2023)], which learns the symmetric dyad of the energy-difference-scaled NACV. The efficiency and accuracy of our neural network architecture are demonstrated through the example of the methaniminium cation CH2NH2+.

A Constraint-Based Orbital-Optimized Excited State Method (COOX).

In this work, we present a novel method to directly calculate targeted electronic excited states within a self-consistent field calculation based on constrained density functional theory (cDFT). The constraint is constructed from the static occupied-occupied and virtual-virtual parts of the excited state difference density from (simplified) linear-response time-dependent density functional theory calculations (LR-TDDFT). Our new method shows a stable convergence behavior, provides an accurate excited state density adhering to the Aufbau principle, and can be solved within a restricted SCF for singlet excitations to avoid spin contamination. This also allows the straightforward application of post-SCF electron-correlation methods like MP2 or direct RPA methods. We present the details of our constraint-based orbital-optimized excited state method (COOX) and compare it to similar schemes. The accuracy of excitation energies will be analyzed for a benchmark of systems, while the quality of the resulting excited state densities is investigated by evaluating excited state nuclear forces and excited state structure optimizations. We also investigate the performance of the proposed COOX method for long-range charge transfer excitations and conical intersections with the ground-state.

Flexoelectronics of a centrosymmetric semiconductor cylindrical nanoshell

Cylindrical shell-type semiconductors are essential for sensing and energy harvesting when integrated into surfaces of certain equipment, such as spacecraft, marine devices, and portable electronics, where mechanical forces play a significant impact on charge transport. Traditionally, such functionalities are only manifested in piezoelectric or pyroelectric crystals that possess non-centrosymmetry. Here, we theoretically investigate electronic behaviors driven by strain gradient-induced flexoelectric polarization in a centrosymmetric semiconductor cylindrical nanoshell, expanding the flexoelectronics in shell structures. The governing equations and accompanying boundary conditions are formulated simultaneously using the principle of virtual work and the fundamental lemma of the calculus of variation. Electromechanical interactions through static bending and forced vibration analyses of the newly developed model are systematically investigated. Under localized force excitation, the distribution of mobile charges is manipulated by tuning loading magnitudes and areas. The effects of doping levels on electric potentials and mobile charges are explored to show the interaction mechanism between flexoelectric and semiconducting properties. Moreover, the natural frequencies and modes of all mechanical displacements, electric potentials, and carrier concentration perturbations within the shell are identified. This paper provides a new approach for designing shell-shaped sensors and energy harvesters specifically for centrosymmetric semiconductors.

Synchronization phenomenon in a vibrating system driven by four eccentric rotors mounted in the orthogonal plane

The engineering application of vibration synchronization of multiple eccentric rotors (ERs) with the same rotational plane in far resonance is limited due to the constraints of motion characteristics and resultant force cancellation. Therefore, a dynamic model of four ERs distributed in two orthogonal planes is proposed in this paper, which is designed to increase the excitation force and drive the vibrating body to achieve the motion in a straight line. Based on the governing equation corresponding to the dynamic model firstly, the synchronous condition of four ERs and its stability condition are deduced. Then, the phase relationship of four ERs is obtained by numerical analysis, and the resultant force of four ERs in each phase difference is further studied to determine the motion trajectory of the vibrating body. Lastly, theoretical results are verified by four sets of experiments, which show that there are two stable motion states of the system. In each motion state, the resultant force of four ERs is increased compared to two ERs, and the system also moves in a straight line. Therefore, the model presented in this paper can provide a theoretical basis for designing large vibration machinery.

Anisotropic elasticity measurements of the retina using optical coherence elastography

Anisotropic elasticity measurements of the retina are essential for retinal disease diagnosis and function assessment. Optical coherence elastography (OCE) is a high-resolution imaging technique for mapping the elasticity distribution of tissues. However, previous OCE measurements quantified the tissue elasticity in a single direction, resulting in a biased estimation of the elastic properties. In this study, we propose an OCE method with acoustic radiation force (ARF) excitation to map the retinal anisotropic elasticity in the depth and lateral directions. The axial elasticity was analyzed using the natural frequency of free vibration, and the lateral elasticity was quantified using the elastic wave velocity. After evaluating the feasibility of the OCE method on the phantoms, the anisotropic elasticity of ex vivo porcine retinas was mapped. The results show that the OCE method with ARF excitation can assess the elasticity in orthogonal directions and provide a comprehensive understanding of the elasticity of the anisotropic tissues.

Effect of Ferrite Core Modification on Electromagnetic Force Considering Spatial Harmonics in an Induction Cooktop

This study investigates the influence of ferrite shape modifications on the performance and noise characteristics of an induction cooktop. The goal is to optimize the air gap dimensions between ferrites and cookware, enhancing efficiency while managing noise levels. Using finite element method (FEM) simulations, we analyze the spatial distribution of magnetic forces and their harmonics. Eight ferrite shape models were examined, focusing on both outer and inner air gaps. Model #8 (reduced outer air gap) and Model #9 (reduced inner air gap) were experimentally validated. Noise measurements indicated that Model #8 reduced 120 Hz harmonic noise components, while Model #9 increased them due to enhanced excitation forces. Current measurements confirmed that Model #9 achieved higher efficiency, with RMS current reduced to 94.54% of the base model. The study reveals a trade-off between performance and noise: inner air gap reduction significantly boosts efficiency but raises noise levels, whereas outer air gap reduction offers balanced improvements. These findings provide insights for optimizing induction cooktop designs, aiming for quieter operation without compromising efficiency.

Experimental Research on Pressure Pulsation and Flow Structures of the Low Specific Speed Centrifugal Pump

The low specific speed centrifugal pump plays a crucial role in industrial applications, and ensuring its efficient and stable operation is extremely important for the safety of the whole system. The pump must operate with an extremely high head, an extremely low flow rate, and a very fast speed. The internal flow structure is complex and there is a strong interaction between dynamic and static components; consequently, the hydraulic excitation force produced becomes a significant factor that triggers abnormal vibrations in the pump. Therefore, this study focuses on a low specific speed centrifugal pump and uses a single-stage model pump to conduct PIV and pressure pulsation tests. The findings reveal that the PIV tests successfully captured the typical jet-wake structure at the outlet of the impeller, as well as the flow separation structure at the leading edge of the guide vanes and the suction surface. On the left side of the discharge pipe, large-scale flow separation and reverse flow happen as a result of the flow-through effect, producing a strong vortex zone. The flow field on the left side of the pressure chamber is relatively uniform, and the low-speed region on the suction surface of the guide vanes is reduced due to the reverse flow. The results of the pressure pulsation test showed that the energy of pressure pulsation in the flow passage of the guide vane occurs at the fBPF and its harmonics, and the interaction between the rotor and stator is significant. Under the same operating condition, the RMS value distribution and amplitude at fBPF of each measurement point are asymmetric in the circumferential direction. The amplitude of fBPF near the discharge pipe is lower, while the RMS value is higher. A complex flow structure is shown by the larger amplitude and RMS value of the fBPF on the left side of the pressure chamber. With the flow rate increasing, the energy at fBPF of each measurement point increases first and then decreases, while the RMS value decreases, indicating a more uniform flow field inside the pump.

Forced Response of a High-Static-Low-Dynamic (HSLD) Stiffness Isolator with Active Stiffness Control

The High-Static-Low-Dynamic (HSLD) stiffness vibration isolators have been exploited in many engineering applications due to its capability in having a wider isolation bandwidth, while maintaining the high static load capacities. However, it will lead to a large payload oscillation at the static equilibrium position, if the source of vibration is an oscillating force originating within the payload. In this case, the considerably large resultant motion of the payload will change the system nonlinearity. An active stiffness control for reducing the displacement amplitude of the payload oscillation subjected to a harmonic force excitation is proposed in this paper. The dynamic model of an actively stiffened HSLD stiffness isolator is introduced, and the approximate analytical expression for forced response is obtained using the Harmonic Balance Method (HBM). The obtained forced response curve has demonstrated that the active stiffness control is able to reduce the system’s force response, particularly at low frequencies with an approximation of 50%. The nonlinearity of the system becomes smaller as the active stiffness control is applied.

Warping-included mixed FE approach of beating characteristics in functionally graded graphene platelet-reinforced composite spatially curved beams under harmonic excitation force

Warping-included mixed FE approach of beating characteristics in functionally graded graphene platelet-reinforced composite spatially curved beams under harmonic excitation force

Experimental-based hydrodynamic simulation of submarine glider for wave gliders

The wave glider is an unmanned surface vehicle propelled by wave energy, consisting of three main components: a surface float, a submarine glider, and a tether. The submarine glider serves as the primary propulsion mechanism, converting the wave-induced motions of the float into forward thrust, which is crucial for the wave glider’s energy absorption efficiency. However, predicting the motion performance of the submarine glider presents a significant challenge due to its complex and unique structure. In this study, we establish a kinematic and dynamic model of the submarine glider’s hydrofoils, considering the elastic effects such as spring stiffness, spring preload, and spring attachment positions. To support this model, wind tunnel tests were conducted to determine the lift and drag coefficients of the submarine glider under various motion states. Utilizing the elastic hydrofoil model and the experimentally obtained lift and drag coefficients, we developed a comprehensive kinematic and dynamic simulation model of the submarine glider under heave excitation forces. To validate the accuracy of this model, performance tests for the submarine glider were designed under different vertical excitation forces , with results compared to simulation outcomes. The findings indicate that the deviation between simulated and experimental outcomes is less than 5%, demonstrating the model’s precision. This accurate simulation capability allows for detailed analysis of the effects of various design parameters on the glider’s performance and lays a solid foundation for high-accuracy motion simulation of the entire wave glider.

Enhancing dynamic stability of HTS maglev systems with preloading method

High temperature superconducting (HTS) bulks have strong flux pinning capabilities and are widely used in various fields. Their self-stabilizing characteristics also provide new ideas for ultra-high-speed rail transit. For HTS maglev systems, operational stability, curve negotiation and safety when subjected to external forces are very important. Due to the hysteresis effect of superconducting bulks, they do not always return to their initial positions after deviating from the levitated position in an alternative external magnetic field. In some cases, the levitation system can be destroyed. Studies have shown that preloading can enhance quasi-static levitation performance. Therefore, this paper conducts a detailed analysis of the quasi-static levitation and guidance forces of HTS bulks above a Halbach permanent magnet guideway (PMG) under conditions with and without preloading. Additionally, the dynamic responses of the HTS bulks under lateral or vertical pulsed excitations are studied, with a particular focus on the final equilibrium position offset after disturbance. The results indicate that preloading can suppress the attenuation of the levitation force, enhance the guidance performance, and raise stiffness in both lateral and vertical directions. It also effectively suppresses position deviation from disturbance and increases the maximum excitation force threshold for system instability. This study provides practical insights for HTS maglev applications.

The broad study of blade cascade under controlled torsional flutter: Dynamics of the flow and stability analysis

The experimental and numerical investigation of the flow instabilities acting on rigid blades and vice versa was conducted for both compressor and turbine configuration. The blade cascade consisted of five rectangular NACA 0010 blades, with three middle blades capable of performing harmonic motion with one degree of freedom (pitching) using force excitation. The base case (all blades fixed) and excited regime were examined. The influence of various angles of attack, harmonic frequency values, amplitude values, inter-blade phase angles and Reynolds numbers (Re) were tested. The mean flow properties as well as the fluid - structure interaction (FSI) were studied using Particle Image Velocimetry (PIV), Reynolds-averaged Navier-Stokes (RANS) CFD methods and using force measurement. Additionally, two different approaches, namely traveling wave mode (TWM) and aerodynamic influence coefficient (AIC), were adopted to estimate the aeroelastic stability of the blade cascade, and the results were compared. The results show significant aeroelastic coupling between the blades in both compressor and turbine configuration. However, the aerodynamic coupling effect for torsional flutter is more prominent in turbine configuration.

Wave excited motion of a body floating on water confined between a semi-infinite ice sheet and a side wall

In this paper, we investigate the diffraction and radiation coupling problem of a floating body confined between a fixed wall and a semi-infinite ice sheet under the action of incident waves. Based on the linear water wave theory and Kirchhoff Love elastic thin plate assumption, the ice sheet is considered as an elastic beam, and the boundary conditions of fluid boundaries covered by the ice sheet are obtained. Dividing flow domains with different upper surfaces, the eigenfunction expansion method was used to obtain the velocity potential expansion equations for each sub-domain. Then, through the matching conditions at the interface of sub-domains, a system of equations was constructed to solve the unknown coefficients of the expansion equations. The influence of the existence of the ice sheet on the diffraction and radiation motion of the floating body is analyzed. The effects of changes in the draft and open water width of the floating body on the wave excitation force and hydrodynamic coefficient of the floating body are discussed. The influence of the reflection effect of the ice sheet on the added mass and damping coefficient of the floating body has been discovered, especially the changes and oscillation rules of their extreme points. This research achievement provides theoretical support for the safety design of floating structures in frozen harbors.

Viscous effects on the hydrodynamic performance of a two-body wave energy converter with a damping plate

In this study, the hydrodynamic forces and power absorption performance of an autonomous underwater vehicle (AUV)-based two-body wave energy converter (2BWEC) are investigated. A theoretical model is developed within the framework of linear potential flow to solve for added mass, radiation damping, and wave excitation force using the matched eigenfunction expansion method (MEEM). A computational fluid dynamics (CFD) model is employed to account for vortex-shedding effects of the floater and inner cylinder with a damping plate under various excitation conditions. Empirical formulas for supplementary added mass and drag coefficients caused by flow separation are proposed based on curve-fitting the differences between CFD results and MEEM calculations. These formulas are integrated into motion equations to enhance accuracy in evaluating the power absorption of the 2BWEC. It has been found that in the context of viscous flow, both the added mass and damping coefficients are increased, particularly for the inner cylinder with a damping plate. In addition, the viscous hydrodynamic coefficients exhibit strong dependence on the Keulegan–Carpenter number, while showing insensitivity to changes in the frequency parameter β. The supplementary (viscous) added mass provides additional inertia for the AUV with a limited mass itself, which is advantageous for the power absorption of the AUV-based 2BWEC. Conversely, the presence of viscous damping from the damping plate impedes wave energy capture.