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Semi-Analytic Solutions for the Bending-Bending-Torsion Coupled Forced Vibrations of a Rotating Wind Turbine Blade by Means of Green’s Functions
Zhao X., Jiang X., Zhu W., Li Y.
Springer Nature
NODYCON Conference Proceedings Series, 2024, цитирований: 0, doi.org, Abstract
In recent years, wind power has received continuous attention as a renewable energy source in the context of carbon neutrality. Blades in wind turbines with elongated structures are susceptible to damage due to aeroelastic instability. In this chapter, the basic solution of the system is derived by Laplace transformation and Green’s function method, and then the system of the second category of Fredholm integral equations about steady-state forced vibration of blades can be derived according to the principle of superposition. The second type of Fredholm integral equation system is discretized numerically, and finally, a semi-analytical solution for the bending-bending-torsion coupled forced vibration of rotating wind turbine blades is obtained. The validity of the solution presented in this chapter is verified by comparing the first-order flag mode and first-order lead/lag mode with previously obtained results. The results show that the inflow ratio at the hub and the angular velocity of rotation have a significant influence on the blade’s flag displacement and lead/lag displacement.
Nonlinear Dynamic Characteristics and Four Contact States of a Spur Gear Pair Considered Tooth Profile Error and Extended Tooth Contact
Li Z., Chen Z., Ning J.
Springer Nature
NODYCON Conference Proceedings Series, 2024, цитирований: 0, doi.org, Abstract
The actual tooth profile of a spur gear will inevitably deviate from the involute tooth profile (ITP) due to machining error, and so on. The nonlinear characteristics and contact state of the gear transmission system will be changed due to tooth profile error, and the system stability will be affected accordingly. A dynamic model of a spur gear pair is established by considering tooth profile error, extended tooth contact, and some time-varying parameters. Tooth profile error and extended tooth contact are directly involved in the calculation of the dynamic meshing force. Besides, the five Poincaré mapping sections Γi and corresponding triggers are established to capture the information on system motion, extended teeth contact, tooth disengagement, and back-side contact. Finally, the bifurcation characteristics and four contact states of the system are studied by using the established Poincaré mapping sections, bifurcation diagrams with multi-mapping sections, and phase portraits. The results indicate that, with the increase of tooth profile error, the system will go through stable periodic motion, alternation between periodic motion and chaotic motion, and unstable chaotic motion. Tooth disengagement and tooth back contact will also occur in turn. The contact of extended teeth is also changed by system bifurcation, tooth disengagement, and back-side contact. This chapter can provide a reference for stability analysis of the gear transmission system.
New Formula of Geometrically Exact Shell Element Undergoing Large Deformation and Finite Rotation
Feng R., Wang J., Zhang S., Jia K., Ren Q.
Springer Nature
NODYCON Conference Proceedings Series, 2024, цитирований: 0, doi.org, Abstract
The paper develops a new geometrically exact shell element that allows large deformation and finite rotation. The new element is based on the Reissner–Mindlin shell theory, where the shell is considered as a surface with oriented directors. Accordingly, an incremental description for rotational fields of oriented directors is given. The description takes advantage of two rotational variables of the pseudo-rotation vector to avoid the vectorial parameterizations of rotation tensor. With the application of Mixed Interpolation of Tensorial Components (MITC), the shell is shear-locking free, features second-order accuracy, and contains nine nodes. Each node has five degrees of freedom, three for translations and two for rotations. Finally, numerical simulations show these new shell elements have the ability of dealing with large deformations and finite rotations with high efficiency and good accuracy.
Investigation on Vibro-Impacts of Electric Powertrain in Regenerative Braking Process
Liu K., Wu W.
Springer Nature
NODYCON Conference Proceedings Series, 2024, цитирований: 0, doi.org, Abstract
Due to gear backlashes of electric powertrain drivelines, vibro-impacts between gear teeth easily cause severe noise and vibration problems. To analyze the vibro-impacts of powertrain excited by regenerative braking, a dynamic model of an electric drive multistage gear system is established. This model considers the permanent magnet motor electromagnetic characteristics and the gearbox translational-rotational vibration. The results show the relationship between the relative deformation of the gear teeth and the relative velocity. The phenomena of multiple impacts and rebounds of the gear teeth in each impact are revealed. The transient impact forces of the bearing and multistage gear are compared and analyzed. The research provides theoretical support for the dynamic load study of the electric powertrain.
A New Koopman-Inspired Approach to Match Flow Field Excitation with Consequent Structure Responses for Nonlinear Fluid-Structure Interactions
Li C.Y., Chen Z., Lin X., Tse T.K., Fu Y.
Springer Nature
NODYCON Conference Proceedings Series, 2024, цитирований: 0, doi.org, Abstract
This work presents a novel method to form constitutive fluid-to-structure, excitation-to-response correspondences for insights into nonlinear fluid-structure interactions (FSI). The method combines the Fourier analysis’s temporal orthogonality to match like-frequency modal components into fluid-structure pairs and utilizes the proper orthogonal decomposition (POD)’s phenomenological visualization to identify each pair’s underlying mechanisms. Exploiting the latest data-driven algorithm, the dynamic mode decomposition (DMD), it serves as a Koopman-inspired, POD-projected, and machine-learning-embedded method that can be seen as an advanced discrete Fourier/Z-transform. Successful implementation with a prism wake with homogenous and anisotropic turbulence attests to its capability to handle a broad spectrum of problems involving nonlinear and stochastic dynamics. A user guideline has been offered in this work, which is pedagogically demonstrated via a classical FSI system.
Synchronization of Fractional Discrete-Time Complex Networks with Time Delays via Event-Triggered Strategy
Yuan X., Ren G., Yu Y., Chen W.
Springer Nature
NODYCON Conference Proceedings Series, 2024, цитирований: 0, doi.org, Abstract
This paper is devoted to the synchronization problem of complex networks (CNs) by designing an event-triggered control scheme. The dynamics of CNs are modeled by fractional discrete-time difference equations with time delays. Then, the pinning event-triggered controlled fractional discrete-time complex networks (FDTCNs) are designed. A novel event-triggered control strategy and some sufficient conditions are derived for achieving synchronization. Finally, a representative example is given for illustration.
An Approach to Monitor Bolt Faults in Two-Dimensional Structures Without Reference
Li Q., Zhao Q., Liao M., Yang F.
Springer Nature
NODYCON Conference Proceedings Series, 2024, цитирований: 0, doi.org, Abstract
Monitoring potential bolt faults is very necessary and meaningful to keep structures in healthy operation. For this purpose, an improved approach to monitor bolt faults in two-dimensional structures without reference is proposed. In the new method, the nonlinear dynamic behaviors of the structure to be monitored are studied by a general multi-degree-of-freedom (MDOF) mode with nonlinear elements. By exciting the structure many times with the same excitation and the local structural modification method, only nonlinear features from the structure to be monitored are defined. Based on these features, a novel fault index and corresponding improved approach are proposed and explained. With some numerical examples on a two-dimensional structure, the effectiveness and reliability of the method are fully verified.
On the Dynamics Analysis of Fractional-Type Microresonator System
Xi T., Xie J., Liu Z.
Springer Nature
NODYCON Conference Proceedings Series, 2024, цитирований: 0, doi.org, Abstract
A fractional-order dynamic model for microresonator is analyzed in this paper. The model is transformed from the integer-order dynamic model by setting the second-order derivative in the integer-order dynamic model as fractional-order p1 and the first-order derivative as fractional-order p2 according to the definition of Caputo fractional-order derivative. The results of simulation show that it is efferent to predict the behavior of the fractional-order dynamic model using the rules from integer-order dynamics provided that the difference between the fractional-order and integer-order is in a small interval. Additionally, the variations of both p1 and p2 certainly cause changes in the motion state of microresonator, while the effect of p1 is more significant than that of p2.
A Novel Vibration Response-Based Approach to Monitor Faults in Bolted Complex Structures
Li Q., Zhao Q., Liao M., Lei X.
Springer Nature
NODYCON Conference Proceedings Series, 2024, цитирований: 0, doi.org, Abstract
Since bolted complex structures are easily subjected to faults like fatigue crack/bolt loosening during their service, monitoring faults is very meaningful and helpful for them. Therefore, a novel vibration response-based approach for monitoring faults in bolted complex structures is proposed in this chapter. In this new approach, bolted complex structures are simplified as some discrete substructures, whose nonlinear dynamics are studied by a nonlinear multi-degree-of-freedom (MDOF) mode. By stimulating the structure many times with different magnitudes, nonlinear features from the substructure to be monitored only are defined, and a novel fault index and corresponding approach are proposed accordingly. With some experimental studies on a lab-bolted complex structure, the effectiveness of the proposed approach is fully vindicated.
Multidimensional Nonlinearity Time Series Forecasting Based on Multi-reservoir Echo State Network
Sun J., Li L., Peng H., Liu S.
Springer Nature
NODYCON Conference Proceedings Series, 2024, цитирований: 0, doi.org, Abstract
Echo state networks (ESNs) are known for their simple structure and excellent forecasting ability. In this chapter, we investigate the nonlinear prediction capabilities of ESNs, analyze their structure and principles, and propose a new prediction model based on the output mode, using multiple reservoirs. The proposed model is then tested using Mackey-Glass and Lorenz chaotic systems with different dimensions. Our results demonstrate that the multi-reservoir ESN model can accurately predict longer time series with high precision.
Critical Dynamics of Kuramoto Model on Erdös–Rényi Random Graphs
Chen H.
Springer Nature
NODYCON Conference Proceedings Series, 2024, цитирований: 0, doi.org, Abstract
Synchronization of interacting elements is ubiquitous in nature and has been widely investigated in many physical and biological systems, such as flashing fireflies, neurons in the brain, electric power grids, and Josephson junction arrays [1, 2]. Kuramoto introduced an analytically solvable model of coupled oscillators and thus inspired extensive studies on phase synchronization research since the 1980s [3–5]. In spite of its mature age, the theory of synchronization is still full of surprises, applications, and new features [6–8].
Reliability Problem of a Fractional Stochastic Dynamical System Based on Stochastic Averaging Method and Data-Driven Deep Learning Algorithm
Guan Y., Li W., Huang D., Trisovic N.
Springer Nature
NODYCON Conference Proceedings Series, 2024, цитирований: 0, doi.org, Abstract
Engineering structures with viscoelastic materials are generally modelled by a fractional-order system. The reliability problem of relative structural vibration under random excitations is always a hot issue in the field of the stochastic dynamical systems. Consider a generalized Van der Pol system with fractional derivatives excited by a white Gaussian noise. Firstly, a generalized harmonic transformation is used to get an approximated expression for fractional derivative by converting the fast-varying variables to the slow-varying variables and then applying stochastic averaging methods with energy envelopes to obtain the Ito differential equations and obtaining the Kolmogorov backward equations (KBE) related to the system energy. Then, combining Monte Carlo sampling to perform data-driven and neural network, a new algorithm is obtained to solve the reliability function that satisfies KBE, which is the innovation of this paper. The algorithm does not need boundary conditions and reduces the need for data volume in high-dimensional problems.
Physics-Informed Sparse Identification of a Bistable Nonlinear Energy Sink
Liu Q., Cao J.
Springer Nature
NODYCON Conference Proceedings Series, 2024, цитирований: 0, doi.org, Abstract
Bistable nonlinear energy sinks have attracted extensive attention due to their efficient broad-band targeted energy transfer over a wide range of input energy levels. The precise identification of local bistability is of significance for predicting and controlling the system performance of vibration energy harvesting and absorption. This paper proposes a new physics-informed sparse identification method for parameter estimation of a three-degree-of-freedom bistable nonlinear energy sink. The restoring force surface is constructed on the local bistable structure, and the nonlinear elastic force trajectory is intercepted by assuming two quasi-zero velocity planes. Furthermore, the candidate functions of the nonlinear elastic force can be physically informed in the sparse identification algorithm. Numerical simulation shows that the proposed method not only gives sparse identification physics information but also improves accuracy by 1.61% under the noise level of 30 dB. Experimental verifications are performed on a three-story beam-type bistable energy sink. The result shows that the identified nonlinear elastic force has a good agreement with the measured one, and the NMSE is only 0.97%.
Constrained Green’s Function for a Beam with Arbitrary Spring and Nonlinear Spring Foundation
Zhao X., Wang Q., Zhu W.D., Li Y.H.
Springer Nature
NODYCON Conference Proceedings Series, 2024, цитирований: 1, doi.org, Abstract
As an important structure of micro-robots, micro-beams play an increasingly important role in daily production and life, especially in the biological and medical fields. During the use of micro-beam instruments, vibrations occur due to the unevenness of the skin, which affect the accuracy and stability of precision instruments. To analyze this problem, this chapter studies the free vibration of beams with spring at arbitrary positions and nonlinear spring foundations. Through the Laplace transform and the principle of linear superposition, the constrained Green’s function is obtained. Numerical calculations are performed to validate the present solutions and the effects of various important physical parameters are investigated. It was found that the mode and deflection of the beams were changed by the springs and foundations.
Design of NARX Model for Dry Friction System of the Three-Piece Bogie
Lyu D., Zhang Q., Hao S.
Springer Nature
NODYCON Conference Proceedings Series, 2022, цитирований: 1, doi.org, Abstract
The discontinuous and non-smooth natures of the dry friction system make it difficult to obtain a universal and accurate friction model for different friction phenomena. In order to reveal the characteristics of the suspension system of a three-piece bogie with dry friction, nonlinear autoregressive with exogenous input (NARX) is studied. Taking the mean squared error (MSE) as the objective function, particle swarm optimization (PSO) algorithm is applied to the datasets for the number of input delays, output delays, and the hidden layer neurons adjustments. An experimental device of the bogie with dry friction structure is designed. The displacement, velocity, and acceleration of the vertical actuator are considered as the input of the system. The output value is the load of force sensor. The experimental results are compared with the predicted results of the NARX and PSO-NARX model. The PSO-NARX model with the present unit of input can predict the dynamic behavior of the system more accurately. It is necessary to optimize the numbers of delay units and the hidden layer neurons in the NARX model, which will improve the accuracy of the network. PSO-NARX can be used as the status monitoring of three-piece bogie with dry friction to improve the safety of the vehicle operation.
A Novel Balancing Method of the Rotor System Using Load Identification and FIR Filter-Based Force Estimation Technique
Zhao S., Ren X., Lu K., Yang Y., Li L., Fu C.
Springer Nature
NODYCON Conference Proceedings Series, 2022, цитирований: 0, doi.org, Abstract
The classical balancing technologies are easily limited by the condition of the rotational speeds and test runs with trail weights. To solve these problems, a novel balancing technology for identifying the unbalance parameters of the rotor system is proposed in this chapter. The Transfer Matrix Method (TMM) is introduced to obtain the dynamical equations of rotor system. Through load identification and FIR filter techniques, the input excitation forces of the rotor system are preliminarily calculated by the load identification technique, while the vibration responses are regarded as output. After that, the ultimate unbalance forces are estimated by FIR filter. The unbalance parameters are identified by analyzing the amplitudes and phases of the calculated excitation forces. The accuracy of the proposed method is demonstrated by numerical simulations of double-disc rotor system. The results obtained prove that the proposed method does not require test runs with trail weights, and the proposed method is suitable for balancing without the limitation of the rotational speed conditions.
Internal Resonances of a Rotating Pre-deformed Blade Under a Harmonic Gas Pressure
Zhang B., Ding H., Chen L.
Springer Nature
NODYCON Conference Proceedings Series, 2022, цитирований: 0, doi.org, Abstract
This study presents the main similarities and differences among a series of resonance responses of a rotating blade under harmonic excitation, considering pre-deformation effects. The possibilities of 10 different types of resonances (such as primary resonances, sub-harmonic resonances, super-harmonic resonances, and even combination resonances) are determined via the theoretical analysis. The response curves and the stability ranges are compared for different types of resonances, respectively. A set of interesting findings are concluded in this study. The quadratic nonlinear terms, which are introduced by the pre-deformation field caused by the thermal gradient, not only introduce the rich phenomena through 2:1 internal resonance but also have dramatic effects on the dynamic response in the case of 3:1 internal resonance. The double jumping and saturation phenomena can be only found in the 2:1 internal resonances. For some of the resonance cases, the frequency response curves or stable regions are quite similar to each other.
Influence of Model Nonlinearities on the Dynamics of Ring-Type Gyroscopes
Gebrel I.F., Wang L., Asokanthan S.F.
Springer Nature
NODYCON Conference Proceedings Series, 2022, цитирований: 0, doi.org, Abstract
This paper investigates the nonlinear dynamic response of a rotating ring that forms an essential element in macro ring-based vibratory gyroscopes that utilize oscillatory nonlinear electromagnetic forces. The derivation of the nonlinear equations that represent the motion of a macro ring gyroscope with nonlinear electromagnetic forces is performed. Understanding the effects of model nonlinearities is considered important for characterizing the dynamic behavior of such devices. Dynamic response analysis in the driving and the sensing directions are investigated via time responses, phase diagram, and Poincare’s map when the angular input rate and the nonlinear electromagnetic forces act together.
Studies on the Liquid Sloshing and Rigid-Liquid-Flexible Coupling Dynamics of Spacecraft
Ma B., Yue B., Tang Y., Yu J.
Springer Nature
NODYCON Conference Proceedings Series, 2022, цитирований: 0, doi.org, Abstract
The numerical model of the rigid-liquid-flexible coupling system of the spacecraft is established, and the flexible appendages are simplified as Euler-Bernoulli beams. The staggered algorithm is adopted to simulate the coupling system, and the liquid module, the rigid body module, and the flexible appendage module are solved by two-step iteration. The coupling model is verified by comparing with previous results. Furthermore, the response of the rigid-liquid-flexible coupling spacecraft under orbital driving forces is studied, and it is found that in the condition of the simulation example, the sloshing of the liquid and the vibration of the flexible appendages influence each other, and there exists complex coupling mechanism between the liquid, the rigid body, and the flexible appendages.
Direct Sensitivity Analysis of Dynamic Responses for Nonlinear Structure
Cao Z., Fei Q., Jiang D., Kapania R.K., Jin H., Zhu R.
Springer Nature
NODYCON Conference Proceedings Series, 2022, цитирований: 0, doi.org, Abstract
The vibration performance of a nonlinear structure can be assessed by analyzing the effects of change in parameters on nonlinear dynamic responses. A direct sensitivity analysis method for nonlinear dynamic responses is proposed in this paper. By directly differentiating the nonlinear equation of motions, the dynamic response and corresponding sensitivity can be synchronously determined using a forward time integration algorithm. The proposed method is applied to perform sensitivity analysis for different nonlinear vibrations of Duffing oscillator and Duffing-type Ueda oscillator. The accuracy of the proposed method is verified by other numerical approaches. Results show that the proposed method, which avoids the errors caused by the secular term in the computation of long-term responses, can be successfully applied to the sensitivity computation of periodic and quasi-periodic vibrations. The dynamic sensitivity of the quasi-periodic response remains bounded and settles into a regular region. When the structure vibrates in a chaotic region, the proposed method gives a more consistent solution than that obtained by the finite difference method.
Dynamics of the Fluid-Structure Coupling Model of a Direct-Acting Relief Valve
Song W., Liao M., Xin Y., Wang X., Fan K., Li Y.
Springer Nature
NODYCON Conference Proceedings Series, 2022, цитирований: 0, doi.org, Abstract
To explain the sudden jump of pressure for a direct-acting relief valve used by torpedo pump as the variation of water depth, a 2-DOF fluid-structure coupling dynamic model is developed. A nonlinear differential pressure model at valve port is applied to model the axial vibration of fluid, and a nonlinear wake oscillator model is used to excite the valve element in the vertical direction; meanwhile, the contact nonlinearity between the valve element and valve seat is also taken into consideration. Based on the developed dynamical model, the water depths for the sudden jumps of pressure can be located precisely when compared with the experimental signals, and the corresponding vibration conditions of the valve element in both the axial and vertical directions are explored. Subsequently, in order to eliminate the sudden jumps of pressure, the result of numerical simulation suggests to decrease the pump inlet pressure from 0.8 MPa to 0.4 MPa, which is verified to be effective by the corresponding experimental test, and thus the proposed dynamical model is further verified.
Vibration Analysis of a Multi-DOF Impact Oscillator with Multiple Motion Constraints
Dai W., Yang J.
Springer Nature
NODYCON Conference Proceedings Series, 2022, цитирований: 0, doi.org, Abstract
This paper investigates the nonlinear dynamic behaviour of a multiple-degree-of-freedom (MDOF) impact oscillator system with multiple constraints. The system model comprises a linear 3DOF chain oscillator and three extra springs as linear constraints for oscillating masses. The steady-state responses of the system subjected to a harmonic excitation force are obtained by the harmonic balance method and a time-marching method. The effects of the spring stiffness of the linear constraints on the dynamic responses of the masses are studied. The results show that the linear constraints can have nonlinear hardening effect on the frequency responses of the system. It can lead to multiple solutions at a specific excitation frequency and bifurcations near the resonance frequencies of different vibration modes. Moreover, super-harmonic responses are observed when the excitation frequency is near the first mode of the system, and an extra resonance peak may be obtained near the corresponding frequency of the second vibration mode. It is also shown that an increase in the spring stiffness of the constraints can bend the response resonance peaks more to the high-frequency range. These findings provide a more comprehensive understanding of the influence of linear constraints on the dynamic vibration behaviour of the impact oscillator system and hence benefit better designs with improved dynamic characteristics.
Axisymmetric Nonlinear Free Vibration of a Conductive Annular Plate Under Toroidal Magnetic Field
Haoran X., Yuda H.
Springer Nature
NODYCON Conference Proceedings Series, 2022, цитирований: 0, doi.org, Abstract
The magnetoelastic nonlinear free vibration of a conductive thin annular plate in non-uniform magnetic field generated by the long straight current-carrying wire is presented. Based on electromagnetic theory, expressions of the non-uniform magnetic field and electromagnetic force are derived. According to the Hamilton principle, magnetoelastic nonlinear vibration equation of plate is derived. The Galerkin integral method is used to derive axisymmetric vibration differential equation. By method of multiple scales, natural frequency is then obtained. In numerical calculation, the nonlinear natural vibration characteristic curves show influence of different control parameters, e.g., current intensity, and plate size on natural frequency and electromagnetic force. Results show that natural frequency decreases first and then stabilizes with current, increases significantly with plate internal radius and thickness. The plate under boundary condition of internal radius simply supported and outer radius clamped exhibits hard characteristics. Magnetic induction intensity and electromagnetic force shows different changing rules along radial direction.
Nonlinear Dynamics Analysis of Electric Energy Regeneration Device Based on Vibration Energy Recovery
Wang W., Li Y., Wu K., Cui Y., Song Y.
Springer Nature
NODYCON Conference Proceedings Series, 2022, цитирований: 1, doi.org, Abstract
An electric energy regeneration device using two one-way clutches is proposed to extend the range of electric vehicles. Under the influence of nonlinear factors, the system will be unstable. To solve this problem, considering the time-varying meshing stiffness, meshing damping, backlash and transmission error, and the reserve clearance of the one-way clutch, a multiple-DOF nonlinear dynamic model is established. The Runge-Kutta method is used to calculate the nonlinear differential equation. The response chart, kinematic phase diagram, Poincare map, and bifurcation diagram are used to analyze the influence of excitation frequency, reserve clearance, and transmission error. The results show that as the meshing frequency changes, the system response changes from period-doubling bifurcation to chaotic motion. In addition, the influence law of parameters on the damping characteristics of the device is revealed.
Galloping Piezoelectric Energy Harvester for Low Wind Speed
Zhao K., Zhang Q., Hao S.
Springer Nature
NODYCON Conference Proceedings Series, 2022, цитирований: 0, doi.org, Abstract
Aiming at the natural environment with low wind velocity, galloping piezoelectric energy harvester (GPEH) is comprehensively optimized in three aspects. First, based on the fluid-solid coupling theory, the square cylinder in the GPEH is modified to improve the conversion of fluid energy into mechanical energy efficiency and reduce the galloping critical velocity of the energy harvester. Second, piezoelectric cantilever beam with variable cross section is established, and the analytical solution is obtained by piecewise Galerkin method, and the beam geometry is optimized by particle swarm optimization method. Third, considering the various connections between the resistors, capacitors, and inductors, the circuit of the energy harvester is optimized. Finite element simulation method established a multi-physics coupling model for the GPEH. The results show that at the uniform wind velocity with the same flow velocity, the output energy of the improved GPEH is significantly improved, and the galloping critical velocity of the system vibration is effectively reduced.
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