Nonlinear Dynamic Performance Research Articles

Design on Hybrid Test System for Dynamic Performance of Viscoelastic Damping Material and Damper

The viscoelastic material is one of most popular shock absorbing materials for mitigating vibrations of building structures due to earthquake. Its dynamic performance is affected by the temperature, the excitation frequency and the excitation amplitude. Therefore, in order to study the nonlinear dynamic performance of the viscoelastic materials, a hybrid test system using the electric exciter is proposed, in which the electric exciter is the actuator, MATLAB is used for the simulation of the numerical substructure and the communication between the upper computer and the lower machine, and STM32 single-chip microcomputer is used to control the work state of the electric exciter. Based on the equivalent force control method and the incremental PID control algorithm, a controller is designed to make sure the electric exciter produces accurate control forces to the nonlinear test component in the physical substructure. It can be shown from the test results that the developed whole hybrid test system is feasible and effective.

Nonlinear dynamic performance of tilting-pad journal bearing with adjustable elastic pivot design

Abstract To improve the security and reliability of a traditional rigid-pivot tilting-pad journal bearing (RPTPJB), a kind of elastic-pivot tilting-pad journal bearing (EPTPJB), which is an adjustable-pivot TPJB that can realize self-adaptive preload factors, is proposed for vertical rotors. The nonlinear movement performance and film load performance of a water-lubricated four-pad EPTPJB are investigated by journal displacements, journal center orbits, minimum film thicknesses, tilting angles and radial displacements of pads using an analytical turbulent hydrodynamic model. The results show a safer film thickness of an EPTPJB and reveal the dynamic performance adjustment mechanism adjusted by pivot stiffness, pre-tightening force and preload factors. This study contributes to the reduction of impact and rubbing between the journal and the pads.

Multi-state data-driven gas path analysis method

Abstract Data-driven gas path analysis is a current research topic for energy fields for it can provide continuous monitoring to ensure safe and reliable operation of energy systems like gas turbine engines, wind turbines and distributed energy systems. The method utilizes information delivered by sensors to track equipment performance degradation during operation. In recent years, the rapid development of novel energy technologies promotes the progress of the method, but it also brings challenges. Energy systems are now becoming more and more complicated with strong nonlinear performance, highly coupled components and complex control laws. At present, an effective and universal diagnostic method to deal with energy systems with highly nonlinear dynamic performance has not been found. In this paper, a method called multi-state gas path analysis method is put forward to address the problem. The core idea of the method is to create sub-models to extend data available for modelling and diagnosing. The method integrates topological data analysis and transfer learning to construct a sub-model diagnostic network for nonlinear modelling. It allows designers to deal with highly nonlinear dynamic systems while preventing prohibitive computation effort. The method has been applied to an engine platform and verified. It achieves the same 92% diagnostic accuracy with only half data acquisition cost compared to a traditional data-driven gas path analysis method.

Optimization on Nonlinear Dynamics of Gear Rattle in Automotive Transmission System

Recently, gear rattle noise is gradually becoming a nonignorable issue involving comfortableness in automotive transmission for a car. Generally, the rattle noise is influenced by nonlinear dynamic of multiple pairs of idler gears in the multistage gear transmission system. Optimization methods based on nonlinear rattle dynamic analysis are worthy of further study to control the noise. In this research, an equivalent rattle dynamic model of the idler gear is proposed, and the nonlinear rattle dynamic responses are solved based on the integral method. The effect laws of key factors on nonlinear dynamic performance are investigated by using a bifurcation diagram, spectrum map, and Poincaré map. Finally, the gear backlash, equivalent mass, and rotational speed are optimized based on Kriging surrogate model (KSM) and differential evolution (DE) algorithm by taking the minimization of the maximum rattle noise as the optimal object. It can be concluded that the rattle dynamics of the idler gear show rich nonlinear characteristics as the parameters change. The proposed method can not only reduce the sound pressure level of rattle noise but also provide a viable path and reference value for the low‐noise design of the gear transmission system.

Nonlinear Dynamic Performance and Safety Assessment of Guardrail Structrues for Roadside Considering a Simplified Tangent Modulus

Nonlinear Dynamic Performance and Safety Assessment of Guardrail Structrues for Roadside Considering a Simplified Tangent Modulus

Chaotic characteristic analysis of spatial parallel mechanism with clearance in spherical joint

The spherical joint is one of the main motion pairs in spatial parallel mechanism, and the spherical clearance has a great effect on the nonlinear dynamic performance of parallel mechanism. Most previous studies mainly focused on planar mechanism with revolute joint, spatial parallel mechanism with spherical clearance researched rarely. In this paper, the chaotic characteristic analysis of spatial 4-UPS (universal joint-prismatic pair-spherical joint)-RPU (revolute joint-prismatic pair-universal joint) parallel mechanism with spherical clearance is investigated. The models of spherical joint with clearance are established, and then the nonlinear dynamics equation of the parallel mechanism with spherical clearance is derived by Lagrange method. The influence of clearance on displacement, velocity and acceleration of moving platform is both analyzed. And the influence of different clearance sizes on contact force and center trajectory of the spherical clearance is analyzed, and the chaotic characteristics of spherical joint and the mechanism are all studied by phase diagram, Poincare section mapping method and Lyapunov exponent. The results show that spherical clearance has great influence on the nonlinear dynamic performance of 4-UPS-RPU parallel mechanism, and chaos exists in the dynamic response of spherical clearance and the mechanism. As the clearance value increases, the stability of the mechanism is weakened. When the clearance value increases to 2.1 mm, chaotic motion appeared on the moving platform of the mechanism. This research is a useful attempt to study the nonlinear dynamics characteristic of parallel mechanisms with spherical clearance, which has guiding significance and practical value for further research on the design and chaotic control of parallel mechanism.

Effects of Surface Waviness on the Nonlinear Vibration of Gas Lubricated Bearing‐Rotor System

This paper presents the effects of the surface waviness on the nonlinear dynamic performance of a gas bearing‐rotor system. The coupled vibration with the elastomer is taken into consideration to fit the actual engineering application. The effects of the directions, the amplitudes, and the numbers of waves to the nonlinear dynamic performance are investigated. The results show that the existence of the surface waviness in the circumferential direction can improve the stability of the system obviously. But the surface waviness in the axial direction is damage to the system. The nonlinear dynamic performance of the system is insensitive to the number of surface waviness. The increase of the amplitude of the waviness in circumferential direction can improve the stability of the system.

A comprehensive study of 2:1 internal-resonance-based piezoelectric vibration energy harvesting

This work exploits a 2:1 internal resonance mechanism to enhance broadband vibration energy harvesting. It is achieved by adding a properly tuned auxiliary oscillator to the primary energy harvesting oscillator coupled by a nonlinear magnetic force. A theoretical study is conducted on the nonlinear dynamic and energy harvesting performance of the proposed harvester by various analytical approximations, and the accuracy of these analytical models is investigated. Given harmonic base excitation, the output voltage frequency response is derived by the multi-scale method and harmonic balance method (HBM), which are then verified by equivalent circuit simulations and experiments. The necessity of taking into account the zeroth-order harmonic component in the HBM is verified and discussed. The HBM result without this component and the multi-scale method fail to accurately predict the nonlinear dynamic behaviour. With the validated HBM model and the equivalent circuit model, key features of internal resonance are revealed by investigating modal interaction and saturation phenomena under varying excitation. By and large, the operational bandwidth of the vibration energy harvester is enlarged due to the 2:1 internal resonance.

Stability performance for primary frequency regulation of hydro-turbine governing system with surge tank

• A novel nonlinear mathematical model of hydro-turbine governing system with surge tank is introduced. • Nonlinear dynamic performance of system under opening control mode and power control mode is investigated. • New feature of nonlinear hydro-turbine governing system is described by comparing with a linear model. • Effect mechanism of nonlinear characteristic of penstock head loss is revealed. • Critical stable sectional area of surge tank for primary frequency regulation is proposed and derived. This paper aims to study the stability for primary frequency regulation of hydro-turbine governing system with surge tank. Firstly, a novel nonlinear mathematical model of hydro-turbine governing system considering the nonlinear characteristic of penstock head loss is introduced. The nonlinear state equations under opening control mode and power control mode are derived. Then, the nonlinear dynamic performance of nonlinear hydro-turbine governing system is investigated based on the stable domain for primary frequency regulation. New feature of the nonlinear hydro-turbine governing system caused by the nonlinear characteristic of penstock head loss is described by comparing with a linear model, and the effect mechanism of nonlinear characteristic of penstock head loss is revealed. Finally, the concept of critical stable sectional area of surge tank for primary frequency regulation is proposed and the analytical solution is derived. The combined tuning and optimization method of governor parameters and sectional area of surge tank is proposed. The results indicate that for the primary frequency regulation under opening control mode and power control mode, the nonlinear hydro-turbine governing system is absolutely stable and conditionally stable, respectively. The stability of the nonlinear hydro-turbine governing system and linear hydro-turbine governing system is the same under opening control model and different under power control model. The nonlinear characteristic of penstock head loss mainly affects the initial stage of dynamic response process of power output, and then changes the stability of the nonlinear system. The critical stable sectional area of surge tank makes the system reach critical stable state. The governor parameters and critical stable sectional area of surge tank jointly determine the distributions of stability states.

Nonlinear dynamic modeling and performance analysis of a redundantly actuated parallel manipulator with multiple actuation modes based on FMD theory

A novel redundantly actuated parallel manipulator (PM) with multiple actuation modes was developed recently by the author. In this paper, the further research is implemented and a systematic methodology is proposed to develop the rigid–flexible coupling dynamic model (RFDM) of the novel PM based on the flexible multi-body dynamics theory. Firstly, under the floating frame of reference, an arbitrary flexible link of the novel PM is regarded as an Euler–Bernoulli beam and the finite element approach is employed to discretize the flexible beam. Then, one kind of planar beam element with lumped masses and moments of inertia at both ends is presented and a corresponding dynamic model is deduced based on the Lagrangian formulation. On this basis, the RFDM of system is formulated by virtue of the augmented Lagrangian multipliers approach. Given the stiff characteristic of system dynamic model, the hybrid TR-BDF2 numerical algorithm combined with Baumgarte stabilization approach is employed to address the nonlinear RFDM so as to balance the solution efficiency and precision. Based on the RFDM and its degradation model, i.e., the rigid dynamic model, one dynamic simulation experiment is designed to investigate the dynamic performance of the PM. Numerical results indicate that the practical motion of the PM manifests rigid–flexible coupling characteristic, and the redundant actuation modes can attenuate the effect of link flexibility and improve the trajectory tracking precision of end-effector in comparison with the non-redundant actuation modes. Finally, to validate the presented methodology, the obtained numerical results are compared with a virtual prototype model developed based on SimMechanics. The results will be helpful for structure optimization and efficient controller design of the PM with multiple actuation modes.

Investigations of nonlinear dynamic performance of top-and-seat with web angle connections subjected to sudden column removal

It is well known that progressive collapse is a complicated dynamic process with geometry and material nonlinearities. Sudden column removal scenario is a simple yet effective method for analysis and design of structures to mitigate progressive collapse. The main objective of this study is to investigate the dynamic performance of top-and-seat with web angle (TSWA) steel beam–column connections under progressive collapse condition. This type of connection represents typical bolted cleat connections with excellent ductility. Each specimen consisted of two adjoining beams pinned at the far ends and connected to a middle column stub. Five dynamic tests for the TSWA connections subjected to sudden removal of the middle columns were conducted in Nanyang Technological University. Another five corresponding static tests were also carried out for comparison with the dynamic behaviour. Test results showed that the release-time durations of the column support force were around 30ms for all the five dynamic tests. Transient dynamic responses with free vibrations were observed for the connections following instantaneous removal of the middle columns. The maximum dynamic displacement was significantly increased compared to the static connection response. In addition, numerical simulations were also conducted using the general-purpose finite element software ABAQUS. The three-dimensional finite element model was validated by comparing the simulation results against the test data. Parametric studies were carried out to investigate the full dynamic connection performance and its structural resistance under push-down analysis to simulate progressive collapse. By comparing the full dynamic response with its corresponding quasi-static response, both the displacement-based dynamic increase factor (DIF) and force-based DIF were investigated, respectively. The paper ends with some discussions on practical applications of displacement-based DIF and force-based DIF.

Bifurcation and chaos analysis of a nonlinear electromechanical coupling transmission system driven by AC asynchronous motor

Considering the torsional vibration in transmission system driven by AC asynchronous motor, this paper proposes a dynamical model of nonlinear electromechanical coupling system by using the energy method. The effect of electromagnetic factors on nonlinear dynamic performance of the electromechanical coupling system is investigated. Firstly, the static bifurcation characteristic under the non-autonomous condition is studied based on the singularity theory of nonlinear system. Secondly, the Hopf bifurcation point and the direction of bifurcation are determined based on the Hopf bifurcation theory. Finally, the bifurcation diagram, Poincare map and the largest Lyapunov exponent are given, which show the influence of electromagnetic stiffness and electromagnetic damping on the chaotic motions of the system.

Nonlinear dynamic performance of long-span cable-stayed bridge under traffic and wind

Long-span cable-stayed bridges exhibit some features which are more critical than typical long span bridges such as geometric and aerodynamic nonlinearities, higher probability of the presence of multiple vehicles on the bridge, and more significant influence of wind loads acting on the ultra high pylon and super long cables. A three-dimensional nonlinear fully-coupled analytical model is developed in this study to improve the dynamic performance prediction of long cable-stayed bridges under combined traffic and wind loads. The modified spectral representation method is introduced to simulate the fluctuating wind field of all the components of the whole bridge simultaneously with high accuracy and efficiency. Then, the aerostatic and aerodynamic wind forces acting on the whole bridge including the bridge deck, pylon, cables and even piers are all derived. The cellular automation method is applied to simulate the stochastic traffic flow which can reflect the real traffic properties on the long span bridge such as lane changing, acceleration, or deceleration. The dynamic interaction between vehicles and the bridge depends on both the geometrical and mechanical relationships between the wheels of vehicles and the contact points on the bridge deck. Nonlinear properties such as geometric nonlinearity and aerodynamic nonlinearity are fully considered. The equations of motion of the coupled wind-traffic-bridge system are derived and solved with a nonlinear separate iteration method which can considerably improve the calculation efficiency. A long cable-stayed bridge, Sutong Bridge across the Yangze River in China, is selected as a numerical example to demonstrate the dynamic interaction of the coupled system. The influences of the whole bridge wind field as well as the geometric and aerodynamic nonlinearities on the responses of the wind-traffic-bridge system are discussed.

Numerical techniques for computing nonlinear dynamic characteristic of rotor-seal system

A transient CFD procedure to compute the nonlinear dynamic characteristic of the coupled rotor-seal system was presented in this study. In each time step, the displacement diffusion model was implemented to govern the mesh deformation, and the URANS (Unsteady Reynolds averaged Navier-Stokes) equations were solved to obtain the transient fluid force on the rotor surface for the free vibrations. With the obtained fluid force from the CFD solver, the nonlinear equations of motion for a simplified rotor-seal system were numerically solved on the basis of external user defined routines. During each transient time step, the computed fluid force from the CFD solver and the rotor motion from the user defined routines were transferred to each other timely. The rotor center trajectories, frequency spectrum and projection of Poincare section were calculated to investigate the nonlinear dynamic performance of the single disk rotor-seal system. The effects of the rotational speed and pressure ratio on the vibration characteristic of the rotor-seal system were analyzed by the bifurcation theorem. The results show that the coupled rotor-seal system experiences a period-one motion, resonance, periodic-doubling motion, quasi-periodic motion, and finally possible chaotic motion as the rotor speed increases. The pressure ratio has pronounced effect on the frequency response of the first-order critical speed; however, it has little influence on the motion state as well as the frequency response of the rotating speed. Although a constant-clearance annular smooth stator seal was selected as the research object in the current paper, the presented transient CFD method is still available for other complex annular seals, such as labyrinth seal, honeycomb seal, pocket damper seal, etc.

A new nonlinear dynamic analysis method of rotor system supported by oil-film journal bearings

The strong nonlinear behavior usually exists in rotor systems supported by oil-film journal bearings. In this paper, the partial derivative method is extended to the second-order approximate extent to predict the nonlinear dynamic stiffness and damping coefficients of finite-long journal bearings. And the nonlinear oil-film forces approximately represented by dynamic coefficients are used to analyze nonlinear dynamic performance of a symmetrical flexible rotor-bearing system via the journal orbit, phase portrait and Poincaré map. The effects of mass eccentricity on dynamic behaviors of rotor system are mainly investigated. Moreover, the computational method of nonlinear dynamic coefficients of infinite-short bearing is presented. The nonlinear oil-film forces model of finite-long bearing is validated by comparing the numerical results with those obtained by an infinite-short bearing-rotor system model. The results show that the representation method of nonlinear oil-film forces by dynamic coefficients has universal applicability and allows one easily to conduct the nonlinear dynamic analysis of rotor systems.

Collective Behavior of a Ring of Van Der Pol Oscillators under Gaussian and Random Coupling Schemes

The collective behavior of a ring of coupled identical van der Pol oscillators is numerically studied in this work. Constant, gaussian and random distributions of the coupling parameter along the ring are considered. Three values of the oscillators constant are assumed in order to cover from quasilinear to nonlinear dynamic performance. Single and multiple coupled frequencies are obtained using power spectra of the long term time series. Phase portraits are obtained from numerical simulations, and the coupled behavior is analyzed, compared and discussed.

Modified PI speed controllers for series-excited dc motors fed by dc/dc boost converters

In drive systems, especially for speed regulation, the use of a series-excited dc-motor is prefered in cases where large load changes may occur. In order to design a controller that achieves a fast torque response, in this paper, a complete system consisting of a dc/dc boost converter and a series-excited dc-motor is considered. For the complete system, a modified nonlinear PI speed controller is proposed that provides directly the duty-ratio input of the converter without needing the conventional current inner-loop. In particular, the constant PI speed controller gains are multiplied by a suitable time function that substantially upgrades the whole nonlinear system dynamic performance. Taking into account the complete nonlinear system model, it is shown that the proposed controller acts on the duty-ratio input of the converter providing a continuous input signal exactly in the permitted range [0,1), achieves precise motor speed regulation independently from system parameters' variations or load torque changes and guarantees closed-loop system stability and convergence to the desired steady-state equilibrium. Finally, the proposed PI controller performance is verified through extended simulation and experimental results under rapid changes of the reference signal and the external load.

Optimal maneuver-based motion planning over terrain and threats using a dynamic hybrid PSO algorithm

Motion planning is a key factor in enhancing the autonomy level of unmanned flying vehicles. A new dynamic hybrid algorithm is developed to solve the motion planning problem in real-time using a heuristic optimization approach. The proposed algorithm effectively combines desired features such as rapid convergence to an optimal path with reduced computational effort. In addition to the terrain obstacles, the proposed algorithm is able to avoid random threats that may arise sporadically in the terrain. Using the maneuver automaton concept, nonlinear dynamic model and performance constraints are also considered in the process of motion planning to further ensure feasible trajectories. Evaluation of the proposed algorithm against several simulated scenarios has effectively demonstrated its potential for generating optimal contour-matching trajectories that succeed in avoiding stochastic obstacles.

Integrated motion planning and trajectory control system for unmanned air vehicles

Motion planning and trajectory control are two basic challenges of unmanned vehicles. In motion planning problem, feasible trajectories are developed while nonlinear dynamic model and performance constraints of the vehicle under utility are considered. In this study, motion planning is performed via an enhanced particle swarm optimization algorithm. The resulting offline generated trajectories are tracked using a nonlinear trajectory control system methodology. The Lyapunov-based constrained backstepping approach and command filters are utilized in designing the trajectory control system. Command filters smoothen the input signals and provide their derivatives. Evaluation of the proposed integrated approach in several simulated scenarios has effectively demonstrated the potential of both algorithms in generating optimal contour matching trajectories as well as excellent tracking capability of the trajectory control system.

Condition-Dependent Maintenance Effectiveness in Dynamic Performance Models for Transportation Infrastructure

Dynamic performance models that combine performance prediction and maintenance effectiveness are required for state-of-the-art optimization techniques such as optimal control. Because records of maintenance effectiveness depend on facility condition, nonlinear models are necessary to include interactions between variables to account for this dependence and estimate condition-dependent maintenance effectiveness. Therefore, this paper proposes a procedure for estimating nonlinear dynamic performance models that capture interactions between variables using panel data. The relationships between maintenance effectiveness and current facility condition and between structural design and traffic impact were found to be polynomial in a numerical example of highway pavements. It was also demonstrated that imposing physical constraints on the maintenance effectiveness based on external data sources generated more reasonable models when self-selected samples were used for estimation.