The dynamics and power flow behaviour of a nonlinear vibration isolation system with a negative stiffness mechanism (NSM) are studied. The mathematical equations governing the nonlinear dynamics of ...the system are derived. The averaging method is used to obtain the frequency response function of the system subject to harmonic excitations. It is found that adding NSM can greatly enlarge the frequency band for effective vibration isolation. Numerical simulations reveal that sub-harmonic resonance may occur even when the excitation frequency is well above the natural frequency of the linearized system. As the effects of sub-harmonic response cannot be reflected by the averaging formulations, numerical integrations are used to obtain the dynamic responses including sub-harmonic and other frequency components. Furthermore, power flow characteristics of this nonlinear isolation system are examined for a better assessment of the isolation performance. The results show that the occurrences of sub-harmonic resonance may considerably increase both the time-averaged input power and the maximum kinetic energy. Compared with linear systems, the power flows of the nonlinear system might be non-unique and sensitive to the initial conditions. Some suggestions on restricting the maximum deflection and suppressing sub-harmonic resonances are provided for effective designs of nonlinear isolation systems.
► A nonlinear isolation system with a negative stiffness mechanism (NSM) is studied. ► Adding NSM extends greatly the frequency range for effective vibration isolation. ► Effects of amplitude/frequency/initial condition/a on power flow are analysed. ► Isolation performance assessed using power flow is better than transmissibility. ► How to suppress sub-harmonic resonances in NSM isolation system is discussed.
This paper proposes a new theoretical method to investigate the thermal behaviors of the inter-shaft bearing considering the nonlinear dynamic characteristics of a dual-rotor system by combining heat ...transfer and nonlinear dynamics. The nonlinearities of the inter-shaft bearing, including the Hertzian contact and the radial clearance, are considered during the dynamic modeling for the system. The dynamic load of the inter-shaft bearing is defined according to the nonlinear dynamic responses of the system. Therefore, some fundamental nonlinear phenomena, i.e., jump and bi-stable phenomena happen to the dynamic load. It makes the dynamic load more appropriate to describe the actual load of the inter-shaft bearing than the static load. Furthermore, a steady-state heat transfer model for the inter-shaft bearing subjected to the dynamic load can be set up with the help of Palmgren’s empirical formula. The variation of temperatures with the rotation speed is obtained by using the Gauss–Seidel iteration. Temperatures of the inter-shaft bearing also show nonlinear thermal behaviors, i.e., jump and bi-stable phenomena. It implies the nonlinear dynamic behaviors of the system have a great impact on the thermal behaviors of the inter-shaft bearing. Moreover, an exhaustive parametric analysis for temperatures and nonlinear thermal behaviors of the inter-shaft bearing affected by dynamic parameters (including the rotation speed ratio, unbalances of rotors, the radial clearance, the stiffness and the roller number of the inter-shaft bearing) and thermal parameters (including the lubricant viscosity and the ambient temperature) is carried out. The results show that the rotation speed ratio has a significant influence on both temperatures and nonlinear thermal behaviors, other dynamic parameters mainly affect nonlinear thermal behaviors, while thermal parameters only affect temperatures. This unique discovery indicates the thermal behaviors of the inter-shaft bearing could be much more complex because of the nonlinear dynamic characteristics of the dual-rotor system. The obtained results will contribute to a better understanding of the nonlinear thermal behaviors of bearings and profoundly reveal the mechanism of the nonlinear thermal behaviors of bearings.
This paper develops a robust iterated extended Kalman filter (EKF) based on the generalized maximum likelihood approach (termed GM-IEKF) for estimating power system state dynamics when subjected to ...disturbances. The proposed GM-IEKF dynamic state estimator is able to track system transients in a faster and more reliable way than the conventional EKF and the unscented Kalman filter (UKF) thanks to its batch-mode regression form and its robustness to innovation and observation outliers, even in position of leverage. Innovation outliers may be caused by impulsive noise in the dynamic state model while observation outliers may be due to large biases, cyber attacks, or temporary loss of communication links of PMUs. Good robustness and high statistical efficiency under Gaussian noise are achieved via the minimization of the Huber convex cost function of the standardized residuals. The latter is weighted via a function of robust distances of the two-time sequence of the predicted state and innovation vectors and calculated by means of the projection statistics. The state estimation error covariance matrix is derived using the total influence function, resulting in a robust state prediction in the next time step. Simulation results carried out on the IEEE 39-bus test system demonstrate the good performance of the GM-IEKF under Gaussian and non-Gaussian process and observation noise.
This paper presents a framework to investigate the dynamics of overall vehicle-track systems with emphasis on theoretical modelling, numerical simulation and experimental validation. A ...three-dimensional vehicle-track coupled dynamics model is developed in which a typical railway passenger vehicle is modelled as a 35-degree-of-freedom multi-body system. A traditional ballasted track is modelled as two parallel continuous beams supported by a discrete-elastic foundation of three layers with sleepers and ballasts included. The non-ballasted slab track is modelled as two parallel continuous beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The vehicle subsystem and the track subsystem are coupled through a wheel-rail spatial coupling model that considers rail vibrations in vertical, lateral and torsional directions. Random track irregularities expressed by track spectra are considered as system excitations by means of a time-frequency transformation technique. A fast explicit integration method is applied to solve the large nonlinear equations of motion of the system in the time domain. A computer program named TTISIM is developed to predict the vertical and lateral dynamic responses of the vehicle-track coupled system. The theoretical model is validated by full-scale field experiments, including the speed-up test on the Beijing-Qinhuangdao line and the high-speed running test on the Qinhuangdao-Shenyang line. Differences in the dynamic responses analysed by the vehicle-track coupled dynamics and by the classical vehicle dynamics are ascertained in the case of vehicles passing through curved tracks.
The field of eco‐evolutionary dynamics is developing rapidly, with a growing number of well‐designed experiments quantifying the impact of evolution on ecological processes and patterns, ranging from ...population demography to community composition and ecosystem functioning. The key challenge remains to transfer the insights of these proof‐of‐principle experiments to natural settings, where multiple species interact and the dynamics are far more complex than those studied in most experiments.
Here, we discuss potential pitfalls of building a framework on eco‐evolutionary dynamics that is based on data on single species studied in isolation from interspecific interactions, which can lead to both under‐ and overestimation of the impact of evolution on ecological processes. Underestimation of evolution‐driven ecological changes could occur in a single‐species approach when the focal species is involved in co‐evolutionary dynamics, whereas overestimation might occur due to increased rates of evolution following ecological release of the focal species.
In order to develop a multi‐species perspective on eco‐evolutionary dynamics, we discuss the need for a broad‐sense definition of “eco‐evolutionary feedbacks” that includes any reciprocal interaction between ecological and evolutionary processes, next to a narrow‐sense definition that refers to interactions that directly feed back on the interactor that evolves.
We discuss the challenges and opportunities of using more natural settings in eco‐evolutionary studies by gradually adding complexity: (a) multiple interacting species within a guild, (b) food web interactions and (c) evolving metacommunities in multiple habitat patches in a landscape. A literature survey indicated that only a few studies on microbial systems so far developed a truly multi‐species approach in their analysis of eco‐evolutionary dynamics, and mostly so in artificially constructed communities.
Finally, we provide a road map of methods to study eco‐evolutionary dynamics in more natural settings. Eco‐evolutionary studies involving multiple species are necessarily demanding and might require intensive collaboration among research teams, but are highly needed.
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This book provides an introduction to discrete dynamical systems -- a framework of analysis commonly used in the fields of biology, demography, ecology, economics, engineering, finance, and physics. ...The book characterizes the fundamental factors that govern the qualitative and quantitative trajectories of a variety of deterministic, discrete dynamical systems, providing solution methods for systems that can be solved analytically and methods of qualitative analysis for systems that do not permit or necessitate an explicit solution. The analysis focuses initially on the characterization of the factors the govern the evolution of state variables in the elementary context of one-dimensional, first-order, linear, autonomous systems. The fundamental insights about the forces that affect the evolution of these elementary systems are subsequently generalized, and the determinants of the trajectory of multi-dimensional, nonlinear, higher-order, non-autonomous dynamical systems are established.
Understanding the behaviour of particles suspended in a fluid has many important applications across a range of fields, including engineering and geophysics. Comprising two main parts, this book ...begins with the well-developed theory of particles in viscous fluids, i.e. microhydrodynamics, particularly for single- and pair-body dynamics. Part II considers many-body dynamics, covering shear flows and sedimentation, bulk flow properties and collective phenomena. An interlude between the two parts provides the basic statistical techniques needed to employ the results of the first (microscopic) in the second (macroscopic). The authors introduce theoretical, mathematical concepts through concrete examples, making the material accessible to non-mathematicians. They also include some of the many open questions in the field to encourage further study. Consequently, this is an ideal introduction for students and researchers from other disciplines who are approaching suspension dynamics for the first time.
A unique adaptive neural network control scheme is proposed for active suspension systems by employing bioinspired nonlinear dynamics, so as to address several critical engineering issues including ...energy efficiency, input delay, and unknown/uncertain dynamics simultaneously. A novel constructive predictor is firstly designed to solve the effect of input delay. Neural networks are then adopted to approximate the uncertain/unknown dynamics, and importantly, a unique finite-time adaptive control is established which can not only online update the input and output weights of the neural networks, but also intentionally introduce beneficial nonlinear dynamics to vibration control. The significant difference from most existing controllers lies in that, the designed controller effectively utilizes beneficial nonlinear stiffness and damping characteristics of a novel bioinspired reference model, and this leads to superior vibration suppression with significant energy-saving performance consequently. Theoretical analysis and experimental results vindicate that the proposed controller can effectively suppress vibration with much more improved control performance and fairly reduced control energy consumption. This should be for the first time to reveal both in theory and experiments that a superior suspension performance is achieved with simultaneously more than 44% control energy saving, by employing beneficial bioinspired nonlinear dynamics, compared to most traditional control methods.
A general methodology for dynamic modeling and analysis of multibody systems with multiple clearance joints is presented and discussed in this paper. The joint components that constitute a real joint ...are modeled as colliding bodies, being their behavior influenced by geometric and physical properties of the contacting surfaces. A continuous contact force model, based on the elastic Hertz theory together with a dissipative term, is used to evaluate the intrajoint contact forces. Furthermore, the incorporation of the friction phenomenon, based on the classical Coulomb’s friction law, is also discussed. The suitable contact-impact force models are embedded into the dynamics of multibody systems methodologies. An elementary mechanical system is used to demonstrate the accuracy and efficiency of the presented approach, and to discuss the main assumptions and procedures adopted. Different test scenarios are considered with the purpose of performing a parametric study for quantifying the influence of the clearance size, input crank speed, and number of clearance joints on the dynamic response of multibody systems with multiple clearance joints. Additionally, the total computation time consumed in each simulation is evaluated in order to test the computational accuracy and efficiency of the presented approach. From the main results obtained in this study, it can be drawn that clearance size and the operating conditions play a crucial role in predicting accurately the dynamic responses of multibody systems.
The intramolecular vibrational redistribution (IVR) dynamics following the excitation of a mode in the first electronically excited states of toluene, toluene-d sub(3) and p-fluorotoluene that has ...predominantly C-CH sub(3) stretching character and an internal energy of similar to 1200 cm super(-1) have been compared using picosecond time-resolved photoelectron imaging spectroscopy as a probe. Temporal changes in the intensities of spectral features in each molecule have enabled IVR lifetimes of 12, 15 and 50 ps, respectively, to be determined. Our measurements show that doorway states are critical in mediating the IVR dynamics in toluene and toluene-d sub(3), and we deduce that these doorway states, which are assigned in the course of this work, are also instrumental in reducing the IVR lifetimes of these molecules relative to p-fluorotoluene.
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