This monograph presents the most recent progress in bifurcation theory of impulsive dynamical systems with time delays and other functional dependence. It covers not only smooth local bifurcations, but also some non-smooth bifurcation phenomena that are unique to impulsive dynamical systems. The monograph is split into four distinct parts, independently addressing both finite and infinite-dimensional dynamical systems before discussing their applications. The primary contributions are a rigorous nonautonomous dynamical systems framework and analysis of nonlinear systems, stability, and invariant manifold theory. Special attention is paid to the centre manifold and associated reduction principle, as these are essential to the local bifurcation theory. Specifying to periodic systems, the Floquet theory is extended to impulsive functional differential equations, and this permits an exploration of the impulsive analogues of saddle-node, transcritical, pitchfork and Hopf bifurcations. Readers will learn how techniques of classical bifurcation theory extend to impulsive functional differential equations and, as a special case, impulsive differential equations without delays. They will learn about stability for fixed points, periodic orbits and complete bounded trajectories, and how the linearization of the dynamical system allows for a suitable definition of hyperbolicity. They will see how to complete a centre manifold reduction and analyze a bifurcation at a nonhyperbolic steady state.

This book demonstrates how mathematical methods and techniques can be used in synergy and create a new way of looking at complex systems. It becomes clear nowadays that the standard (graph-based) network approach, in which observable events and transportation hubs are represented by nodes and relations between them are represented by edges, fails to describe the important properties of complex systems, capture the dependence between their scales, and anticipate their future developments. Therefore, authors in this book discuss the new generalized theories capable to describe a complex nexus of dependences in multi-level complex systems and to effectively engineer their important functions. The collection of works devoted to the memory of Professor Valentin Afraimovich introduces new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to molecular biology, genetics, neurosciences, artificial intelligence as well as classic problems in physics, machine learning, brain and urban dynamics. The book can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, urban planners, and even musicians (with some mathematical background).

This book describes the modelling and optimisation of vibration reduction systems in an integrated fashion using nonlinear equations of motion. It proposes an effective optimisation method for determining the basic characteristics of the non-linear visco-elastic elements used in passive vibration reduction systems. In the case of semi-active and active vibration isolators, a design process of the advanced control systems is proposed that makes possible to optimise the controller settings relatively to the selected vibro-isolation criteria. The approach developed here is subsequently tested by means of experimental investigations conducted on various sample vibration reduction systems: passive, semi-active and active. The book presents a biomechanical modelling approach that allows users to select the properties of vibro-isolation systems for different types of oscillation and different optimisation criteria - and can significantly reduce the harmful vibrations that can affect the human body in the process. Further, the book equips readers to evaluate the viscoelastic characteristics of passive systems and design control systems for semi-active and active systems. Modelling and Control Design of Vibration Reduction Systems offers a valuable guide for researchers and practitioners alike. It also provides students and academics with systematic information on the procedures to be followed in the design process for semi-active or active vibration reduction systems.

Imparts the theory and analysis regarding the dynamics of rotating machinery in order to design such rotating devices as turbines, jet engines, pumps and power-transmission shafts. Takes into account the forces acting upon machine structures, bearings and related components. Provides numerical techniques for analyzing and understanding rotor systems with examples of actual designs. Features an excellent treatment of numerical methods available to obtain computer solutions for authentic design problems.

Many dynamical systems are described by differential equations that can be separated into one part, containing linear terms with constant coefficients, and a second part, relatively small compared with the first, containing nonlinear terms. Such a system is said to be weakly nonlinear. The small terms rendering the system nonlinear are referred to as perturbations. A weakly nonlinear system is called quasi-linear and is governed by quasi-linear differential equations. We will be interested in systems that reduce to harmonic oscillators in the absence of perturbations. This book is devoted primarily to applied asymptotic methods in nonlinear oscillations which are associated with the names of N. M. Krylov, N. N. Bogoli ubov and Yu. A. Mitropolskii. The advantages of the present methods are their simplicity, especially for computing higher approximations, and their applicability to a large class of quasi-linear problems. In this book, we confine ourselves basi cally to the scheme proposed by Krylov, Bogoliubov as stated in the monographs 6,211. We use these methods, and also develop and improve them for solving new problems and new classes of nonlinear differential equations. Although these methods have many applications in Mechanics, Physics and Technique, we will illustrate them only with examples which clearly show their strength and which are themselves of great interest. A certain amount of more advanced material has also been included, making the book suitable for a senior elective or a beginning graduate course on nonlinear oscillations."

Research in vibration response control deals not only with prevention of catastrophic failures of structures during natural or accidental/manmade hazards but also ensures the comfort of occupants through serviceability. Therefore, the focus of this book is on the theory of dynamic response control of structures by using different kinds of passive vibration control devices. The strategies used for controlling displacement, velocity, and acceleration response of structures such as buildings, bridges, and liquid storage tanks under the action of dynamic loads emanating from earthquake, wind, wave, and so forth are detailed. The book: Explains fundamentals of vibration response control devices and their practical applications in response mitigation of structures exposed to earthquake, wind, and wave loading Offers a comprehensive overview of each passive damper, its functioning, and mathematical modeling in a dynamical system Covers practical aspects of employing the passive control devices to some of the benchmark problems that are developed from existing buildings and bridges in different countries worldwide Includes MATLAB (R) codes for determining the dynamic response of single degree of freedom (SDOF) and multi-degree of freedom (MDOF) systems along with computational models of the passive control devices This book is aimed at senior undergraduate students, graduate students, and researchers in civil, earthquake, aerospace, automotive, mechanical engineering, engineering dynamics, and vibration control, including structural engineers, architects, designers, manufacturers, and other professionals.

This book offers up novel research which uses analytical approaches to explore nonlinear features exhibited by various dynamic processes. Relevant to disciplines across engineering and physics, the asymptotic method combined with the multiple scale method is shown to be an efficient and intuitive way to approach mechanics. Beginning with new material on the development of cutting-edge asymptotic methods and multiple scale methods, the book introduces this method in time domain and provides examples of vibrations of systems. Clearly written throughout, it uses innovative graphics to exemplify complex concepts such as nonlinear stationary and nonstationary processes, various resonances and jump pull-in phenomena. It also demonstrates the simplification of problems through using mathematical modelling, by employing the use of limiting phase trajectories to quantify nonlinear phenomena. Particularly relevant to structural mechanics, in rods, cables, beams, plates and shells, as well as mechanical objects commonly found in everyday devices such as mobile phones and cameras, the book shows how each system is modelled, and how it behaves under various conditions. It will be of interest to engineers and professionals in mechanical engineering and structural engineering, alongside those interested in vibrations and dynamics. It will also be useful to those studying engineering maths and physics.

This book describes in detail the physical and mathematical foundations of ultrasonic phased array measurements.The book uses linear systems theory to develop a comprehensive model of the signals and images that can be formed with phased arrays. Engineers working in the field of ultrasonic nondestructive evaluation (NDE) will find in this approach a wealth of information on how to design, optimize and interpret ultrasonic inspections with phased arrays. The fundamentals and models described in the book will also be of significant interest to other fields, including the medical ultrasound and seismology communities. A unique feature of this book is that it presents a unified theory of imaging with phased arrays that shows how common imaging methods such as the synthetic aperture focusing technique (SAFT), the total focusing method (TFM), and the physical optics far field inverse scattering (POFFIS) imaging method are all simplified versions of more fundamental and quantitative imaging approaches, called imaging measurement models.

To enhance learning, this book first describes the fundamentals of phased array systems using 2-D models, so that the complex 3-D cases normally found in practice can be more easily understood.In addition to giving a detailed discussion of phased array systems, Fundamentals of Ultrasonic Phased Arrays also provides MATLAB(r) functions and scripts, allowing the reader to conduct simulations of ultrasonic phased array transducers and phased array systems with the latest modeling technology."

This essential textbook concerns analysis and control of engineering mechanisms, which includes almost any apparatus with moving parts used in daily life, from musical instruments to robots. A particular characteristic of this book is that it presents with considerable breadth and rigor both vibrations and controls. Many contemporary texts combine both of these topics in a single, one term course. This text supports the more favorable circumstance where the material is covered in a one year sequence contains enough material for a two semester sequence, but it can also be used in a single semester course combining two topics. "Mechanical Systems: A Unified Approach to Vibrations and Controls" presents a common notation and approach to these closely related areas. Examples from the both vibrations and controls components are integrated throughout this text.

This book opens with an explanation of the vibrations of a single degree-of-freedom (dof) system for all beginners. Subsequently, vibration analysis of multi-dof systems is explained by modal analysis. Mode synthesis modeling is then introduced for system reduction, which aids understanding in a simplified manner of how complicated rotors behave. Rotor balancing techniques are offered for rigid and flexible rotors through several examples. Consideration of gyroscopic influences on the rotordynamics is then provided and vibration evaluation of a rotor-bearing system is emphasized in terms of forward and backward whirl rotor motions through eigenvalue (natural frequency and damping ratio) analysis. In addition to these rotordynamics concerning rotating shaft vibration measured in a stationary reference frame, blade vibrations are analyzed with Coriolis forces expressed in a rotating reference frame. Other phenomena that may be assessed in stationary and rotating reference frames include stability characteristics due to rotor internal damping and instabilities due to asymmetric shaft stiffness and thermal unbalance behavior.

The book examines advanced, non-standardized techniques that have been developed for determining different properties of cement paste, mortar and concrete, and provides state-of-the-art information on methods for monitoring hydration-induced changes in cement-based materials (CBMs). These methods are often nondestructive and allow quasi-continuous monitoring covering the time span from placement of the material to formation of a fully hardened cement composite. The book also presents various applications of acoustic emission for characterizing fresh concrete, recent developments in ultrasonic methods for characterizing CBMs since placement, application of ambient response methods for measuring elastic modulus, methods for determining deformational characteristics of CBMs since setting and methods for in situ measurements of stresses in concrete elements during hardening.

This monograph presents computational models that describe electro-mechanical characteristics of tapered and cylinder roller bearings in various industrial applications. Applying the Levenberg-Marquardt's algorithm to solving strongly nonlinear coupled equation systems, the computational models consisting of many circular slices per rolling element enable computations of the local Hertzian pressures at the elastohydrodynamic (EHD) contact area, the relating oil-film thickness in elastohydrodynamic lubrication (EHL), the limiting voltage of electro-pitting, bearing frictions, and fatigue lifetimes of the bearings for various load spectra. Using the best-known machine-learning method for clustering, the load spectrum is clustered in k cluster means based on the invariant damage number to accelerate the load spectrum. Furthermore, the accelerated load spectrum is used for the testing procedure of the bearings to reduce the testing time and costs as well. The target audience of this book primarily comprises graduate students in mechanical engineering and practicing engineers of electro-machines and transmission systems who want to computationally design tapered and cylinder roller bearings for the automotive industry and other industries, and to deeply dive into these relating working fields.

This book demonstrates how to formulate the equations of mechanical systems. Providing methods of analysis of complex mechanical systems, the book has a clear focus on efficiency, equipping the reader with knowledge of algorithms that provide accurate results in reduced simulation time. The book uses Kane's method due to its efficiency, and the simple resulting equations it produces in comparison to other methods and extends it with algorithms such as order-n. Kane's method compensates for the errors of premature linearization, which are often inherent within vibrations modes found in a great deal of public domain software. Describing how to build mathematical models of multibody systems with elastic components, the book applies this to systems such as construction cranes, trailers, helicopters, spacecraft, tethered satellites, and underwater vehicles. It also looks at topics such as vibration, rocket dynamics, simulation of beams, deflection, and matrix formulation. Flexible Multibody Dynamics will be of interest to students in mechanical engineering, aerospace engineering, applied mechanics and dynamics. It will also be of interest to industry professionals in aerospace engineering, mechanical engineering and construction engineering.

The Symposium was aimed at the theoretical and numerical problems involved in modelling the dynamic response of structures which have uncertain properties due to variability in the manufacturing and assembly process, with automotive and aerospace structures forming prime examples. It is well

known that the difficulty in predicting the response statistics of such structures is immense, due to the complexity of the structure, the large number of variables which might be uncertain, and the inevitable lack of data regarding

the statistical distribution of these variables.

The Symposium participants presented the latest thinking in this very active research area, and novel techniques were presented covering the full frequency spectrum of low, mid, and high frequency vibration problems. It was demonstrated that for high frequency vibrations the response statistics

can saturate and become independent of the detailed distribution of the uncertain system parameters. A number of presentations exploited this physical behaviour by using and extending methods originally developed in both

phenomenological thermodynamics and in the fields of quantum mechanics and random matrix theory.

For low frequency vibrations a number of presentations focussed on parametric uncertainty modelling (for example, probabilistic models, interval analysis, and fuzzy descriptions) and on methods of propagating this uncertainty through a large dynamic model in an effi cient way. At mid frequencies

the problem is mixed, and various hybrid schemes were proposed.

It is clear that a comprehensive solution to the problem of predicting the vibration response of uncertain structures across the whole frequency range requires expertise across a wide range of areas (including probabilistic and non-probabilistic methods, interval and info-gap analysis, statistical energy analysis, statistical thermodynamics, random wave approaches, and large

scale computations) and this IUTAM symposium presented a unique opportunity to bring together outstanding international experts in these fields."

Vibration presents a major challenge to advanced experiments and technological processes in engineering, physics and life sciences that rely on optics and optoelectronics. This compendium discusses ways in which vibration may affect optical performance and describes methods and means of reducing this impact. Principal methods of vibration control, namely, damping and isolation are highlighted using mathematical models and real-life examples.The unique text covers some topics that are important for optomechanical applications but are lacking in general vibration texts, such as dynamics and stability of elastically supported systems with high centers of gravity, physics of pneumatic isolators, and application of dynamic absorbers to vibration-isolated systems.This useful reference book enables the reader to apply the vibration control tools properly and perform basic analytical and experimental tasks of estimating and verifying their performance. It is also a must-have textbook for undergraduate or graduate-level courses in vibration control and optomechanics.

Too often the Eartha (TM)s surface acted as a divide between seismologists and engineers. Now it is becoming clear that the building behaviour largely depends on the seismic input and the buildings on their turn act as seismic sources, in an intricate interplay that non-linear phenomena make even more complex. These phenomena are often the cause of observed damage enhancement during past earthquakes. While research may pursue complex models to fully understand soil dynamics under seismic loading, we need also simple models valid on average, whose results can be easily transferred to end users.

Under the title a oeIncreasing Seismic Safety by Combining Engineering Technologies and Seismological Dataa, we grouped several topics to be discussed together by engineers and seismologists: (1) Can we use ambient noise building and soil characterisation to extract useful information for engineers? (2) How we can tell apart a frequency decrease due to distributed damage, concentrated damage, time- varying building and soil behaviour? (3) Which is the role of transients in ambient noise analysis? (4) Can we quantify the influence of existing buildings on ground-motion recordings? (5) To which extent soil-building resonance is a cause of damage enhancement? (6) How to couple soil and building non-linear behaviour?

On most questions there is an unanimous answer, but in some cases different views are present and the disagreement is faithfully reported.

At the dawn of the 21st century, computational stochastic dynamics is an emerging research frontier. This book focuses on advanced computational methods and software tools which can highly assist in tackling complex problems in stochastic dynamic/seismic analysis and design of structures. The book is primarily intended for researchers and post-graduate students in the fields of computational mechanics and stochastic structural dynamics. Nevertheless, practice engineers as well could benefit from it as most code provisions tend to incorporate probabilistic concepts in the analysis and design of structures. The book addresses mathematical and numerical issues in stochastic structural dynamics and connects them to real-world applications. It consists of 16 chapters dealing with recent advances in a wide range of related topics (dynamic response variability and reliability of stochastic systems, risk assessment, stochastic simulation of earthquake ground motions, efficient solvers for the analysis of stochastic systems, dynamic stability, stochastic modelling of heterogeneous materials). Numerical examples demonstrating the significance of the proposed methods are presented in each chapter.

This book reports on a comprehensive study addressing the dynamic responses of hydropower plants under diverse conditions and disturbances, and analyzes their stability and oscillations. Multiple models based on eight existing hydropower plants in Sweden and China were developed and used for simulations and theoretical analysis with various degrees of complexity and for different purposes, and compared with on-site measurements for validations. The book offers important insights into the understanding of the hydraulic, mechanical and electrical coupling mechanisms, up to market conditions and incentives. It recommends control strategies for a more stable and efficient operation of hydropower plants.

Small satellite technology is opening up a new era in space exploration offering reduced cost of launch and maintenance, operational flexibility with on-orbit reconfiguration, redundancy etc. The true power of such missions can be harnessed only from close and precise formation flying of satellites. Formation flying missions support diverse application areas such as reconnaissance, remote sensing, solar observatory, deep space observatories, etc. A key component involved in formation flying is the guidance algorithm that should account for system nonlinearities and unknown disturbances. The main focus of this book is to present various nonlinear optimal control and adaptive guidance ideas to ensure precise close formation flying in presence of such difficulties. In addition to in-depth discussion of the relevant topics, MATLAB program files for the results included are also provided for the benefit of the readers. Since this book has concise information about the various guidance techniques, it will be useful reference for researchers and practising engineers in the space field.

This volume contains the edited version of selected papers presented at the Nato Advanced Study Institute on "Computer Aided Analysis of Rigid and Flexible Mechanical Systems," held in Portugal, from the 27 June to 9 July, 1994. The present volume can be viewed as a natural extension of the material addressed in the Institute which was published by KLUWER in the NATO ASI Series, Vol. 268, in 1994. The requirements for accurate and efficient analysis tools for design of large and lightweight mechanical systems has driven a strong interest in the challenging problem of multibody dynamics. The development of new analysis and design formulations for multi body systems has been more recently motivated with the need to include general features such as: real-time simulation capabilities, active control of machine flexibilities and advanced numerical methods related to time integration of the dynamic systems equations. In addition to the presentation of some basic formulations and methodologies in dynamics of multibody systems, including computational aspects, major applications of developments to date are presented herein. The scope of applications is extended to vehicle dynamics, aerospace technology, robotics, mechanisms design, intermittent motion and crashworthiness analysis. Several of these applications are explored by many contributors with a constant objective to pace development and improve the dynamic performance of mechanical systems avoiding different mechanical limitations and difficult functional requirements, such as, for example, accurate positioning of manipulators.

The control of vibrating systems is a significant issue in the design of aircraft, spacecraft, bridges, and high-rise buildings. This book discusses the control of vibrating systems, integrating structural dynamics, vibration analysis, modern control, and system identification. By integrating these subjects engineers will need only one book, rather than several texts or courses, to solve vibration control problems. The authors cover key developments in aerospace control and identification theory, including virtual passive control, observer and state-space identification, and data-based controller synthesis. They address many practical issues and applications, and show examples of how various methods are applied to real systems. Some methods show the close integration of system identification and control theory from the state-space perspective, rather than from the traditional input-output model perspective of adaptive control. This text will be useful for advanced undergraduate and beginning graduate students in aerospace, mechanical, and civil engineering, as well as for practicing engineers.

This book applies vibration engineering to turbomachinery, covering installation, maintenance and operation. With a practical approach based on clear theoretical principles and formulas, the book is an essential how-to guide for all professional engineers dealing with vibration issues within turbomachinery. Vibration problems in turbines, large fans, blowers, and other rotating machines are common issues within turbomachinery. Applicable to industries such as oil and gas mining, cement, pharmaceutical and naval engineering, the ability to predict vibration based on frequency spectrum patterns is essential for many professional engineers. In this book, the theory behind vibration is clearly detailed, providing an easy to follow methodology through which to calculate vibration propagation. Describing lateral and torsional vibration and how this impacts turbine shaft integrity, the book uses mechanics of materials theory and formulas alongside the matrix method to provide clear solutions to vibration problems. Additionally, it describes how to carry out a risk assessment of vibration fatigue. Other topics covered include vibration control techniques, the design of passive and active absorbers and rigid, non-rigid and Z foundations. The book will be of interest to professionals working with turbomachinery, naval engineering corps and those working on ISO standards 10816 and 13374. It will also aid mechanical engineering students working on vibration and machine design.

Examines all the major types of mechatronic systems used in railway applications Surveys rail vehicle mechatronic design processes with practical sources and references Outlines modelling approaches for rail vehicles, from concept to finishined prototype Analyzes system integration of complex railway mechatronic systems Presents numerical experiments and mechatronic models with railway transport applications