Bücher der Reihe Synthesis Lectures on Mechanical Engineering

Engineering Dynamics is an introductory textbook covering the kinematics and dynamics of particles, systems of particles, and kinematics and dynamics of rigid bodies. It has been developed from lecture notes given by the author since 1982. It includes sufficient topics normally covered in a single-semester three credit hour course taken by sophomores in an undergraduate degree program majoring in various engineering disciplines.The primary focus of the book is on kinematics and dynamics of particles, kinematics and dynamics of systems of particles, and kinematics and dynamics of rigid bodies in two- and three-dimensional spaces. It aims at providing a short book, relative to many available in literature, but with detailed solutions to representative examples. Exercise questions are included.

This book describes the Asymptotic Modal Analysis (AMA) method to predict the high-frequency vibroacoustic response of structural and acoustical systems. The AMA method is based on taking the asymptotic limit of Classical Modal Analysis (CMA) as the number of modes in the structural system or acoustical system becomes large in a certain frequency bandwidth. While CMA requires both the computation of individual modes and a modal summation, AMA evaluates the averaged modal response only at a center frequency of the bandwidth and does not sum the individual contributions from each mode to obtain a final result. It is similar to Statistical Energy Analysis (SEA) in this respect. However, while SEA is limited to obtaining spatial averages or mean values (as it is a statistical method), AMA is derived systematically from CMA and can provide spatial information as well as estimates of the accuracy of the solution for a particular number of modes. A principal goal is to present the state-of-the-art of AMA and suggest where further developments may be possible. A short review of the CMA method as applied to structural and acoustical systems subjected to random excitation is first presented. Then the development of AMA is presented for an individual structural system and an individual acoustic cavity system, as well as a combined structural-acoustic system. The extension of AMA for treating coupled or multi-component systems is then described, followed by its application to nonlinear systems. Finally, the AMA method is summarized and potential further developments are discussed.

This book is intended for students taking a Machine Design course leading to a Mechanical Engineering Technology degree. It can be adapted to a Machine Design course for Mechanical Engineering students or used as a reference for adopting systems engineering into a design course. The book introduces the fundamentals of systems engineering, the concept of synthesis, and the basics of trade-off studies. It covers the use of a functional flow block diagram to transform design requirements into the design space to identify all success modes. The book discusses fundamental stress analysis for structures under axial, torsional, or bending loads. In addition, the book discusses the development of analyzing shafts under combined loads by using Mohr's circle and failure mode criterion. Chapter 3 provides an overview of fatigue and the process to develop the shaft-sizing equations under dynamic loading conditions. Chapter 4 discusses power equations and the nomenclature and stress analysis for spur and straight bevel gears and equations for analyzing gear trains. Other machine component topics include derivation of the disc clutch and its relationship to compression springs, derivation of the flat belt equations, roller and ball bearing life equations, roller chains, and keyways. Chapter 5 introduces the area of computational machine design and provides codes for developing simple and powerful computational methods to solve: cross product required to calculate the torques and bending moments on shafts, 1D stress analysis, reaction loads on support bearings, Mohr's circle, shaft sizing under dynamic loading, and cone clutch. The final chapter shows how to integrate Systems Engineering into machine design for a capstone project as a project-based collaborative design methodology. The chapter shows how each design requirement is transformed through the design space to identify the proper engineering equations.

Fluid mechanics is one of the most challenging undergraduate courses for engineering students. The fluid mechanics lab facilitates students' learning in a hands-on environment. The primary objective of this book is to provide a graphical lab manual for the fluid mechanics laboratory. The manual is divided into six chapters to cover the main topics of undergraduate-level fluid mechanics. Chapter 1 begins with an overview of laboratory objectives and the introduction of technical laboratory report content. In Chapter 1, error analysis is discussed by providing examples. In Chapter 2, fluid properties including viscosity, density, temperature, specific weight, and specific gravity are discussed. Chapter 3 revolves around the fluid statics include pressure measurement using piezometers and manometers. Additionally, hydrostatic pressure on the submerged plane and curved surfaces as well as buoyancy and Archimedes' Principle are examined in Chapter 3. In Chapter 4, several core concepts of fluid dynamics are discussed. This chapter begins with defining a control system based on which momentum analysis of the flow system is explained. The rest of the chapter is allotted to the force acting on a control system, the linear momentum equation, and the energy equation. Chapter 4 also covers the hydraulic grade line and energy grade line experiment. The effect of orifice and changing cross-sectional area by using Bernoulli's' equation is presented in Chapter 4. The application of the siphon is extended from Chapter 4 by applying Bernoulli's' equation. The last two chapters cover various topics in both internal and external flows which are of great importance in engineering design. Chapter 5 deals with internal flow including Reynolds number, flow classification, flow rate measurement, and velocity profile. The last experiment in Chapter 5 is devoted to a deep understanding of internal flow concepts in a piping system. In this experiment, students learn how to measure minor and major head losses as well as the impact of piping materials on the hydrodynamics behavior of the flow. Finally, open channels, weirs, specific energy, and flow classification, hydraulic jump, and sluice gate experiments are covered in Chapter 6.

In this book, the global sequential scenario of bifurcation trees of periodic motions to chaos in nonlinear dynamical systems is presented for a better understanding of global behaviors and motion transitions for one periodic motion to another one. A 1-dimensional (1-D), time-delayed, nonlinear dynamical system is considered as an example to show how to determine the global sequential scenarios of the bifurcation trees of periodic motions to chaos. All stable and unstable periodic motions on the bifurcation trees can be determined. Especially, the unstable periodic motions on the bifurcation trees cannot be achieved from the traditional analytical methods, and such unstable periodic motions and chaos can be obtained through a specific control strategy.The sequential periodic motions in such a 1-D time-delayed system are achieved semi-analytically, and the corresponding stability and bifurcations are determined by eigenvalue analysis. Each bifurcation tree of a specific periodic motion to chaos are presented in detail. The bifurcation tree appearance and vanishing are determined by the saddle-node bifurcation, and the cascaded period-doubled periodic solutions are determined by the period-doubling bifurcation. From finite Fourier series, harmonic amplitude and harmonic phases for periodic motions on the global bifurcation tree are obtained for frequency analysis. Numerical illustrations of periodic motions are given for complex periodic motions in global bifurcation trees. The rich dynamics of the 1-D, delayed, nonlinear dynamical system is presented. Such global sequential periodic motions to chaos exist in nonlinear dynamical systems. The frequency-amplitude analysis can be used for re-construction of analytical expression of periodic motions, which can be used for motion control in dynamical systems.

This book provides a short introduction and easy-to-follow implementation steps of deep learning using Google Cloud Platform. It also includes a practical case study that highlights the utilization of Python and related libraries for running a pre-trained deep learning model.In recent years, deep learning-based modeling approaches have been used in a wide variety of engineering domains, such as autonomous cars, intelligent robotics, computer vision, natural language processing, and bioinformatics. Also, numerous real-world engineering applications utilize an existing pre-trained deep learning model that has already been developed and optimized for a related task. However, incorporating a deep learning model in a research project is quite challenging, especially for someone who doesn't have related machine learning and cloud computing knowledge. Keeping that in mind, this book is intended to be a short introduction of deep learning basics through the example of a practical implementation case.The audience of this short book is undergraduate engineering students who wish to explore deep learning models in their class project or senior design project without having a full journey through the machine learning theories. The case study part at the end also provides a cost-effective and step-by-step approach that can be replicated by others easily.

In general, nanofluid is suspension of nanometer-sized particle in base fluids such as water, oil, ethylene glycol mixture etc. Nanofluid has more thermal conductivity compared to the base fluids. As such, the nanofluid has more heat transfer capacity than the base fluids. In order to study nanofluid flow problems, we need to solve related nonlinear differential equations analytically or numerically. But in most cases, we may not get an analytical solution. Accordingly, the related nonlinear differential equations need to be solved by efficient numerical methods.Accordingly, this book addresses various challenging problems related to nanofluid flow. In this regard, different efficient numerical methods such as homotopy perturbation method, Galerkin's method, and least square method are included. Further, the above practical problems are validated in special cases. We believe that this book will be very beneficial for readers who want firsthand knowledge on how to solve nanofluid flow problems.

Mechatronic Systems consist of components and/or sub-systems which are from different engineering domains. For example, a solenoid valve has three domains that work in a synergistic fashion: electrical, magnetic, and mechanical (translation). Over the last few decades, engineering systems have become more and more mechatronic. Automobiles are transforming from being gasoline-powered mechanical devices to electric, hybrid electric and even autonomous. This kind of evolution has been possible through the synergistic integration of technology that is derived from different disciplines. Understanding and designing mechatronic systems needs to be a vital component of today's engineering education. Typical engineering programs, however, mostly continue to train students in academic silos (otherwise known as majors) such as mechanical, electrical, or computer engineering. Some universities have started offering one or more courses on this subject and a few have even started full programs around the theme of Mechatronics. Modeling the behavior of Mechatronic systems is an important step for analysis, synthesis, and optimal design of such systems. One key training necessary for developing this expertise is to have comfort and understanding of the basic physics of different domains. A second need is a suitable software tool that implements these laws with appropriate flexibility and is easy to learn.This short text addresses the two needs: it is written for an audience who will likely have good knowledge and comfort in one of the several domains that we will consider, but not necessarily all; the book will also serve as a guide for the students to learn how to develop mechatronic system models with Simscape (a MATLAB tool box). The book uses many examples from different engineering domains to demonstrate how to develop mechatronic system models and what type of information can be obtained from the analyses.

This book provides readers with a design approach to the automatic flight control systems (AFCS). The AFCS is the primary on-board tool for long flight operations, and is the foundation for the airspace modernization initiatives. In this text, AFCS and autopilot are employed interchangeably. It presents fundamentals of AFCS/autopilot, including primary subsystems, dynamic modeling, AFCS categories/functions/modes, servos/actuators, measurement devices, requirements, functional block diagrams, design techniques, and control laws. The book consists of six chapters. The first two chapters cover the fundamentals of AFCS and closed-loop control systems in manned and unmanned aircraft. The last four chapters present features of Attitude control systems (Hold functions), Flight path control systems (Navigation functions), Stability augmentation systems, and Command augmentation systems, respectively.

The inherent complex dynamics of a parametrically excited pendulum is of great interest in nonlinear dynamics, which can help one better understand the complex world.Even though the parametrically excited pendulum is one of the simplest nonlinear systems, until now, complex motions in such a parametric pendulum cannot be achieved. In this book, the bifurcation dynamics of periodic motions to chaos in a damped, parametrically excited pendulum is discussed. Complete bifurcation trees of periodic motions to chaos in the parametrically excited pendulum include:period-1 motion (static equilibriums) to chaos, andperiod-,,,, motions to chaos (,,,, = 1, 2, , 6, 8, , 12).The aforesaid bifurcation trees of periodic motions to chaos coexist in the same parameter ranges, which are very difficult to determine through traditional analysis. Harmonic frequency-amplitude characteristics of such bifurcation trees are also presented to show motion complexity and nonlinearity in such a parametrically excited pendulum system. The non-travelable and travelable periodic motions on the bifurcation trees are discovered. Through the bifurcation trees of travelable and non-travelable periodic motions, the travelable and non-travelable chaos in the parametrically excited pendulum can be achieved. Based on the traditional analysis, one cannot achieve the adequate solutions presented herein for periodic motions to chaos in the parametrically excited pendulum. The results in this book may cause one rethinking how to determine motion complexity in nonlinear dynamical systems.

A component will not be reliable unless it is designed with required reliability. Reliability-Based Mechanical Design uses the reliability to link all design parameters of a component together to form a limit state function for mechanical design. This design methodology uses the reliability to replace the factor of safety as a measure of the safe status of a component. The goal of this methodology is to design a mechanical component with required reliability and at the same time, quantitatively indicates the failure percentage of the component. Reliability-Based Mechanical Design consists of two separate books: Volume 1: Component under Static Load, and Volume 2: Component under Cyclic Load and Dimension Design with Required Reliability. This book is Reliability-Based Mechanical Design, Volume 2: Component under Cyclic Load and Dimension Design with Required Reliability. It begins with a systematic description of a cyclic load. Then, the books use two probabilistic fatigue theories to establish the limit state function of a component under cyclic load, and further to present how to calculate the reliability of a component under a cyclic loading spectrum. Finally, the book presents how to conduct dimension design of typical components such as bar, pin, shaft, beam under static load, or cyclic loading spectrum with required reliability. Now, the designed component will be reliable because it has been designed with the required reliability. The book presents many examples for each topic and provides a wide selection of exercise problems at the end of each chapter. This book is written as a textbook for senior mechanical engineering students after they study the course Design of Machine Elements or a similar course. This book is also a good reference for design engineers and presents design methods in such sufficient detail that those methods are readily used in the design.

A component will not be reliable unless it is designed with required reliability. Reliability-Based Mechanical Design uses the reliability to link all design parameters of a component together to form a limit state function for mechanical design. This design methodology uses the reliability to replace the factor of safety as a measure of the safe status of a component. The goal of this methodology is to design a mechanical component with required reliability and at the same time, quantitatively indicates the failure percentage of the component. Reliability-Based Mechanical Design consists of two separate books: Volume 1: Component under Static Load, and Volume 2: Component under Cyclic Load and Dimension Design with Required Reliability. This book is Reliability-Based Mechanical Design, Volume 1: Component under Static Load. It begins with a brief discussion on the engineering design process and the fundamental reliability mathematics. Then, the book presents several computational methods for calculating the reliability of a component under loads when its limit state function is established. Finally, the book presents how to establish the limit state functions of a component under static load and furthermore how to calculate the reliability of typical components under simple typical static load and combined static loads. Now, we do know the reliability of a component under static load and can quantitively specify the failure percentage of a component under static load. The book presents many examples for each topic and provides a wide selection of exercise problems at the end of each chapter. This book is written as a textbook for junior mechanical engineering students after they study the course of Mechanics of Materials. This book is also a good reference book for design engineers and presents design check methods in such sufficient detail that those methods are readily used in the design check of a component under static load.

Regarding the vast use of chemical components in different human activities, they are susceptible to corrosion because of contact with aggressive environments. Therefore, the use of inhibitors for the control of corrosion of chemical components in corrosive media is an urgent affair. Numerous investigations were carried out and are still being done to study the corrosion inhibition potential of organic compounds. Remarkable inhibition efficiency was achieved by all these compounds particularly some with N, S, and O atoms in their structure. Unfortunately, most of these compounds are not only expensive but also toxic to living beings. Hence, it is essential to mention the importance of natural inhibitors as eco-friendly, readily available, and renewable sources. The main goal of this book is to point out the influence of these components in terms of physical and, in some cases, chemical, processes on different components in aggressive media. Different methods of measuring corrosion, adsorption behavior, mechanism of inhibitors, and some related information is presented in this book. There is a lack of comprehensive and relevant books on this subject, so we decided to write this book in order to accumulate useful information about the influence of natural inhibitors on metals in corrosive areas and to make it accessible to researchers.

This book aims to provide the basic theory of fractional calculus and its applications based on practical schemes and approaches, illustrated with applicable engineering and technical examples, especially focusing on the fractional-order controller design. In the development of this book, the essential theorems and facts in the first two chapters are proven with rigorous mathematical analyses. In addition, the commonly used definitions of Grunwald-Letnikov, Riemann-Liouville, Caputo, and Miller-Ross fractional derivatives are introduced with their properties proved and linked to fractional-order controller design. The last chapter presents several enlightening scenarios of fractional-order control designs, for example, the suppression of machining chatter, the nonlinear motion control of a multilink robot, the simultaneous tracking and stabilization control of a rotary inverted pendulum, and the idle speed control of an internal combustion engine (ICE).

Engineering Thermodynamics is a core course for students majoring in Mechanical and Aerospace Engineering. Before taking this course, students usually have learned \textit{Engineering Mechanics}-Statics and Dynamics, and they are used to solving problems with calculus and differential equations. Unfortunately, these approaches do not apply for Thermodynamics. Instead, they have to rely on many data tables and graphs to solve problems. In addition, many concepts are hard to understand, such as entropy. Therefore, most students feel very frustrated while taking this course.The key concept in Engineering Thermodynamics is state-properties: If one knows two properties, the state can be determined, as well as the other four properties. Unlike most textbooks, the first two chapters of this book introduce thermodynamic properties and laws with the ideal gas model, where equations can be engaged. In this way, students can employ their familiar approaches, and thus can understand them much better. In order to help students understand entropy in depth, interpretation with statistical physics is introduced. Chapters 3 and 4 discuss control-mass and control-volume processes with general fluids, where the data tables are used to solve problems. Chapter 5 covers a few advanced topics, which can also help students understand the concepts in thermodynamics from a broader perspective.

Engineering Mechanics is one of the fundamental branches of science that is important in the education of professional engineers of any major. Most of the basic engineering courses, such as mechanics of materials, fluid and gas mechanics, machine design, mechatronics, acoustics, vibrations, etc. are based on an Engineering Mechanics course. In order to absorb the materials of Engineering Mechanics, it is not enough to consume just theoretical laws and theorems-a student also must develop an ability to solve practical problems. Therefore, it is necessary to solve many problems independently. This book is a part of a four-book series designed to supplement the Engineering Mechanics courses in the principles required to solve practical engineering problems in the following branches of mechanics: Statics, Kinematics, Dynamics, and Advanced Kinetics. Each book contains 6-8 topics on its specific branch and each topic features 30 problems to be assigned as homework, tests, and/or midterm/final exams with the consent of the instructor. A solution of one similar sample problem from each topic is provided.This third book in the series contains seven topics on Dynamics, the branch of mechanics that is concerned with the relation existing between the forces acting on the objects and the motion of these objects. This book targets undergraduate students at the sophomore/junior level majoring in science and engineering.

This book is aimed at those in engineering/scientific fields who have never learned programming before but are eager to master the C language quickly so as to immediately apply it to problem solving in numerical analysis. The book skips unnecessary formality but explains all the important aspects of C essential for numerical analysis. Topics covered in numerical analysis include single and simultaneous equations, differential equations, numerical integration, and simulations by random numbers. In the Appendices, quick tutorials for gnuplot, Octave/MATLAB, and FORTRAN for C users are provided.

Fundamentals of mathematical magnetohydrodynamics (MHD) start with definitions of major variables and parameters in MHD fluids (also known as MHD media) and specifically plasmas encountered in nature as well as in engineering sytems, e.g., metallurgy or thermonuclear fusion power. Then collisions of fluids in such fluids are examined as well as motion of individual particles. Then the basic principles of MHD fluids are introduced along with transport phenomena, medium boundaries, and surface interactions. Then, waves and resonances of all sorts in MHD media are presented. The account concludes with the description of main MHD fluid types including plasma in fusion power generation.

Introduction to Kinematics and Dynamics of Machinery is presented in lecture notes format and is suitable for a single-semester three credit hour course taken by juniors in an undergraduate degree program majoring in mechanical engineering. It is based on the lecture notes for a required course with a similar title given to junior (and occasionally senior) undergraduate students by the author in the Department of Mechanical Engineering at the University of Calgary from 1981 and since 1996 at the University of Nebraska, Lincoln. The emphasis is on fundamental concepts, theory, analysis, and design of mechanisms with applications. While it is aimed at junior undergraduates majoring in mechanical engineering, it is suitable for junior undergraduates in biological system engineering, aerospace engineering, construction management, and architectural engineering.

Microcontroller education has experienced tremendous change in recent years. This book attempts to keep pace with the most recent technology while holding an opposing attitude to the No Need to Reinvent the Wheel philosophy. The choice strategies are in agreement with the employment of today's flexible and low-cost Do-It-Yourself (DYI) microcontroller hardware, along with an embedded C programming approach able to be adapted by different hardware and software development platforms. Modern embedded C compilers employ built-in features for keeping programs short and manageable and, hence, speeding up the development process. However, those features eliminate the reusability of the source code among diverse systems. The recommended programming approach relies on the motto Code More to Learn Even More, and directs the reader toward a low-level accessibility of the microcontroller device. The examples addressed herein are designed to meet the demands of Electrical & Electronic Engineering discipline, where the microcontroller learning processes definitely bear the major responsibility. The programming strategies are in line with the two virtues of C programming language, that is, the adaptability of the source code and the low-level accessibility of the hardware system. Some accompanying material of the book can be found at http://bit.ly/mcu-files.

The early chapters of this book provide thorough coverage of resistance spot welding fundamentals and principles. Topics covered include lobe and current range curves, contact resistance vs. electrode force, dynamic resistance, heat balance, nugget growth, etc. Equipment issues such as machine types, power supplies, and electrodes are addressed. Subsequent chapters focus on specific spot welding challenges to modern automotive manufacturing. Approaches to welding modern materials including advanced high-strength steels, coated steels, and aluminum alloys are covered in much detail. The final chapters focus on many common production and quality control issues, such as electrode wear, monitoring and testing, computational modeling, and welding codes. The overall goal of the book is to provide a comprehensive resource for automotive engineers and technicians who work with modern spot welding equipment and automotive materials.

Micro-Electro-Mechanical-Systems (MEMS) sensors constitute perhaps the most exciting technology of our age. The present effort incorporates all the information needed by scientists and engineers who work on research projects and/or product systems, which apply to air pressure acquisition and to its rearrangement into altitude data. Some of the potential implementations of this method (regularly referred to as barometric altimetry) include, but are not limited to, Position Location Application, Navigation Systems, Clinical Monitoring Applications, and Aircraft Instrumentation.This book holds the key to such applications, providing readers with the theoretical basis as well as the practical perspective of the subject matter. At first, the reader is introduced to the background theory, methods, and applications of barometric altimetry. Thereafter, the book incorporates the development of wireless barometers and a (real-time monitoring) wireless sensor network system for scheduling low-cost experimental observations. Finally, a deepened understanding to the analysis procedure of pressure measurements (using Matlab script code) is performed. Some accompanying material can be found at http://bit.ly/mems-files.

Finite element analysis is a basic foundational topic that all engineering majors need to understand in order for them to be productive engineering analysts for a variety of industries. This book provides an introductory treatment of finite element analysis with an overview of the various fundamental concepts and applications. It introduces the basic concepts of the finite element method and examples of analysis using systematic methodologies based on ANSYS software. Finite element concepts involving one-dimensional problems are discussed in detail so the reader can thoroughly comprehend the concepts and progressively build upon those problems to aid in analyzing two-dimensional and three-dimensional problems. Moreover, the analysis processes are listed step-by-step for easy implementation, and an overview of two-dimensional and three-dimensional concepts and problems is also provided. In addition, multiphysics problems involving coupled analysis examples are presented to further illustrate the broad applicability of the finite element method for a variety of engineering disciplines.The book is primarily targeted toward undergraduate students majoring in civil, biomedical, mechanical, electrical, and aerospace engineering and any other fields involving aspects of engineering analysis.

The use of sensors and instrumentation for measuring and control is growing at a very rapid rate in all facets of life in today's world. This Part II of Instrumentation: Theory and Practice is designed to provide the reader with essential knowledge regarding a broad spectrum of sensors and transducers and their applications. This textbook is intended for use as an introductory one-semester course at the junior level of an undergraduate program. It is also very relevant for technicians, engineers, and researchers who had no formal training in instrumentation and wish to engage in experimental measurements. The prerequisites are: a basic knowledge of multivariable calculus, introductory physics, college algebra, and a familiarity with basic electrical circuits and components. This book emphasizes the use of simplified electrical circuits to convert the change in the measured physical variable into a voltage output signal. In each chapter, relevant sensors and their operation are presented and discussed at a fundamental level and are integrated with the essential mathematical theory in a simplified form. The book is richly illustrated with colored figures and images. End-of-chapter examples and problems complement the text in a simple and straight forward manner.

Engineering Dynamics Course Companion, Part 2: Rigid Bodies: Kinematics and Kinetics is a supplemental textbook intended to assist students, especially visual learners, in their approach to Sophomore-level Engineering Dynamics. This text covers particle kinematics and kinetics and emphasizes Newtonian Mechanics ``Problem Solving Skills'' in an accessible and fun format, organized to coincide with the first half of a semester schedule many instructors choose, and supplied with numerous example problems. While this book addresses Rigid Body Dynamics, a separate book (Part 1) is available that covers Particle Dynamics.

The Brusselator is a mathematical model for autocatalytic reaction, which was proposed by Ilya Prigogine and his collaborators at the Université Libre de Bruxelles. The dynamics of the Brusselator gives an oscillating reaction mechanism for an autocatalytic, oscillating chemical reaction. The Brusselator is a slow-fast oscillating chemical reaction system. The traditional analytical methods cannot provide analytical solutions of such slow-fast oscillating reaction, and numerical simulations cannot provide a full picture of periodic evolutions in the Brusselator. In this book, the generalized harmonic balance methods are employed for analytical solutions of periodic evolutions of the Brusselator with a harmonic diffusion. The bifurcation tree of period-1 motion to chaos of the Brusselator is presented through frequency-amplitude characteristics, which be measured in frequency domains. Two main results presented in this book are:¿ analytical routes of periodical evolutions tochaos and¿ independent period-(2¿¿¿¿ + 1) evolution to chaos.This book gives a better understanding of periodic evolutions to chaos in the slow-fast varying Brusselator system, and the bifurcation tree of period-1 evolution to chaos is clearly demonstrated, which can help one understand routes of periodic evolutions to chaos in chemical reaction oscillators. The slow-fast varying systems extensively exist in biological systems and disease dynamical systems. The methodology presented in this book can be used to investigate the slow-fast varying oscillating motions in biological systems and disease dynamical systems for a better understanding of how infectious diseases spread.