Bifurcation Dynamics Of A Damped Parametric Pendulum

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Bifurcation Dynamics of a Damped Parametric Pendulum

Yu Guo,Albert C.J. Luo
Bifurcation Dynamics of a Damped Parametric Pendulum Book PDF

Author : Yu Guo,Albert C.J. Luo
Publisher : Morgan & Claypool Publishers
Page : 100 pages
File Size : 54,9 Mb
Release : 2019-12-02
Category : Technology & Engineering
ISBN : 9781681736853

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Bifurcation Dynamics of a Damped Parametric Pendulum by Yu Guo,Albert C.J. Luo Pdf

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, and period-m motions to chaos (m = 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.

Bifurcation Dynamics of a Damped Parametric Pendulum

Yu Guo,Albert C.J. Luo
Bifurcation Dynamics of a Damped Parametric Pendulum Book PDF

Author : Yu Guo,Albert C.J. Luo
Publisher : Springer Nature
Page : 84 pages
File Size : 45,9 Mb
Release : 2022-06-01
Category : Technology & Engineering
ISBN : 9783031796456

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Bifurcation Dynamics of a Damped Parametric Pendulum by Yu Guo,Albert C.J. Luo Pdf

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, and period- 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.

The Chaotic Pendulum

M. Gitterman
The Chaotic Pendulum Book PDF

Author : M. Gitterman
Publisher : World Scientific
Page : 157 pages
File Size : 41,9 Mb
Release : 2010
Category : Science
ISBN : 9789814322003

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The Chaotic Pendulum by M. Gitterman Pdf

The chaotic behavior of pendulum is usually associated with the random force acting on a pendulum (Brownian motion). This book presents a comprehensive description of these phenomena going on in underdamped and overdamped pendula subject to additive and multiplicative periodic and random forces.

Sequential Bifurcation Trees to Chaos in Nonlinear Time-Delay Systems

Siyuan Xing,Albert C.J. Luo
Sequential Bifurcation Trees to Chaos in Nonlinear Time Delay Systems Book PDF

Author : Siyuan Xing,Albert C.J. Luo
Publisher : Springer Nature
Page : 73 pages
File Size : 51,5 Mb
Release : 2022-05-31
Category : Technology & Engineering
ISBN : 9783031796692

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Sequential Bifurcation Trees to Chaos in Nonlinear Time-Delay Systems by Siyuan Xing,Albert C.J. Luo Pdf

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.

Polynomial Functional Dynamical Systems

Albert Luo
Polynomial Functional Dynamical Systems Book PDF

Author : Albert Luo
Publisher : Springer Nature
Page : 151 pages
File Size : 53,5 Mb
Release : 2022-05-31
Category : Technology & Engineering
ISBN : 9783031797095

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Polynomial Functional Dynamical Systems by Albert Luo Pdf

The book is about the global stability and bifurcation of equilibriums in polynomial functional systems. Appearing and switching bifurcations of simple and higher-order equilibriums in the polynomial functional systems are discussed, and such bifurcations of equilibriums are not only for simple equilibriums but for higher-order equilibriums. The third-order sink and source bifurcations for simple equilibriums are presented in the polynomial functional systems. The third-order sink and source switching bifurcations for saddle and nodes are also presented, and the fourth-order upper-saddle and lower-saddle switching and appearing bifurcations are presented for two second-order upper-saddles and two second-order lower-saddles, respectively. In general, the (2 + 1)th-order sink and source switching bifurcations for (2)th-order saddles and (2 +1)-order nodes are also presented, and the (2)th-order upper-saddle and lower-saddle switching and appearing bifurcations are presented for (2)th-order upper-saddles and (2)th-order lower-saddles (, = 1,2,...). The vector fields in nonlinear dynamical systems are polynomial functional. Complex dynamical systems can be constructed with polynomial algebraic structures, and the corresponding singularity and motion complexity can be easily determined.

The Engineering Dynamics Course Companion, Part 2

Edward Diehl
The Engineering Dynamics Course Companion Part 2 Book PDF

Author : Edward Diehl
Publisher : Springer Nature
Page : 217 pages
File Size : 48,8 Mb
Release : 2022-05-31
Category : Technology & Engineering
ISBN : 9783031796814

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The Engineering Dynamics Course Companion, Part 2 by Edward Diehl Pdf

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 Engineering Dynamics Course Companion, Part 1

Edward Diehl
The Engineering Dynamics Course Companion Part 1 Book PDF

Author : Edward Diehl
Publisher : Springer Nature
Page : 231 pages
File Size : 41,8 Mb
Release : 2022-05-31
Category : Technology & Engineering
ISBN : 9783031796777

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The Engineering Dynamics Course Companion, Part 1 by Edward Diehl Pdf

Engineering Dynamics Course Companion, Part 1: Particles: 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 Particle Dynamics, a separate book (Part 2) is available that covers Rigid Body Dynamics.

Instrumentation: Theory and Practice Part II

Issam Abu-Mahfouz
Instrumentation Theory and Practice Part II Book PDF

Author : Issam Abu-Mahfouz
Publisher : Morgan & Claypool Publishers
Page : 145 pages
File Size : 43,6 Mb
Release : 2022-03-16
Category : Technology & Engineering
ISBN : 9781636393124

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Instrumentation: Theory and Practice Part II by Issam Abu-Mahfouz Pdf

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.

Solving Practical Engineering Mechanics Problems

Sayavur Bakhtiyarov
Solving Practical Engineering Mechanics Problems Book PDF

Author : Sayavur Bakhtiyarov
Publisher : Springer Nature
Page : 77 pages
File Size : 41,9 Mb
Release : 2022-05-31
Category : Technology & Engineering
ISBN : 9783031796975

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Solving Practical Engineering Mechanics Problems by Sayavur Bakhtiyarov Pdf

Fluid Mechanics is the study of liquid or gas behavior in motion or at rest. It is one of the fundamental branches of Engineering Mechanics, which is important to educate professional engineers of any major. Many of the engineering disciplines apply Fluid Mechanics principles and concepts. In order to absorb the materials of Fluid Mechanics, it is not enough just to consume 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 supplement to the Fluid Mechanics course in learning and applying the principles required to solve practical engineering problems in the following branches of Fluid Mechanics: Hydrostatics, Fluid Kinematics, Fluid Dynamics, Turbulent Flow and Gas Dynamics (Compressible Fluid Flow). This book contains practical problems in Fluid Mechanics, which are a complement to Fluid Mechanics textbooks. The book is the product of material covered in many classes over a period of four decades at several universities. It consists of 18 sets of problems where students are introduced to various topics of the Fluid Mechanics. Each set involves 30 problems, which can be assigned as individual homework as well as test/exam problems. The solution of a similar problem for each set is provided. The sequence of the topics and some of the problems were adopted from Fluid Mechanics by R. C. Hibbeler, 2nd edition, 2018, Pearson.

Fluid Mechanics Experiments

Robabeh Jazaei
Fluid Mechanics Experiments Book PDF

Author : Robabeh Jazaei
Publisher : Springer Nature
Page : 101 pages
File Size : 49,9 Mb
Release : 2022-05-31
Category : Technology & Engineering
ISBN : 9783031796739

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Fluid Mechanics Experiments by Robabeh Jazaei Pdf

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.

Cold Atmospheric Plasma (CAP) Technology and Applications

Zhitong Chen,Richard Wirz
Cold Atmospheric Plasma CAP Technology and Applications Book PDF

Author : Zhitong Chen,Richard Wirz
Publisher : Springer Nature
Page : 191 pages
File Size : 41,7 Mb
Release : 2022-05-31
Category : Technology & Engineering
ISBN : 9783031797019

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Cold Atmospheric Plasma (CAP) Technology and Applications by Zhitong Chen,Richard Wirz Pdf

Cold atmospheric plasma (CAP) is a promising and rapidly emerging technology for a wide range of applications, from daily life to industry. CAP’s key advantage is its unique ability to effectively deliver reactive species to subjects including biological materials, liquid media, aerosols, and manufactured surfaces. This book assesses the state-of-art in CAP research and implementation for applications including agriculture, medicine, environment, materials, catalysis, and energy. The mechanisms of generation and transport of the key reactive species in the plasma are introduced and examined in the context of their applications. Opportunities and challenges for novel technologies, fresh ideas/concepts, expanded multidisciplinary study, and new applications are discussed. The authors’ vision for the converging trends across diverse disciplines is proposed to stimulate critical discussions, research directions, and collaborations.

Capstone Engineering Design

Ramana Pidaparti
Capstone Engineering Design Book PDF

Author : Ramana Pidaparti
Publisher : Springer Nature
Page : 81 pages
File Size : 43,8 Mb
Release : 2022-05-31
Category : Technology & Engineering
ISBN : 9783031796937

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Capstone Engineering Design by Ramana Pidaparti Pdf

Capstone Design: Project Process and Reviews (Student Engineering Design Workbook) provides a brief overview of the design process as well as templates, tools, and student design notes. The goal of this workbook is to provide students in multiple disciplines with a systematic iterative process to follow in their Capstone Design projects and get feedback through design reviews. Students should treat this workbook as a working document and document individual/team decisions, make sketches of their concepts, and add additional design documentation. This workbook also assists in documenting student responsibility and accountability for individual contributions to the project. Freshman- and sophomore-level students may also find this workbook helpful for design projects. Finally, this workbook will also serve as an evaluation and assessment tool for the faculty mentor/advisor.

Machine Design for Technology Students

Anthony D'Angelo Jr.
Machine Design for Technology Students Book PDF

Author : Anthony D'Angelo Jr.
Publisher : Springer Nature
Page : 113 pages
File Size : 42,6 Mb
Release : 2022-05-31
Category : Technology & Engineering
ISBN : 9783031796852

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Machine Design for Technology Students by Anthony D'Angelo Jr. Pdf

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.

Asymptotic Modal Analysis of Structural and Acoustical Systems

Shung Sung,Dean Culver,Donald Nefske,Earl Dowell
Asymptotic Modal Analysis of Structural and Acoustical Systems Book PDF

Author : Shung Sung,Dean Culver,Donald Nefske,Earl Dowell
Publisher : Springer Nature
Page : 110 pages
File Size : 50,5 Mb
Release : 2022-06-01
Category : Technology & Engineering
ISBN : 9783031796890

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Asymptotic Modal Analysis of Structural and Acoustical Systems by Shung Sung,Dean Culver,Donald Nefske,Earl Dowell Pdf

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.

Automatic Flight Control Systems

Mohammad Sadraey
Automatic Flight Control Systems Book PDF

Author : Mohammad Sadraey
Publisher : Springer Nature
Page : 159 pages
File Size : 48,9 Mb
Release : 2022-05-31
Category : Technology & Engineering
ISBN : 9783031796494

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Automatic Flight Control Systems by Mohammad Sadraey Pdf

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.