Engineering Dynamics 2.0: Fundamentals and Numerical Solutions

ISBN-13: 9783319984698 / Angielski / Twarda / 2019 / 707 str.

Lester W. Schmerr

Spis treści

1 Basic Elements of Dynamics

1.1 Introduction

1.2 Systems of Units

1.3 Describing Motion in Different Coordinate Systems

1.3.1 Cartesian (Rectangular) Coordinates

1.3.2 Cylindrical and Polar Coordinates

1.3.3 Spherical Coordinates

1.4 Vectors and Matrices

1.5 Angular Velocity and the Time Derivative of Unit Vectors

1.6 Objective and Organization of the Book

1.7 Problems

2 Dynamics of a Particle

2.1 Governing Equations

2.2 The Dynamics of Unconstrained Motion of a Particle 

2.2.1 Equations of Motion

2.2.2 A Projectile Problem

2.2.3 Potential Energy

2.2.4 Kinetic Energy and Conservative Systems

2.2.5 Work-Energy

2.2.6 A Projectile Problem with Drag Forces

2.3 The Dynamics of Constrained Motion of a Particle

2.3.1 Constrained Motion of a Bead on a Wire

2.3.2 A Roller-Coaster Problem

2.4 Constraints and Equations of Motion – A Matrix Approach

2.4.1 Types of Constraints

2.4.2 Constraints for Motion in Three Dimensions

2.4.3 Augmented Solutions for Ideal Constraint Forces and the Equations of 

        Motion in Cartesian Coordinates

2.5 Constraints and Equations of Motion in Generalized Coordinates

2.5.1 Solutions in Generalized Coordinates

2.5.2 Unconstrained Motion of a Spring-Pendulum

2.5.3 Constrained Motion of a Pendulum

2.5.4 Constraints and the Motion of the Planets

2.6 Generalized Coordinates and the Equations Motion – A Geometric Approach

2.6.1 Embedding of Constraints

2.6.2 Augmented Approach with Generalized Coordinates

2.7 Lagrange's Equations

2.7.1 Generalized Momenta and Ignorable Coordinates

2.8 Analytical Dynamics and Virtual Work

2.9 Other Principles and Virtual Quantities

2.10 Non-Ideal Constraint Forces

2.11 Explicit Embedding of Constraints – A General Approach

2.12 The Augmented Approach and Constraint Satisfaction

2.13 Problems

2.14 References

3 Dynamics of a System of Particles

3.1 Internal Forces

3.2 Newton-Euler Laws for a System of Particles

3.2.1 Motion of the Center of Mass

3.2.2 Impulse and Linear Momentum

3.2.3 The Moment Equation and Angular Momentum 

3.2.4 Angular Impulse and Angular Momentum

3.2.5 Work and Energy

3.2.5.1 Kinetic Energy and Angular Momentum for a Rigid System of Particles

3.2.5.2 Work-Kinetic Energy for an Elastically Connected System of Particles

3.3 Dynamics of a Rigidly Constrained System of Particles (Rigid Body)

3.4 Equations of Motion in Generalized Coordinates 

3.4.1 Motion of a Double Pendulum

3.5 A Non-Holonomic Constrained System of Particles

3.6 Dependent Constraints

3.7 Problems

3.8 References

4 Kinematics and Relative Motion

4.1 Relative Velocity and Acceleration

4.1.1 Relative Motion – Cylindrical and Spherical Coordinates

4.2 Relative Motion and the Transport Theorem

4.2.1 Relative Velocity and Acceleration – More Explicit Forms

4.2.2 Relative Motion for Rigid Bodies

4.2.3 The Analysis of Kinematically Driven Systems – I

4.2.4 Singular Configurations

4.2.5 Numerical Solution of the Position Equations

4.2.6 Velocity and Acceleration Constraints

4.2.7 The Analysis of Kinematically Driven Systems – II

4.3 Motion on the Rotating Earth

4.4 Matrix Kinematics of Rigid Body Planar Motion

4.4.1 Positional Analysis

4.4.2 Velocity Analysis

4.4.3 Acceleration Analysis

4.4.4 General Relative Velocity and Acceleration Relations

4.5 Matrix-Vector Kinematics of Constraints and Kinematically Driven Systems

4.6 Three-Dimensional Motion – Finite Rotations and Relative Position

4.7 Angular Velocity and Relative Velocity

4.8 Angular Velocity and Euler Angles

4.9 Acceleration and the Equations of Motion

4.10 Euler Parameters

4.11 The Commonly Used Euler Angle Sets

4.12 Problems

4.13 References

5 Planar Dynamics of Rigid Bodies

5.1 Governing Equations for a Rigid Body in Plane Motion

5.1.1 A System of Rigid Bodies in Plane Motion

5.2 Moment of Inertia

5.3 Planar Problems and Constraint Forces

5.3.1 A Newton-Euler Approach

5.3.2 An Augmented Approach

5.3.3 Rolling without Slipping

5.4 Kinetic Energy and Work-Energy

5.4.1 Kinetic Energy of a Rigid Body in Plane Motion

5.4.2 Work-Energy Principle for a Rigid Body in Plane Motion

5.5 Angular Momentum and the Moment Equation

5.5.1 Motion Relative to a Point that Moves with a Rigid  Body

5.5.2 Motion Relative to a General Point

5.6 Solving Systems of Rigid Bodies in Plane Motion 

5.6.1 Lagrange's Equations

5.7 Problems

6 Dynamic and Static Stability

6.1 Dynamic Stability

6.2 Stability of a Natural, Conservative System Near Equilibrium

6.3 Stability of a Non-Natural System Near Equilibrium

6.4 Stability Analysis through Linearization

6.5 Static Stability

6.6 Bifurcations and Buckling

6.7 Limit Load Instability

6.8 Snap-Through Instability

6.9 Problems

6.10 References

7 Vibrations of Dynamical Systems

7.1 An Overview of Linearized Vibrating Systems

7.2 Linearized Motion Near Equilibrium

7.3 Free Vibrations without Damping

7.4 Forced Vibrations without Damping

7.4.1 Harmonic Driving Forces

7.5 Free Vibrations with Damping

7.6 Forced Vibration with Damping

7.6.1 Harmonic Driving Forces

7.6.1 System Impulse Response 

7.6.2 Convolution Integrals

7.7 Problems

8 General Spatial Dynamics of Rigid Bodies 

8.1 Angular Momentum

8.1.1 Angular Momentum About a Body-Fixed Point

8.1.2 Angular Momentum About a General Point

8.2 Kinetic Energy

8.3 Impulse-Momentum and Work-Energy Principles for a Rigid Body

8.4 Newton-Euler Equations of Motion

8.4.1 Governing Equations -  General Case

8.4.2 Governing Equations for a Rigid Body – Use of a Body-Fixed Point 

8.5 Solutions of Euler's Equations for Rotational Motion

8.6 Rotational Motion and the Euler Parameters Constraint

8.7 Solving Systems of Rigid Bodies

8.7.1 Lagrange's Equations

8.8 The Rolling Disk

8.9 Problems

8.10 References

9 Dynamics of Deformable Bodies

9.1 Longitudinal Wave Motion

9.1.1 The Method of Finite Differences

9.1.2 The Finite Element Method

9.2 Problems

Appendices

A Matrices

A.1 Basic Matrix Algebra

A.2 Vectors as Matrices

A.3 Determinants and Cofactors

A.4 Inverses and Solutions of Linear Equations

A.5 References

B Mass Moments and Products of Inertia

B.1 Definitions

B.2 Parallel Axis Theorem

B.3 Rotation of Axes

B.4 Principal Moments of Inertia

B.5 Some Moments of Inertia

C Numerical Methods

C.1 Numerical Solutions of Ordinary Differential Equations

C.2 Numerical Solutions of Non-Linear Algebraic Equations

D Vibrations of One Degree of Freedom Systems

D.1 General Solutions

D.1.1 Homogeneous Solutions

D.1.2 Free Vibration Solutions

D.1.3 Impulse Response and a Particular Solution as a Convolution Integral

D.1.4 The Steady-State Response of One Degree of Freedom Systems

D.1.5 Combining Homogeneous and Particular Solutions 

D.2 References

E Fourier Transforms

E.1 Fourier Transforms and Discrete Fourier Transforms

E.2 Fast Fourier Transforms and Numerical Fourier Analysis

E.3 Different Forms of the Fourier Transform

F MATLAB® Functions and Scripts

O autorze

Les Schmerr received a B.S. degree in Aeronautics and Astronautics from the Massachusetts Institute of Technology in 1965 and a Ph.D. in Mechanics from the Illinois Institute of Technology in 1970. Since 1969 he has been at Iowa State University where he is currently Professor of Aerospace Engineering and Associate Director of the Center for Nondestructive Evaluation. He is also the Permanent Secretary of the World Federation of NDE Centers. His research interests include ultrasonics, elastic wave propagation and scattering, and artificial intelligence. He has developed and taught Ultrasonics and Nondestructive Evaluation courses at both the undergraduate and graduate level. He is the author of several books, including Ultrasonic Nondestructive Evaluation Systems (2007), Fundamentals of Ultrasonic Phased Arrays (2015), and most recently, the second edition of Fundamentals of Ultrasonic Nondestructive Evaluation (2016). He is a member of IEEE, ASME, ASNT and AIAA.

Blurb

This book presents a new approach to learning the dynamics of particles and rigid bodies at an intermediate to advanced level. There are three distinguishing features of this approach. First, the primary emphasis is to obtain the equations of motion of dynamical systems and to solve them numerically. As a consequence, most of the analytical exercises and homework found in traditional dynamics texts written at this level are replaced by MATLAB®-based simulations. Second, extensive use is made of matrices. Matrices are essential to define the important role that constraints have on the behavior of dynamical systems. Matrices are also key elements in many of the software tools that engineers use to solve more complex and practical dynamics problems, such as in the multi-body codes used for analyzing mechanical, aerospace, and biomechanics systems. The third and feature is the use of a combination of Newton-Euler and Lagrangian (analytical mechanics) treatments for solving dynamics problems. Rather than discussing these two treatments separately, Engineering Dynamics 2.0 uses a geometrical approach that ties these two treatments together, leading to a more transparent description of difficult concepts such as "virtual" displacements.

Some important highlights of the book include: 

• Extensive discussion of the role of constraints in formulating and solving dynamics problems.
  
• Implementation of a highly unified approach to dynamics in a simple context suitable for a second-level course.
  
• Descriptions of non-linear phenomena such as parametric resonances and chaotic behavior.
  
• A treatment of both dynamic and static stability.
  
• Overviews of the numerical methods (ordinary differential equation solvers, Newton-Raphson method) needed to solve dynamics problems.
  
• An introduction to the dynamics of deformable bodies and the use of finite difference and finite element methods.

Engineering Dynamics 2.0 provides a unique, modern treatment of dynamics problems that is directly useful in advanced engineering applications. It is a valuable resource for undergraduate and graduate students and for practicing engineers.