# System Dynamics for Engineering Students

Concepts and Applications

By

• Nicolae Lobontiu, Associate Professor of Mechanical Engineering, University of Alaska Anchorage

System Dynamics for Engineering Students: Concepts and Applications discusses the basic concepts of engineering system dynamics. Engineering system dynamics focus on deriving mathematical models based on simplified physical representations of actual systems, such as mechanical, electrical, fluid, or thermal, and on solving the mathematical models. The resulting solution is utilized in design or analysis before producing and testing the actual system. The book discusses the main aspects of a system dynamics course for engineering students; mechanical, electrical, and fluid and thermal system modeling; the Laplace transform technique; and the transfer function approach. It also covers the state space modeling and solution approach; modeling system dynamics in the frequency domain using the sinusoidal (harmonic) transfer function; and coupled-field dynamic systems. The book is designed to be a one-semester system-dynamics text for upper-level undergraduate students with an emphasis on mechanical, aerospace, or electrical engineering. It is also useful for understanding the design and development of micro- and macro-scale structures, electric and fluidic systems with an introduction to transduction, and numerous simulations using MATLAB and SIMULINK.
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### Audience

Junior and senior undergraduate students in mechanical, electrical and aerospace engineering programs

### Book information

• Published: March 2010
• ISBN: 978-0-240-81128-4

### Reviews

"This is without doubt a text that can be used with relative ease by instructors and students alike, and that would likely serve as a useful and practical reference for many years after graduation, especially given its systematic approach to the essential physical modeling elements. The content is nicely laid out with good quality illustrations and clean lines and achieves an appropriate balance between theoretical derivations and examples."--Journal of Mechanical Engineering Science

Foreword

Preface

Resources That Accompany This Book

Chapter Introduction

1.1 Engineering System Dynamics

1.2 Modeling Engineering System Dynamics

1.2.1 Modeling Variants

1.2.2 Dynamical Systems Lumped-Parameter Modeling and Solution

1.3 Components, System, Input, and Output

1.4 Compliant Mechanisms and Microelectromechanical Systems

1.5 System Order

1.5.1 Zero-Order Systems

1.5.2 First-Order Systems

1.5.3 Second- and Higher-Order Systems

1.6 Coupled-Field (Multiple-Field) Systems

1.7 Linear and Nonlinear Dynamic Systems

Chapter 2 Mechanical Systems I

Objectives

Introduction

2.1 Basic Mechanical Elements: Inertia, Stiffness, Damping, and Forcing

2.1.1 Inertia Elements

2.1.2 Spring Elements

2.1.3 Damping Elements

2.1.4 Actuation (Forcing)

2.2 Basic Mechanical Systems

2.2.1 Newtonās Second Law of Motion Applied to Mechanical Systems Modeling

2.2.2 Free Response

Summary

Problems

Chapter 3 Mechanical Systems II

Objectives

Introduction

3.1 Lumped Inertia and Stiffness of Compliant Elements

3.1.1 Inertia Elements

3.1.2 Spring Elements

3.2 Natural Response of Compliant Single Degree-of-Freedom Mechanical Systems

3.3 Multiple Degree-of-Freedom Mechanical Systems

3.3.1 Configuration, Degrees of Freedom

3.3.2 Conservative Mechanical Systems

Summary

Problems

Chapter 4 Electrical Systems

Objectives

Introduction

4.1 Electrical Elements: Voltage and Current Sources, Resistor, Capacitor, Inductor, Operational Amplifier

4.1.1 Voltage and Current Source Elements

4.1.2 Resistor Elements

4.1.3 Capacitor Elements

4.1.4 Inductor Elements

4.1.5 Operational Amplifiers

4.2 Electrical Circuits and Networks

4.2.1 Kirchhoffās Laws

4.2.2 Configuration, Degrees of Freedom

4.2.3 Methods for Electrical Systems Modeling

4.2.4 Free Response

4.2.5 Operational Amplifier Circuits

Summary

Problems

Chapter 5 Fluid and Thermal Systems

Objectives

Introduction

5.1 Liquid Systems Modeling

5.1.1 Bernoulliās Law and the Law of Mass Conservation

5.1.2 Liquid Elements

5.1.3 Liquid Systems

5.2 Pneumatic Systems Modeling

5.2.1 Gas Laws

5.2.2 Pneumatic Elements

5.2.3 Pneumatic Systems

5.3 Thermal Systems Modeling

5.3.1 Thermal Elements

5.3.2 Thermal Systems

Summary

Problems

Chapter 6 The Laplace Transform

Objectives

Introduction

6.1 Direct Laplace and Inverse Laplace Transformations

6.1.1 Direct Laplace Transform and Laplace Transform Pairs

6.1.2 Properties of the Laplace Transform

6.2 Solving Differential Equations by the Direct and Inverse Laplace Transforms

6.2.1 Analytical and MATLABĀ® Partial-Fraction Expansion

6.2.2 Linear Differential Equations with Constant Coefficients

6.2.3 Use of MATLABĀ® to Calculate Direct and Inverse Laplace Transforms

6.2.4 Linear Differential Equation Systems with Constant Coefficients

6.2.5 Laplace Transformation of Vector-Matrix Differential Equations

6.2.6 Solving Integral and Integral-Differential Equations by the Convolution Theorem

6.2.7 Linear Differential Equations with Time-Dependent Coefficients

6.3 Time-Domain System Identification from Laplace-Domain Information

Summary

Problems

Chapter 7 Transfer Function Approach

Objectives

Introduction

7.1 The Transfer Function Concept

7.2 Transfer Function Model Formulation

7.2.1 Analytical Approach

7.2.2 MATLABĀ® Approach

7.3 Transfer Function and the Time Response

7.3.1 SISO Systems

7.3.2 MIMO Systems

7.4 Using SimulinkĀ® to Transfer Function Modeling

Summary

Problems

Chapter 8 State Space Approach

Objectives

Introduction

8.1 The Concept and Model of the State Space Approach

8.2 State Space Model Formulation

8.2.1 Analytical Approach

8.2.2 MATLABĀ® Approach

8.3 State Space and the Time-Domain Response

8.3.1 Analytical Approach: The State-Transition Matrix Method

8.3.2 MATLABĀ® Approach

8.4 Using SimulinkĀ® for State Space Modeling

Summary

Problems

Chapter 9 Frequency-Domain Approach

Objectives

Introduction

9.1 The Concept of Complex Transfer Function in Steady-State Response and Frequency-Domain Analysis

9.2 Calculation of Natural Frequencies for Conservative Dynamic Systems

9.2.1 Analytical Approach

9.2.2 MATLABĀ® Approach

9.3 Steady-State Response of Dynamic Systems to Harmonic Input

9.3.1 Analytical Approach

9.3.2 Using MATLABĀ® for Frequency Response Analysis

9.4 Frequency-Domain Applications

9.4.1 Transmissibility in Mechanical Systems

9.4.3 Filters

Summary

Problems

Chapter 10 Coupled-Field Systems

Objectives

Introduction

10.1 Concept of System Coupling

10.2 System Analogies

10.2.1 First-Order Systems

10.2.2 Second-Order Systems

10.3 Electromechanical Coupling

10.3.1 Mechanical Strain, Electrical Voltage Coupling

10.3.2 Electromagnetomechanical Coupling

10.3.3 Electromagnetomechanical Coupling with Optical Detection in MEMS

10.3.4 Piezoelectric Coupling

10.4 Thermomechanical Coupling: The Bimetallic Strip

10.5 Nonlinear Electrothermomechanical Coupled-Field Systems

10.6 SimulinkĀ® Modeling of Nonlinear Coupled-Field Systems

Summary

Problems