Nonlinear Structural Dynamics Using FE Methods emphasizes fundamental mechanics principles and outlines a modern approach to understanding structural dynamics. The book will be useful to practicing engineers, giving them a richer understanding of their tools and thus accelerating learning on new problems. Independent workers will find access to advanced topics presented in an accessible manner. The book successfully tackles the challenge of how to present the fundamentals of structural dynamics and infuse it with finite-element (FE) methods. First, the author establishes and develops mechanics principles that are basic enough to form the foundations of FE methods. Second, the book presents specific computer procedures to implement FE methods so that general problems can be “solved” – that is, responses can be produced given the loads, initial conditions, and so on. Finally, the book introduces methods of analysis to leverage and expand the FE solutions.

Notation page xi

Introduction 1

PART I MECHANICS AND MODELS 5

1 Dynamics of Simple Elastic Systems 7

1.1 Motion of Simple Systems 7

1.2 Transient Excitations and Responses 20

1.3 Forced Vibrations through Periodic Loadings 28

1.4 Spectral Analysis of Periodic Loadings 37

Problem Set 51

2 Dynamics of Discretized Systems 54

2.1 Principle of Virtual Work 54

2.2 Lagrangian Dynamics 64

2.3 System Nonlinearities 79

Problem Set 89

3 Modeling Elastic Structures 92

3.1 Review of the Mechanics of 3D Solids 92

3.2 Ritz Method for Dynamic Problems 105

3.3 Finite-Element Formulation for Frames 129

3.4 Finite-Element Formulation for Solids 162

3.5 Modeling Large Deformations of Solids 183

Problem Set 201

4 Modeling Applied Loads 206

4.1 Some Interaction Loadings 206

4.2 Long-Term Periodic Loadings 222

4.3 Conservative Loads and Systems 238

4.4 Classification of Problems Based on Load Types 259

Problem Set 269

5 Computational Methods 271

5.1 Solving Large Systems of Equations 271

5.2 Direct Time Integration of Linear Systems 282

5.3 Time Integration of Nonlinear Systems 298

5.4 Solving Large Eigensystems 316

Problem Set 338

PART II DYNAMIC ANALYSES 341

6 Modal Analysis of Large Systems 343

6.1 Modal Matrix 343

6.2 Modal Superposition Method 353

6.3 Damped Motions 359

6.4 Advanced Modal Analyses 370

Problem Set 383

7 Vibration of Rods and Beams 385

7.1 Strong Formulation of Problems 385

7.2 Spectral Analysis of Continuous Members 390

7.3 Distributed Elastic Constraints 414

Problem Set 423

8 Vibration of Plates and Shells 427

8.1 Flexural Behavior of Flat Plates 427

8.2 Membrane Behavior of Thin Flat Plates 444

8.3 Deep Beams with Shear Deformations 455

8.4 Thin-Walled Shells 466

8.5 Nonlinear Vibrations of Panels 475

Problem Set 484

9 Wave Propagation 487

9.1 Introduction to Wave Propagation 487

9.2 Spectral Analysis of Wave Motions 496

9.3 Waves in Extended Solids 519

9.4 Relation of Wave Responses to Vibrations 530

Problem Set 535

10 Stability of the Motion 538

10.1 Some Preliminary Stability Ideas 538

10.2 Deformation-Dependent Loadings 552

10.3 Stability of Parametrically Excited Systems 566

10.4 Motions in the Large 581

Problem Set 596

Project-Level Problem Set 599

References 613

Index 619

James F. Doyle is a professor in the School of Aeronautics and Astronautics at Purdue University. His main area of research is experimental mechanics, wave propagation, and structural dynamics. Special emphasis is placed on solving inverse problems such as force and system-identification problems. He is a dedicated teacher and pedagogical innovator. He is a winner of the Frocht Award for Teaching and the Hetenyi Award for Research, both from the Society for Experimental Mechanics. This is his sixth book dealing with the mechanics of structures.

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