TY  - BOOK
AU  - Craig, Roy R.
AU  - kurdila, Andrew J.
TI  - Fundamentals of structural dynamics
SN  - 0471430447
U1  - 624.171 
PY  - 2006///
CY  - New Jersey
PB  - John Wiley & Sons 
N1  - Preface to Structural Dynamics-An Introduction to Computer Methodsxi Preface to Fundamentals of Structural Dynamics  xi: About the Authors xv 1The Science and Art of Structural Dynamics 1 1.1 Introduction to Structural Dynamics1 1.2Modeling of Structural Components and Systems  2 1.3Prototype Spring-Mass Model  7 1.4 Vibration Testing of Structures 12 1.5 Scope of the Book12 1.6Computer Simulations; Supplementary Material on the Website 15 References16 Problems16 Part I Single-Degree-of-Freedom Systems19 2Mathematical Models of SDOF Systems 21 Brief Review of the Dynamics of Particles and Rigid Bodies21 Elements of Lumped-Parameter Models24 Application of Newton's Laws to Lumped-Parameter Models  27 Application of the Principle of Virtual Displacements to Lumped-Parameter Models  34 Application of the Principle of Virtual Displacements to Continuous Models: Assumed-Modes Method  41 References Problems 3Free Vibration of SDOF Systems56 3.1 Free Vibration of Undamped SDOF Systems  58 3.2 Free Vibration of Viscous-Damped SDOF Systems  61 3.3 Stability of Motion66 3.4 Free Vibration of an SDOF System with Coulomb Damping  70 3.5 Experimental Determination of the Natural Frequency and Damping Factor of an SDOF System  72 References77 Problems  78 4Response of SDOF Systems to Harmonic Excitation  81 4.1 Response of Undamped SDOF Systems to Harmonic F.xcitation 82 4.2 Response of Viscous-Damped SDOF Systems to Harmonic Excitation: Frequency-Response Functions 87 4.3 Complex Frequency Response  93 4.4 Vibration Isolation: Force Transmissibilhy and Base Motion 96 4.5 Vibration Measuring Instruments: Accelerometers and Vibrometers101 4.6 Use of Frequency-Response Data to Determine the Natural Frequency and Damping Factor of a Lightly Damped SDOF System 104 4.7 Equivalent Viscous Damping107 4.8 Structural Damping111 References112 Problems  113  ' 5Response  of  SDOF  Systems  to  Nonpcriodic Excitation 117  ___________ 5.1 Response of a Viscous-Damped SDOF System to an Ideal Step Input 117 5.2 Response of Undamped SDOF Systems to Rectangular Pulse and Ramp Loadings119 5.3 Response of Undamped SDOF Systems to a Short-Duration Impulse: Unit Impulse Response123 5.4 Response of SDOF Systems to General Dynamic Excitation: Convolution Integral Method125 5.5 Response Spectra128 5.6 System Response by the Laplace Transform Method: System Transfer Function136 References142 Problems143 6Numerical Evaluation of the Dynamic Response of SDOF Systems 147_____________ 6.1 Integration of Second-Order Ordinary Differential Equations 148 6.2 Integration of First-Order Ordinary Differential Equations 159 6.3 Nonlinear SDOF Systems171 References181 Problems 182 7Response of SDOF Systems to Periodic Excita-tion: Frequency-Domain Analysis 184 7.1 Response to Periodic Excitation: Real Fourier Series184 7.2 Response to Periodic Excitation: Complex Fourier Series 189 7.3 Response to Nonperiodic Excitation: Fourier Integral195 7.4 Relalionship Between Complex Frequency Response and Unit Impulse Response199 7.5 Discrete Fourier Transform and Fast Fourier Transform  200 References205 Problems205 Part II  Multiple-Degree-of-Freedom Systems- _______Basic Topics 209____________ 8Mathematical Models of MDOF Systems211 8.1 Application of Newton's Laws to Lumped-Parameter Models 212 8.2 Introduction to Analytical Dynamics: Hamilton's Principle and Lagrange's Equations 218 8.3 Application of Lagrange's Equations to Lumped-Parameter Models 223 8.4 Application of Lagrange's Equations to Continuous Models: Assumed-Modes Method  228 8.5 Constrained Coordinates and Lagrange Multipliers  238 References240 Problems241 9Vibration of Undamped 2-DOF Systems 248 9.1 Free Vibration of 2-DOF Systems: Natural Frequencies and Mode Shapes  249 9.2 Beat Phenomenon  254 9.3 Additional Examples of Modes and Frequencies of 2-DOF Systems: Assumed-Modes Models  258 9.4 Free Vibration of Systems with Rigid-Body Modes  266 9.5 Introduction to Mode Superposition: Frequency Response of an Undamped 2-DOF System  268 9.6 Undamped Vibration Absorber  272 Reference  275 Problems  275 10 Vibration Properties of MDOF Systems: Modes, Frequencies, and Damping 281 10.1  Some Properties of Natural Frequencies and Natural Modes of Undamped MDOF Systems282 10.2  Model Reduction: Rayleigh, Rayleigh-Rit/, and Assumed-Modes Methods  298 10.3  Uncoupled Damping in MDOF Systems302 10.4  Structures with Arbitrary Viscous Damping: Complex Modes 307 10.5  Natural Frequencies and Mode Shapes of Damped Structures with Rigid-Body Modes  316 References  322 Problems  322 11  Dynamic Response of MDOF Systems:  Mode-Superposition Method 325____ ____ 11.1  Mode-Superposition Method: Principal Coordinates325 11.2  Mode-Superposition Solutions for MDOF Systems with Modal Damping: Frequency-Response Analysis  330 11.3  Mode-Displacement Solution for the Response of MDOF Systems 342 11.4  Mode-Acceleration Solution for the Response of Undamped MDOF Systems  349 11.5  Dynamic Stresses by Mode Superposition  351 11.6  Mode Superposition for Undamped Systems with Rigid-Body Modes 353 References  359 Problems  360 Part III Continuous Systems365 12 Mathematical Models of Continuous Systems367 12.1  Applications of Newton's Laws: Axial Deformation and Torsion 367 12.2  Application of Newton's Laws: Transverse Vibration of Linearly Elastic Beams (Bernoulli-Euler Beam Theory)  374 12.3  Application of Hamilton's Principle: Torsion of a Rod with Circular Cross Section  379 12.4  Application of the Extended Hamilton's Principle: Beam Flexure Including Shear Deformation and Rotatory Inertia (Timoshenko Beam Theory) 382 References  385 385 Problems 13 Free Vibration of Continuous Systems388 13.1  Free Axial and Torsional Vibration  388 13.2  Free Transverse Vibration of Bernoulli-Euler Beams  392 13.3  Rayleigh's Method for Approximating the Fundamental Frequency of a Continuous System  398 13.4  Free Transverse Vibration of Beams Including Shear Deformation and Rotatory Inertia  400 13.5  Some Properties of Natural Modes of Continuous Systems  401 13.6  Free Vibration of Thin Flat Plates  405 References  409 Problems409 Part IV  Computational  Methods  in  Structural Dynamics415 14 Introduction  to  Finite  Element  Modeling  of Structures 417 14.1  Introduction to the Finite Element Method  418 14.2  Element Stiffness and Mass Matrices and Element Force Vector 419 14.3  Transformation of Element Matrices  430 14.4  Assembly of System Matrices: Direct Stiffness Method  438 14.5  Boundary Conditions  445 14.6  Constraints: Reduction of Degrees of Freedom  447 14.7  Systems with Rigid-Body Modes  451 14.8  Finite Element Solutions for Natural Frequencies and Mode Shapes 453 References  462 Problems  463 15 Numerical Evaluation of Modes and Frequencies of MDOF Systems 469_____________ 15.1  Introduction to Methods for Solving Algebraic Eigenproblems 469 15.2  Veclor Iteration Methods  471 15.3  Subspacc Iteration  480 15.4  QR Method for Symmetric Eigenproblems  483 15.5  Lanczos Eigensolver  489 15.6  Numerical Case Study  496 References  498 Problems 498 16 Direct Integration Methods for Dynamic Response of MDQF Systems 500_______ 16.1  Damping in MDOF Systems  501 16.2  Numerical Integration: Mathematical Framework  504 16.3  Integration of Second-Order MDOF Systems  510 16.4  Single-Step Methods and Spectral Stability  516 16.5  Numerical Case Study  525 References527 Problems 528 17  Component-Mode Synthesis531 17.1  Introduction lo Component-Mode Synthesis532 17.2  Component Modes: Normal, Constraint, and Rigid-Body Modes 534 17.3  Component Modes: Attachment and Inertia-Relief Attachment Modes  539 17.4  Flexibility Matrices and Residual Flexibility  544 17.5Substructure Coupling Procedures549 17.6  Component-Mode Synthesis Methods: Fixed-Interface Methods 557 17.7  Component-Mode Synthesis Methods: Free-Interface Methods 559 17.8  Brief Introduction to Multilevel Substructuring  564 References  571 Problems  572 Part VAdvanced Topics in Structural Dynamics577 18 Introduction to Experimental Modal Analysis579 18.1  Introduclion  580 18.2  Frequency-Response Function Representations584 18.3Vibration Test Hardware590 18.4  Fourier Transforms, Digital Signal Processing, and F:stimation of FRFs594 18.5  Modal Parameter Estimation  604 18.6  Mode Shape Estimation and Model Verification612 References 615 Problems  616 19 Introduction to Active Structures 19.1  Introduction to Piezoelectric Materials  617 19.2  Constitutive Laws of Linear Piezoelectricity620 19.3  Application of Newton's Laws to Piezostructural Systems  624 19.4  Application of Exlended Hamilton's Principle to Piezoelectricity 627 19.5  Active Truss Models630 19.6Active Beam Models  637 19.7  Active Composite Laminates  641 References  646 Problems 647 20 Introduction to Earthquake Response of Structures650 20.1  Introduction  650 20.2  Response of a SDOF System to Earthquake Excitation: Response Spectra  652 20.3  Response of MDOF Systems to Earthquake Excitation  660 20.4  Further Considerations  664 References665 Problems 666 A  Units BComplex Numbers 671 C  Elements of Laplace Transforms674 D  Fundamentals of Linear Algebra682 EIntroduction to the Use of MATI.AB 697
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