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| Preface to Structural Dynamics-An Introduction to Computer Methods | |
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| Preface to Fundamentals of Structural Dynamics | |
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| About the Authors | |
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| The Science and Art of Structural Dynamics | |
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| Introduction to Structural Dynamics | |
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| Modeling of Structural Components and Systems | |
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| Prototype Spring-Mass Model | |
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| Vibration Testing of Structures | |
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| Scope of the Book | |
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| Computer Simulations; Supplementary Material on the Website | |
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| References | |
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| Problems | |
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| Single-Degree-of-Freedom Systems | |
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| Mathematical Models of SDOF Systems | |
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| Brief Review of the Dynamics of Particles and Rigid Bodies | |
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| Elements of Lumped-Parameter Models | |
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| Application of Newton's Laws to Lumped-Parameter Models | |
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| Application of the Principle of Virtual Displacements to Lumped-Parameter Models | |
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| Application of the Principle of Virtual Displacements to Continuous Models: Assumed-Modes Method | |
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| References | |
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| Problems | |
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| Free Vibration of SDOF Systems | |
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| Free Vibration of Undamped SDOF Systems | |
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| Free Vibration of Viscous-Damped SDOF Systems | |
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| Stability of Motion | |
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| Free Vibration of an SDOF System with Coulomb Damping | |
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| Experimental Determination of the Natural Frequency and Damping Factor of an SDOF System | |
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| References | |
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| Problems | |
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| Response of SDOF Systems to Harmonic Excitation | |
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| Response of Undamped SDOF Systems to Harmonic Excitation | |
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| Response of Viscous-Damped SDOF Systems to Harmonic Excitation: Frequency-Response Functions | |
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| Complex Frequency Response | |
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| Vibration Isolation: Force Transmissibility and Base Motion | |
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| Vibration Measuring Instruments: Accelerometers and Vibrometers | |
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| Use of Frequency-Response Data to Determine the Natural Frequency and Damping Factor of a Lightly Damped SDOF System | |
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| Equivalent Viscous Damping | |
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| Structural Damping | |
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| References | |
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| Problems | |
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| Response of SDOF Systems to Nonperiodic Excitation | |
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| Response of a Viscous-Damped SDOF System to an Ideal Step Input | |
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| Response of Undamped SDOF Systems to Rectangular Pulse and Ramp Loadings | |
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| Response of Undamped SDOF Systems to a Short-Duration Impulse: Unit Impulse Response | |
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| Response of SDOF Systems to General Dynamic Excitation: Convolution Integral Method | |
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| Response Spectra | |
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| System Response by the Laplace Transform Method: System Transfer Function | |
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| References | |
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| Problems | |
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| Numerical Evaluation of the Dynamic Response of SDOF Systems | |
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| Integration of Second-Order Ordinary Differential Equations | |
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| Integration of First-Order Ordinary Differential Equations | |
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| Nonlinear SDOF Systems | |
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| References | |
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| Problems | |
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| Response of SDOF Systems to Periodic Excitation: Frequency-Domain Analysis | |
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| Response to Periodic Excitation: Real Fourier Series | |
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| Response to Periodic Excitation: Complex Fourier Series | |
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| Response to Nonperiodic Excitation: Fourier Integral | |
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| Relationship Between Complex Frequency Response and Unit Impulse Response | |
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| Discrete Fourier Transform and Fast Fourier Transform | |
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| References | |
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| Problems | |
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| Multiple-Degree-of-Freedom Systems-Basic Topics | |
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| Mathematical Models of MDOF Systems | |
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| Application of Newton's Laws to Lumped-Parameter Models | |
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| Introduction to Analytical Dynamics: Hamilton's Principle and Lagrange's Equations | |
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| Application of Lagrange's Equations to Lumped-Parameter Models | |
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| Application of Lagrange's Equations to Continuous Models: Assumed-Modes Method | |
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| Constrained Coordinates and Lagrange Multipliers | |
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| References | |
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| Problems | |
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| Vibration of Undamped 2-DOF Systems | |
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| Free Vibration of 2-DOF Systems: Natural Frequencies and Mode Shapes | |
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| Beat Phenomenon | |
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| Additional Examples of Modes and Frequencies of 2-DOF Systems: Assumed-Modes Models | |
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| Free Vibration of Systems with Rigid-Body Modes | |
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| Introduction to Mode Superposition: Frequency Response of an Undamped 2-DOF System | |
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| Undamped Vibration Absorber | |
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| Reference | |
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| Problems | |
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| Vibration Properties of MDOF Systems: Modes, Frequencies, and Damping | |
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| Some Properties of Natural Frequencies and Natural Modes of Undamped MDOF Systems | |
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| Model Reduction: Rayleigh, Rayleigh-Ritz, and Assumed-Modes Methods | |
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| Uncoupled Damping in MDOF Systems | |
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| Structures with Arbitrary Viscous Damping: Complex Modes | |
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| Natural Frequencies and Mode Shapes of Damped Structures with Rigid-Body Modes | |
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| References | |
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| Problems | |
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| Dynamic Response of MDOF Systems: Mode-Superposition Method | |
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| Mode-Superposition Method: Principal Coordinates | |
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| Mode-Superposition Solutions for MDOF Systems with Modal Damping: Frequency-Response Analysis | |
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| Mode-Displacement Solution for the Response of MDOF Systems | |
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| Mode-Acceleration Solution for the Response of Undamped MDOF Systems | |
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| Dynamic Stresses by Mode Superposition | |
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| Mode Superposition for Undamped Systems with Rigid-Body Modes | |
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| References | |
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| Problems | |
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| Continuous Systems | |
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| Mathematical Models of Continuous Systems | |
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| Applications of Newton's Laws: Axial Deformation and Torsion | |
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| Application of Newton's Laws: Transverse Vibration of Linearly Elastic Beams (Bernoulli-Euler Beam Theory) | |
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| Application of Hamilton's Principle: Torsion of a Rod with Circular Cross Section | |
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| Application of the Extended Hamilton's Principle: Beam Flexure Including Shear Deformation and Rotatory Inertia (Timoshenko Beam Theory) | |
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| References | |
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| Problems | |
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| Free Vibration of Continuous Systems | |
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| Free Axial and Torsional Vibration | |
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| Free Transverse Vibration of Bernoulli-Euler Beams | |
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| Rayleigh's Method for Approximating the Fundamental Frequency of a Continuous System | |
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| Free Transverse Vibration of Beams Including Shear Deformation and Rotatory Inertia | |
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| Some Properties of Natural Modes of Continuous Systems | |
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| Free Vibration of Thin Flat Plates | |
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| References | |
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| Problems | |
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| Computational Methods in Structural Dynamics | |
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| Introduction to Finite Element Modeling of Structures | |
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| Introduction to the Finite Element Method | |
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| Element Stiffness and Mass Matrices and Element Force Vector | |
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| Transformation of Element Matrices | |
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| Assembly of System Matrices: Direct Stiffness Method | |
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| Boundary Conditions | |
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| Constraints: Reduction of Degrees of Freedom | |
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| Systems with Rigid-Body Modes | |
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| Finite Element Solutions for Natural Frequencies and Mode Shapes | |
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| References | |
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| Problems | |
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| Numerical Evaluation of Modes and Frequencies of MDOF Systems | |
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| Introduction to Methods for Solving Algebraic Eigenproblems | |
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| Vector Iteration Methods | |
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| Subspace Iteration | |
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| QR Method for Symmetric Eigenproblems | |
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| Lanczos Eigensolver | |
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| Numerical Case Study | |
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| References | |
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| Problems | |
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| Direct Integration Methods for Dynamic Response of MDOF Systems | |
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| Damping in MDOF Systems | |
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| Numerical Integration: Mathematical Framework | |
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| Integration of Second-Order MDOF Systems | |
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| Single-Step Methods and Spectral Stability | |
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| Numerical Case Study | |
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| References | |
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| Problems | |
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| Component-Mode Synthesis | |
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| Introduction to Component-Mode Synthesis | |
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| Component Modes: Normal, Constraint, and Rigid-Body Modes | |
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| Component Modes: Attachment and Inertia-Relief Attachment Modes | |
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| Flexibility Matrices and Residual Flexibility | |
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| Substructure Coupling Procedures | |
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| Component-Mode Synthesis Methods: Fixed-Interface Methods | |
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| Component-Mode Synthesis Methods: Free-Interface Methods | |
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| Brief Introduction to Multilevel Substructuring | |
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| References | |
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| Problems | |
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| Advanced Topics in Structural Dynamics | |
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| Introduction to Experimental Modal Analysis | |
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| Introduction | |
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| Frequency-Response Function Representations | |
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| Vibration Test Hardware | |
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| Fourier Transforms, Digital Signal Processing, and Estimation of FRFs | |
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| Modal Parameter Estimation | |
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| Mode Shape Estimation and Model Verification | |
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| References | |
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| Problems | |
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| Introduction to Active Structures | |
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| Introduction to Piezoelectric Materials | |
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| Constitutive Laws of Linear Piezoelectricity | |
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| Application of Newton's Laws to Piezostructural Systems | |
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| Application of Extended Hamilton's Principle to Piezoelectricity | |
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| Active Truss Models | |
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| Active Beam Models | |
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| Active Composite Laminates | |
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| References | |
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| Problems | |
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| Introduction to Earthquake Response of Structures | |
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| Introduction | |
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| Response of a SDOF System to Earthquake Excitation: Response Spectra | |
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| Response of MDOF Systems to Earthquake Excitation | |
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| Further Considerations | |
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| References | |
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| Problems | |
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| Units | |
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| Complex Numbers | |
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| Elements of Laplace Transforms | |
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| Fundamentals of Linear Algebra | |
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| Introduction to the Use of Matlab | |
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| Index | |