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| Foreword | |
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| Preface | |
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| Acknowledgments | |
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| Single-Degree-Of-Freedom Systems | |
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| Equations of Motion, Problem Statement, and Solution | |
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| Methods | |
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| Simple Structures | |
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| Single-Degree-of-Freedom System | |
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| Force-Displacement Relation | |
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| Damping Force | |
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| Equation of Motion: External Force | |
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| Mass-Spring-Damper System | |
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| Equation of Motion: Earthquake Excitation | |
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| Problem Statement and Element Forces | |
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| Combining Static and Dynamic Responses | |
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| Methods of Solution of the Differential Equation | |
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| Study of SDF Systems: Organization | |
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| Stiffness Coefficients for a Flexural | |
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| Element | |
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| Free Vibration | |
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| Undamped Free Vibration | |
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| Viscously Damped Free Vibration | |
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| Energy in Free Vibration | |
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| Coulomb-Damped Free Vibration | |
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| Response to Harmonic and Periodic Excitations | |
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| Viscously Damped Systems: Basic Results | |
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| Harmonic Vibration of Undamped Systems | |
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| Harmonic Vibration with Viscous Damping | |
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| Viscously Damped Systems: Applications | |
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| Response to Vibration Generator | |
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| Natural Frequency and Damping from Harmonic | |
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| Tests | |
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| Force Transmission and Vibration Isolation | |
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| Response to Ground Motion and Vibration | |
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| Isolation | |
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| Vibration-Measuring Instruments | |
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| Energy Dissipated in Viscous Damping | |
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| Equivalent Viscous Damping | |
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| Systems with Nonviscous Damping | |
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| Harmonic Vibration with Rate-Independent | |
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| Damping | |
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| Harmonic Vibration with Coulomb Friction | |
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| Response to Periodic Excitation | |
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| Fourier Series Representation | |
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| Response to Periodic Force | |
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| Four-Way Logarithmic Graph | |
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| Paper | |
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| Response to Arbitrary, Step, and Pulse Excitations | |
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| Response to Arbitrarily Time-Varying Forces | |
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| Response to Unit Impulse | |
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| Response to Arbitrary Force | |
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| Response to Step and Ramp Forces | |
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| Step Force | |
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| Ramp or Linearly Increasing Force | |
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| Step Force with Finite Rise Time | |
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| Response to Pulse Excitations | |
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| Solution Methods | |
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| Rectangular Pulse Force | |
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| Half-Cycle Sine Pulse Force | |
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| Symmetrical Triangular Pulse Force | |
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| Effects of Pulse Shape and Approximate Analysis for | |
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| Short Pulses | |
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| Effects of Viscous Damping | |
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| Response to Ground Motion | |
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| Numerical Evaluation of Dynamic Response | |
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| Time-Stepping Methods | |
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| Methods Based on Interpolation of Excitation | |
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| Central Difference Method | |
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| Newmark's Method | |
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| Stability and Computational Error | |
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| Nonlinear Systems: Central Difference Method | |
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| Nonlinear Systems: Newmark's Method | |
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| Earthquake Response of Linear Systems | |
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| Earthquake Excitation | |
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| Equation of Motion | |
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| Response Quantities | |
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| Response History | |
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| Response Spectrum Concept | |
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| Deformation, Pseudo-velocity, and Pseudo-acceleration | |
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| Response Spectra | |
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| Peak Structural Response from the Response | |
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| Spectrum | |
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| Response Spectrum Characteristics | |
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| Elastic Design Spectrum | |
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| Comparison of Design and Response Spectra | |
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| Distinction between Design and Response | |
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| Spectra | |
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| Velocity and Acceleration Response Spectra | |
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| El Centro, 1940 Ground Motion | |
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| Earthquake Response of Inelastic Systems | |
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| Force-Deformation Relations | |
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| Normalized Yield Strength, Yield Strength Reduction | |
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| Factor, and Ductility Factor | |
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| Equation of Motion and Controlling Parameters | |
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| Effects of Yielding | |
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| Response Spectrum for Yield Deformation and Yield | |
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| Strength | |
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| Yield Strength and Deformation from the Response | |
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| Spectrum | |
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| Yield Strength-Ductility Relation | |
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| Relative Effects of Yielding and Damping | |
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| Dissipated Energy | |
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| Supplemental Energy Dissipation Devices | |
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| Inelastic Design Spectrum | |
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| Applications of the Design Spectrum | |
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| Comparison of Design and Response | |
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| Spectra | |
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| Generalized Single-Degree-of-Freedom Systems | |
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| Generalized SDF Systems | |
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| Rigid-Body Assemblages | |
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| Systems with Distributed Mass and Elasticity | |
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| Lumped-Mass System: Shear Building | |
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| Natural Vibration Frequency by Rayleigh's | |
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| Method | |
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| Selection of Shape Function | |
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| Inertia Forces for Rigid Bodies | |
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| Multi-Degree-Of-Freedom Systems | |
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| Equations of Motion, Problem Statement, and Solution | |
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| Methods | |
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| Simple System: Two-Story Shear Building | |
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| General Approach for Linear Systems | |
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| Static Condensation | |
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| Planar or Symmetric-Plan Systems: Ground | |
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| Motion | |
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| One-Story Unsymmetric-Plan Buildings | |
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| Multistory Unsymmetric-Plan Buildings | |
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| Multiple Support Excitation | |
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| Inelastic Systems | |
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| Problem Statement | |
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| Element Forces | |
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| Methods for Solving the Equations of Motion: | |
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| Overview | |
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| Free Vibration | |
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| Natural Vibration Frequencies and Modes | |
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| Systems without Damping | |
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| Natural Vibration Frequencies and Modes | |
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| Modal and Spectral Matrices | |
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| Orthogonality of Modes | |
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| Interpretation of Modal Orthogonality | |
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| Normalization of Modes | |
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| Modal Expansion of Displacements | |
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| Free Vibration Response | |
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| Solution of Free Vibration Equations: Undamped | |
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| Systems | |
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| Systems with Damping | |
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| Solution of Free Vibration Equations: Classically | |
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| Damped Systems | |
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| Computation of Vibration Properties | |
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| Solution Methods for the Eigenvalue Problem | |
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| Rayleigh's Quotient | |
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| Inverse Vector Iteration Method | |
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| Vector Iteration with Shifts: Preferred Procedure | |
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| Transformation ofk � = � 2m � to the Standard | |
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| Form | |
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| Damping in Structures | |
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| Experimental Data and Recommended Modal | |
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| Damping Ratios | |
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| Vibration Properties of Millikan Library Building | |
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| Estimating Modal Damping Ratios | |
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| Construction of Damping Matrix | |
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| Damping Matrix | |
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| Classical Damping Matrix | |
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| Nonclassical Damping Matrix | |
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| Dynamic Analysis and Response of Linear Systems | |
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| Two-Degree-of-Freedom Systems | |
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| Analysis of Two-DOF Systems without Damping | |
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| Vibration Absorber or Tuned Mass Damper | |
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| Modal Analysis | |
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| Modal Equations for Undamped Systems | |
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| Modal Equations for Damped Systems | |
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| Displacement Response | |
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| Element Forces | |
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| Modal Analysis: Summary | |
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| Modal Response Contributions | |
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| Modal Expansion of Excitation Vector | |
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| p ( t ) =s p ( t ) | |
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| Modal Analysis forp ( t ) =s p ( t ) | |
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| Modal Contribution Factors | |
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| Modal Responses and Required Number of Modes | |
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| Special Analysis Procedures | |
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| Static Correction Method | |
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| Mode Acceleration Superposition Method | |
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| Mode Acceleration Superposition Method: Arbitrary | |
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| Excitation | |
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| Earthquake Analysis of Linear Systems | |
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| Response History Analysis | |
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| Modal Analysis | |
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| Multistory Buildings with Symmetric Plan | |
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| Multistory Buildings with Unsymmetric Plan | |
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| Torsional Response of Symmetric-Plan Buildings | |
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| Response Analysis for Multiple Support | |
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| Excitation | |
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| Structural Idealization and Earthquake Response | |
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| Response Spectrum Analysis | |
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| Peak Response from Earthquake Response | |
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| Spectrum | |
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| Multistory Buildings with Symmetric Plan | |
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| Multistory Buildings with Unsymmetric Plan | |
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| A Response-Spectrum-Based Envelope for | |
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| Simultaneous Responses | |
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| Response to Multi-Component Ground | |
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| Motion | |
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| Analysis of Nonclassically Damped Linear Systems | |
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| Classically Damped Systems: Reformulation | |
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| Natural Vibration Frequencies and Modes | |
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| Free Vibration | |
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| Unit Impulse Response | |
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| Earthquake Response | |
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| Nonclassically Damped Systems | |
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| Natural Vibration Frequencies and Modes | |
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| Orthogonality of Modes | |
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| Free Vibration | |
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| Unit Impulse Response | |
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| Earthquake Response | |
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| Systems with Real-Valued Eigenvalues | |
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| Response Spectrum Analysis | |
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| Summary | |
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| Derivations | |
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| Reduction of Degrees of Freedom | |
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| Kinematic Constraints | |
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| Mass Lumping in Selected DOFs | |
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| Rayleigh-Ritz Method | |
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| Selection of Ritz Vectors | |
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| Dynamic Analysis Using Ritz Vectors | |
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| Numerical Evaluation of Dynamic Response | |
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| Time-Stepping Methods | |
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| Linear Systems with Nonclassical Damping | |
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| Nonlinear Systems | |
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| Systems with Distributed Mass and Elasticity | |
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| Equation of Undamped Motion: Applied Forces | |
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| Equation of Undamped Motion: Support | |
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| Excitation | |
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| Natural Vibration Frequencies and Modes | |
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| Modal Orthogonality | |
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| Modal Analysis of Forced Dynamic Response | |
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| Earthquake Response History Analysis | |
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| Earthquake Response Spectrum Analysis | |
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| Difficulty in Analyzing Practical Systems | |
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| Introduction to the Finite Element Method | |
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| Rayleigh-Ritz Method | |
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| Formulation Using Conservation of Energy | |
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| Formulation Using Virtual Work | |
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| Disadvantages of Rayleigh-Ritz Method | |
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| Finite Element Method | |
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| Finite Element Approximation | |
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| Analysis Procedure | |
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| Element Degrees of Freedom and Interpolation | |
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| Functions | |
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| Element Stiffness Matrix | |
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| Element Mass Matrix | |
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| Element (Applied) Force Vector | |
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| Comparison of Finite Element and Exact | |