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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 | |