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Course curriculum

  • 1

    Introduction and Concepts

    • Introduction to Structural Dynamics

    • Introduction: Dynamic Equilibrium

    • Introduction: Introductory Examples

    • Introduction: Frame-Element Stiffness Coefficients

  • 2

    Fundamentals of Dynamics

    • Fundamentals: Introduction

    • Fundamentals: Equation of Motion

    • Fundamentals: Assembling a Mass Matrix

    • Fundamentals: Assembling a Damping Matrix

    • Fundamentals: Assembling a Stiffness Matrix

    • Fundamentals: Introduction of Static Condensation

    • Fundamentals: Converting N Equations to Matrices

    • Fundamentals: Earthquake Excitation

  • 3

    Structural-Analysis and Matrix Fun

    • Assembling an Element Stiffness Matrix

    • Assembly of the Stiffness Matrix for a Portal Frame with Mixed Boundary Conditions

    • Assembling a Frame Stiffness Matrix

    • Assembling the full 12x12 Stiffness Matrix of a Portal Frame

    • More Stiffness-Matrix Fun

    • Partitions and Condensation of the Stiffness Matrix

    • Degrees of Freedom: Truss System vs. Frame system

  • 4

    Free-Vibration Response of Undamped SDOF

    • Free-Vibration Response of a SDOF System

    • Solving Ordinary Differential Equations (ODE)

    • Solving the Equation of Motion (EOM) as an ODE

    • Free-Vibration Response of Undamped SDOF

    • Natural Frequency/Period of Vibration

    • Free-Vibration Response of Undamped SDOF -- Review

  • 5

    Free-Vibration Response of Damped SDOF

    • Free-Vibration Response of Damped SDOF System: Introduction

    • Free-Vibration Response of Underdamped SDOF System

    • Free-Vibration Response of Critically-Damped SDOF System

    • Free-Vibration Response of Overdamped SDOF System

    • Logarithmic Decay in Free Vibration of Damped SDOF System

    • Summary of Free-Vibration Response of Undamped and Damped SDOF System

    • Coulomb Damping

  • 6

    Forced-Vibration Response of SDOF -- Constant Force

    • Forced-Vibration Response: Review of Free-Vibration Response and ODEs

    • Forced-Vibration Response: Solution to ODE

    • Forced-Vibration Response: Constant-Force Excitation

    • Response to Constant Force, Revisited

    • Forced-Vibration Response: Static vs. Dynamic Problem

    • How Do You Compute the Damping Ratio from the Response?

  • 7

    Forced-Vibration Response of SDOF -- Harmonic Excitation

    • Forced-Vibration Response -- Harmonic Force, Undamped SDOF

    • Forced-Vibration Response -- Harmonic Force, Undamped SDOF

    • Forced-Vibration Response -- Harmonic Force, Damped SDOF

    • Forced-Vibration Response -- Harmonic Force, Undamped SDOF, Revisited

    • Forced-Vibration Response -- Harmonic Force, Damped SDOF, Revisited

    • Forced-Vibration Response -- Applications of Harmonic Excitation

    • Forced-Vibration Response -- Energy Concepts

    • Forced-Vibration Response -- More Applications of Harmonic Excitation

    • Response to Harmonic Excitation, Revisited

  • 8

    Forced-Vibration Response of SDOF -- Periodic Excitation

    • Response To Periodic Function

    • Response to Periodic Excitation, Revisited

    • Reading the Displacement Amplification and Phase Lag Plots

  • 9

    Forced-Vibration Response of SDOF -- Arbitrary Time-Varying Excitation

    • Response to Arbitrary Time-Varying Force

    • Response to Arbitrary Time-Varying Force, Revisited

    • Response To Pulse Excitation, Part I

    • Response To Pulse Excitation, Part II

    • Review of Response to Arbitrary Time-Varying Excitation

    • Response to Pulse Excitation

    • Response to Pulse Excitation Example: Square Pulse

  • 10

    Numerical Methods

    • Time-Stepping Numerical Methods

    • Time-Stepping Numerical Methods, Revisited

  • 11

    Generalized SDOF System

    • Generalized SDOF System

  • 12

    Dynamics of Multiple-Degree-Of-Freedom Systems (MDOF)

    • First View of Dynamics of MDOF

    • Dynamics of MDOF Systems, Fundamentals: Developing the Equation of Motion

    • Dynamics of MDOF Systems, Fundamentals: Developing the Equation of Motion, Revisited

    • MDOF Systems: Static Condensation

    • MDOF Systems: Static Condensation, Revisited

    • MDOF Systems: Ground-Motion Input

    • StructuralDynamics_SilviaMazzoni_OverviewofMDOF

    • MDOF Systems: Modes of Vibration, Eigenvalues, & Eigenvectors

    • MDOF Systems: Free-Vibration Response & The Eigenvalue Problem

    • MDOF Systems: Free-Vibration Response & The Eigenvalue Problem, Revisited

  • 13

    Free-Vibration Response of MDOF

    • Free-Vibration Response of MDOF System: Undamped

    • Free-Vibration Response of MDOF System: Example of Undamped System

    • Free-Vibration Response of MDOF System: Damped System

    • Free-Vibration Response of MDOF System: Damped System, continued

    • Free-Vibration Response of MDOF System: Assembling the Damping Matrix

  • 14

    Forced-Vibration Response of MDOF Systems

    • Forced-Vibration Response of MDOF

    • Forced-Vibration Response of MDOF -- Example

    • Modal Expansion of the Excitation Vector

    • MDOF-System Response Demos..... and an Introduction to the Response Spectrum

    • Modal Expansion of the Excitation Vector, Revisited

  • 15

    Dynamic Response to Ground Motions

    • Modal Analysis of Ground-Motion Excitation

    • Response-Spectrum Analysis

    • Review of the Response Spectrum

    • Introduction to Design Spectra

    • Question: Is PSA the equal to Relative Acceleration?

    • Question: Is Fourier Spectrum the same as Response Spectrum?

    • Question: Why do we use 5% as the Default Value for Damping??

    • Response-Spectrum Analysis for MDOFs

  • 16

    Structural Dynamics Review

    • Structural Dynamics Review: Part I

    • Structural Dynamics Review: Part II

  • 17

    Old Lectures From 1999 on MDOF Systems

    • Introduction of MDOF Systems

    • Assembling the Equation of Motion of MDOF

    • Free Vibration of MDOF Systems (Eigenvalues, etc)

  • 18

    ALL Lecture Notes

    • StrxDyn00-CoverPage

    • StrxDyn01-Introduction

    • StrxDyn02a-FundamentalsReview

    • StrxDyn02b-FundamentalsReview -- StiffnessMatrix

    • StrxDyn02c-FundamentalsReview -- FourierSeries

    • StrxDyn03-FreeVibrationResponse

    • StrxDyn04-FreeVibrationResponse_Damped

    • StrxDyn05a-ForcedVibrationResponse_ConstForce

    • StrxDyn05b-ForcedVibrationResponse_Harmonic_Undamped

    • StrxDyn06-ForcedVibrationResponse_Harmonic

    • StrxDyn07a-ForcedVibrationResponse_HarmonicApplications

    • StrxDyn07b-ForcedVibrationResponse_moreHarmonicApplications

    • StrxDyn07c-ForcedVibrationResponse_EnergyConcepts

    • StrxDyn08a-ForcedVibrationResponse_PeriodicExcitation

    • StrxDyn08b-ForcedVibrationResponse_PeriodicExcitationExamples

    • StrxDyn09-ForcedVibrationResponse_ArbitraryTimeVaryingforce

    • StrxDyn10a-ResponseToPulse

    • StrxDyn10b-ResponseToArbitrary_Summary

    • StrxDyn11a-NumericalMethods

    • StrxDyn11b-NumericalMethodsSummary

    • StrxDyn12-GeneralizedSDOF

    • StrxDyn13a-MDOFsystems

    • StrxDyn13b-MDOFsystems_GroundMotions

    • StrxDyn14a-MDOFsystems

    • StrxDyn14b-MDOF_EigenvalueProblem

    • StrxDyn15-MDOF_unsymmPlan

    • StrxDyn16-MDOFfreeVib

    • StrxDyn17-MDOFfreeVib

    • StrxDyn18-MDOFmodalAnalysis

    • StrxDyn19-MDOFmodalExpansionOfExcitation

    • StrxDyn20-MDOFgroundExcitation

    • StrxDyn21-ResponseSpectrumAnalysis

    • StrxDyn22-MDOF_ResponseSpectrumAnalysis

    • StrxDyn23-DesignSpectra

    • StrxDyn101-PartI_SDOF_ReviewSummary

    • StrxDyn102-PartII_FinalReviewSummary