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

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

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

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

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?

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

Response To Periodic Function

Response to Periodic Excitation, Revisited

Reading the Displacement Amplification and Phase Lag Plots

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

Time-Stepping Numerical Methods

Time-Stepping Numerical Methods, Revisited

Generalized SDOF System

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

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

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

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

Structural Dynamics Review: Part I

Structural Dynamics Review: Part II

Introduction of MDOF Systems

Assembling the Equation of Motion of MDOF

Free Vibration of MDOF Systems (Eigenvalues, etc)

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