Course Outline

1.General Introduction (Lecture 1)

a.Fundamental Objectives

b.Types of Loads

c.Method of Discretization

d.Equation of Motion

2.Review of Fundamentals (Lecture 2)

a.Assembling a Stiffness Matrix

b.Linear Algebra

c.Solving Differential Equations

d.Fourier Series

3.Free Vibration Single Degree of Freedom Systems (with and without damping) (Lecture 3-4)

a.Components and Equation of Motion (EOM) of Dynamic Systems

b.Definition of natural frequency/period

c.Influence of gravitational forces

d.Influence of support excitation

e.Simple harmonic motion

f.Undamped Free Vibration

g.Damped Free Vibration

4.Response to harmonic loading (Lecture 5-6)

a.Undamped systems, damped systems

b.Resonant response

c.Accelerometers and displacement meters

d.Vibration Isolation, Evaluation of damping in SDOF

5.Response to Periodic loading (Lecture 7-8)

a.Fourier Series expression of the loading

b.Response to Fourier Series loading

c.Exponential form of Fourier series solution

6.Response to impulsive loads (Lecture 9-10)

a.General nature

b.sine-wave impulses

c.rectangular pulses

d.Shock (or response) spectra, Approximate analysis

7.Response to general dynamic loading (Lecture 11-12)

a.Time domain: Duhamel integral for undamped systems

b.Numerical evaluation

c.Response of damped system

8.Formulation of MODF EOM and evaluation of matrices (Lecture 13-14)

a.Dynamic equilibrium conditions

b.Axial-force effects

c.Elastic properties

d.Mass properties

e.Static condensation

f.Damping properties

9.MDOF of undamped free vibration (Lecture 15-16)

a.Vibration frequencies

b.vibration mode shapes

c.Flexibility formulation

d.Orthogonality conditions

10.MDOF analysis of dynamic response: superposition (Lecture 17-18)

a.Normal coordinates

b.Uncoupled equations of motion (undamped)

c.Proportional viscous damping matrices

d.Uncoupled equations of motion (damped)

e.Linear modal superposition procedures

11.Earthquake Analysis (Lecture 19-20)

a.Numerical Methods

b.Response Spectra

c.Modal Analysis