STRUCTURAL DYNAMICS
CE 72501

Course Objectives:
To provide fundamental concepts of structural dynamics, and the dynamic behavior of structures along with the underlying principles, necessary to deal with the dynamic problems of structures.

1. Introduction:
   (4 hours)
1. Time Dependent Problems.
2. Types of Dynamic Loading.
3. Degrees of Freedom
4. Simple Harmonic Motion
5. Structural Vibration
6. Damping
7. Types of Vibration
8. Response of Structures to Vibration
2. Single Degree Of Freedom (SDOF) System
   (12 hours)
1. Equations of Motion and Natural Frequency
2. Modeling of SDOF Structures
3. Undamped Free Vibration Response
4. Critically - Damped, Under - Damped and Over - Damped Systems
5. Damped Free Vibration Response
6. Logarithmic Decrement
7. Forced Harmonic Response
8. Vibration Isolation and Force Transmissibility
9. Vibration Measuring Instruments
10. Energy Dissipated by Damping
11. Forced Vibration Response to Periodic Forces
12. Forced Vibration Response to Impulsive Forces
13. Forced Vibration Response to General Dynamic Loading
14. Convolution Integral and Duhamel Integral
15. Time Domain Analysis
16. Frequency Domain Analysis
3. Multi Degree Of Freedom (MDOF) System
   (14 hours)
1. Simple MDOF Systems
2. Reduction of DOF's and Static Condensation
3. Modeling of MDOF System Structures
4. Concept of Generalized Coordinate
5. Lagrange's Equations of Motion
6. Free Vibration Analysis of Undamped MDOF System
7. Natural Vibration Frequencies and Mode Shapes
8. Modal Expansion
9. Free Vibration Response of MDOF Systems
10. Normal Coordinates and Normal Mode Theory
11. Uncoupled Equations of Motion
12. Mode Superposition Method
13. Dynamic Analysis of Linear MDOF Systems
14. Modal Response Analysis of Undamped and Damped Systems
15. Element Forces
16. Modal Contribution Factors.
17. Forced Vibration Response of MDOF System
18. Practical Methods to Determine Natural Frequencies and Mode Shapes (Rayleigh's Method, Stodola's Method, Holzer's Method)
4. Linear Dynamic Analysis for MDOF System
   (7 hours)
1. Time Domain Analysis for General Dynamic Loading
2. Frequency Domain Analysis for General Dynamic Loading
3. Frequency Domain Analysis for Support Motion
5. Continuous Systems
   (8 hours)
1. Partial Differential Equations of Motion (for String, Bar, Beam)
2. Transverse Vibration of a String
3. Transverse Vibration of a Beam
4. Axial Vibration of a Bar
5. Approximate Methods to Determine Natural Frequencies and Mode Shapes in cases where Orthogonality Conditions are not satisfied.

Tutorial/Practical:

1. Each of the students shall work on a number of individual assignments with problems following the progress of the lectures.
2. The assignments will generally be related to the application of software packages, such as FORTRAN, Matlab, Mathematica and SAP 2000.
3. All the assignments shall be submitted within the prescribed time, and will be evaluated as the practical work.

References:

1. Clough R. W., Penzien 3, "Dynamics of Structures", McGraw Hill.
2. Chopra A. K., "Dynamics of Structures : Theory and Applications to Earthquake Engineering", Prentice Hall.
3. Paz, M.,and Leigh, W., "Dynamics of Structures- Theory and Computation", Kluwer Academic Publisher.,
4. Thompson, W. T., "Theory of Vibration with Applications", Prentice-Hall.

Evaluation Scheme:
The questions will cover all the chapters in the syllabus. The evaluation scheme will be as indicated in the table below:

Chapter	Hours	Marks Distribution*
1	4	4
2	12	24
3	14	28
4	7	12
5	8	12
Total	45	80

*There could be minor deviation in mark distribution.