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.


  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.


  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:



Marks Distribution*



















*There could be minor deviation in mark distribution.

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