CE G551 Dynamics of Structures

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Course info

Credit: 3 Units (3-0-0).

Instructor: Dr. Md Rushdie Ibne Islam and Dr. Subhasis Pradhan, Email: rushdie.islam@pilani.bits-pilani.ac.in, Office: 1212-A (FD-I, first floor).

Class timings:

• Lecture: Monday, Tuesday, and Thursday (11 AM - 11.50 AM); 1220 (FD-I, first floor)

TAs: Will be announced later.

Office hours: Either stop by instructor's office (for quick discussion) or take an email appointment (for longer discussion).

Important note: Please include CEG551 (without space) in the subject line for all email communications related to this course.

Syllabus

• Part I: Introduction and Fundamentals
  • Introduction and scope of dynamic analysis of structures.
  • Origins of vibration theory and experiments.
  • Review of earlier concepts: d’Alembert’s principle, equations of motion.
• Part II: Fundamentals of Dynamics
  • Structural elements – springs, dashpots, and masses.
  • Springs in parallel and series configuration.
  • Methods for formulating equations of motion.
• Part III: Free Vibration Analysis of SDOF Systems
  • Equation of motion and solution for undamped and damped free vibration.
• Part IV: Forced Vibration Analysis of SDOF Systems
  • Equation of motion and solution for undamped and damped forced vibration.
• Part V: General Dynamic Loading and Response
  • Forced vibration under harmonic, periodic, impulse, step, ramp, and general dynamic forces (time and frequency domain analysis).
  • Response spectrum loading, support excitation, seismic pickups.
• Part VI: Numerical Methods for Dynamic Response
  • Numerical techniques for SDOF systems: time domain analysis, direct integration, finite difference (Central Difference Method), Newmark-β method, average and linear acceleration methods.
• Part VII: Analysis of Two Degree of Freedom (2DOF) Systems
  • Development of equations of motion for 2DOF systems.
  • Analytical solutions and response behavior.
• Part VIII: Free Vibration Analysis of MDOF Systems
  • Eigenvalue problem for lumped MDOF systems; frequencies, mode shapes, and response analysis.
  • Orthogonality of mode shapes.
• Part IX: Eigenvalue Solution Techniques
  • Approximate methods – Holzer, Stodola, Rayleigh, and Rayleigh–Ritz methods.
  • Inverse iteration, vector iteration, Rayleigh quotient iteration, matrix iteration techniques.
• Part X: Forced Vibration of MDOF Systems
  • Damping matrix generation; modal damping, classical damping.
  • Damped response analysis using Rayleigh and Caughey damping.
  • Mode superposition and mode acceleration methods.
  • Modal combination rules: Absolute Sum, SRSS, and CQC.
  • Response spectrum analysis and brief on continuous systems.
• Please see course handout for details.

References

• Primary
  • Chopra, A.K. Dynamics of Structures: Theory and applications to earthquake engineering.
• Additional
  • Clough, R.W. and Penzien, J. Dynamics of Structures.

Grading

• Quiz #1: 10%
• Mid semester exam: 30%
• Quiz #2: 10%
• Comprehensive exam: 30%
• Assignments: 10%
• Term paper: 10%

Quizzes, mid semester and comprehensive exams

• Two quizzes will be conducted; one (quiz #1) before and another (quiz #2) after the minor exam. Exact date, time and place will be notified later.
• Mid semester and comprehensive exams will be scheduled based on the institute timetable.

Homework

• Homework will be assigned almost every week. These will not be graded. Hence, submission is not necessary.
• Students are strongly encouraged to try the homework problems.

Make-up policy

• If the student is unable to appear for the Regular Test/Examination due to genuine exigencies, the student must refer to the procedure for applying for Make-up Test/Examination. No make up for the assignments.
• Academic honesty and integrity are to be maintained by all the students throughout the semester and no type of academic dishonesty is acceptable.