16.221 Structural Dynamics (Fall '99)



Dr. Mauro J. Atalla (instructor) 37-331, x8-5920, mjatalla@mit.edu

Prof. Carlos Cesnik (instructor) 33-313, x2-1518, ccesnik@mit.edu

Mary C. Jones (course secretary) 37-315, x2-1536, mcj@mit.edu


Monday, Wednesday, and Friday 10:00-11:00 Rm. 33-419

Course web page


http://command.mit.edu (to register)

Course Prerequisites

The prerequisite is 16.20 (or equivalent), from where the student is expected to be familiar with fundamental concepts of three-dimensional elasticity, two-dimensional plane stress and plane strain problems, classical beam theory, and fundamentals of beam vibration.

Course Objectives/Philosophy

This course will address issues related to the dynamical behavior of elastic structures (interaction of elastic and inertial forces). It also introduces students to the concepts and tools used in structural dynamics. It is intended that the student will become familiar with the important issues and philosophies associated with dynamic response, will become conversant in the terminology of structural dynamics, and will achieve a working understanding of these issues applied to various aeronautical systems.


Principles and Techniques of Vibration by Meirovitch is the main book for reference. Complementary, a list of references related to the course material is provided, and some of them are also on reserve in the Aero & Astro Library.

Course Requirements/Grading

There will be three types of assignments during the term: problem sets, a course project and quizzes. No final exam is schedule for this subject. There will be approximately six problem sets during the term. These will be handed out on a relatively regular basis and it is expected that the assignments will be handed in on time.


There will be two quizzes during the term at approximately mid-term and last week of classes. Several days will be given for the completion of the exam. The exact handout and due dates will be announced at least two weeks prior to the exam.


Late submissions of problem sets and quizzes will be docked 25% before the solutions are handed out, and they will be corrected but not graded afterwards. They can be delayed or rescheduled for very good reason by prior arrangements.


Regarding the presentation of information, the clarity and "neatness" of it are very important for this class as they are for the engineers' professional life. For the assignments that involve the use of computer programming, the printouts should be attached but they will not count as a source for key information to the solution of the given assignment. So, make sure that all the steps are described in the main text along with the results.


The final grade will be calculated as follows:

Attendance, participation, general evaluation 5%

The course will be graded on an absolute scale using the letter grades as defined in the MIT Faculty Rules and Regulations:

A - Exceptionally good performance, demonstrating a superior understanding of the subject matter, a foundation of extensive knowledge and a skillful use of concepts and/or materials.

B - Good performance, demonstrating capacity to use the appropriate concepts, a good understanding of the subject matter, and an ability to handle the problems and materials encountered in the subject.

C - Adequate performance, demonstrating an adequate understanding of the subject matter, an ability to handle relatively simple problems, and adequate preparation for moving on to more advanced work in the field.

D - Minimally acceptable performance, demonstrating at least partial familiarity with the subject matter and some capacity to deal with relatively simple problems, but also demonstrating deficiencies serious enough to make it inadvisable to proceed further in the field without additional work.

F - Unsatisfactory performance.

Plusses and minuses will be used in conjunction with the letters in grading term-time work, as well as the final grade.

Office Hours

Dr. Atalla can be consulted by appointment. In addition, the time immediately after class is a good opportunity to get answers to quick questions.


The topics to be covered during the term will deal with single and multiple degree-of-freedom systems; continuous systems: bars, strings, rods, beams, plates; variational principles in dynamics: Hamilton's Principle, Lagrange's equations; formulation and application of diverse methods: Galerkin, integral equation, numerical collocation; and self-excited vibrations. A post factum syllabus will be handed out at the end of the term.

Academic Honesty

It is expected that the submission of each student represents the work of that, and only that, individual student. Students should feel free to consult each other, as well as the course faculty, in developing solutions to problem sets. However, it is expected that the final submission represents the effort of only that student. No consultation with fellow students is allowed on the take-home examinations.

Any material used from another source or person must be properly referenced. An individual   engineer/reviewer/researcher does not need to come up with all the ideas. In fact, a good engineer knows how to incorporate the good ideas and thoughts of others. However, it is essential to "give credit where credit is due".

Cases of academic dishonesty are a severe breach of the student's and engineer's codes and will be treated appropriately.


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