Links to lessons

The links to the slides etc will be posted below

  • 2010-06-24, Non-linear Response to Earthquake Excitation, Response Spectra.
  • 2010-06-17, Linear Response to Earthquake Excitation, Response Spectra.
  • 2010-06-03, Continuous systems with an infinite number of degrees of freedom.
  • 2010-05-27, Derived Ritz Vectors, Direct Numerical Integration, Multiple Support Excitation.
  • 2010-05-20, Matrix Iteration, end. Modal Contributions and Truncation Errors analysis. Static Correction Procedure.
  • 2010-05-13, Superposition. Matrix Iteration.
  • 2010-05-06, Structural matrices. Properties, additional orthogonality properties, assemblage of, static condensation.
  • 2010-04-29, MDOF systems, vector formulations, eigenvalues and eigenvectors, modal coordinates and uncoupling, exercises.
  • 2010-04-22, rigid body assemblages, SDOF models of flexible systems, Rayleigh's quotient.
  • 2010-04-15, step by step methods, stability, non-linearity, modified Newton-Raphson. Homework with support material.
  • 2010-04-08, Fourier Tranforms, DFT's and FFT's, frequency response and impulse response are a Fourier pair.
  • 2010-04-01, Easter Holidays!
  • 2010-03-25, SDOF response to periodic and general loadings, Fourier Series and Duhamel Integral, home assignment.
  • 2010-03-18, response to sinusoidal excitation and applications. Blackboard exercises of 3/11 and 3/18 available.
  • 2010-03-11, an intro to dynamics, the SDOF linear oscillator, free vibrations.

Solutions and grades for the summer assignment

The solutions of the exercises in the summer assigment are finally online (I had to wait until I was sure that no one would make a late submission for the last session of exams).

The grades are as follows: mat. 708980 is under 90 points, mat. 708980 133/150. Other submissions were previously discussed face à face.

September is very close!

The summer assignment is here to download. This assignment is for (a) all the people who have not submitted assignment number 1 and (b) all the people who desire to better the degrees they got for the 1st assignment.

Please tell me about any problem you have in understanding the text of the problems.

September is nearing

All the students that have not submitted the 1st home assignment shall submit a different home assignment, that will be posted here sometimes before friday 23th of July. Details of the submission will be given in the text of the assignment

Multiple support excitation

As a stop gap measure, i post a link to the notes of the lesson i gave in 2008-09. The material covered is the same as this year lesson, the format of the file is a bit unusual, so you need a specific plugin to read the notes

1st Home Assignment Results

I have mailed to all interested parties the file with your results. In case somebody finds a problem with the attachment, i post here the results.

Home assignment number two

The text of the second home assignment are available. You must submit your solutions when you substain your oral examination.

The corrections of the first assignment are almost finished, I'll post the results here tomorrow.

Home assignment solutions

The solutions of the first home assignment are available [2010-06-15].

Corrections and graduations proceed slowly. I hope to publish the results before the end of the month.

Red Alert

The first home assignment is out! The assignment is due on thursday 3rd of June and is now available here.

Introduction

The course deals with the dynamical response of mechanical systems, linear and non-linear, under the assumption of small displacements.

Focus is given to analytical and numerical methods for the integration of the equations of motion, both in time and in frequency domain, to the numerical methods for the eigen-analysis of multiple degrees of freedom systems and to earthquake engineering applications.

Classes include tutorials and computational exercises.

During the semester, you'll be given two home assignments, the first one approximately in mid may, the second at the end of the lessons. Your degree will be based on the home assignments and on a final oral exam.

The slides i use in classes will be made available on this page in a short time after the classes, but older versions of the slides are already available, as i taught the same course, more or less the same course, in the previous academic years, and if you want to peek at the material i posted during the previous year, 2008-2009, it is still on line.

Similar materials regarding the 2007-2008 course were put in the attic but are still available should you need it.

Recommended books

  • Ray W,Clough, Joseph Penzien, Dynamics of Structures.

    Please note that the standard 2nd edition is out of press, but the link points to a software house that has bought the rights and issued a revised edition of the classic book by Clough and Penzien.
  • Anil K.Chopra, Dynamics of Structures (Theory and Applications to Earthquake Engineering), 3rd ed.

    A number of copies of this book are available from the campus library in Lecco.

    Should you find a hugely discounted used copy of the 2nd edition of prof. Chopra's book, don't worry and buy it, the 2nd ed. is good enough for our purposes.

90% of the material you'll see in the first part of the course is inspired from Clough and Penzien's book, 90% of the material of the second part of the course from Chopra's.

While it is very easy to follow the first part of the course using Chopra as your reference (the difference being in some notational convention and a more liberal use of examples in Chopra), following the second part of the course using the book from Clough and Penzien as a reference may be difficult.

In short, should you prefer to buy a single book, buy Chopra's.

Home assignments

In general, the home assignments that you're supposed to do require no more than paper, pencil and a hand-held calculatur (or a decent spreadsheet program, Excel or OpenOffice Calc the names that spring to mind...)

Of course, anything more sophisticated than Excel (think of Mathematica and Matlab, or of Matlab's free clone Octave) can be helpful.

When i work preparing and solving the assignments, my setup comprises:

  • Calc, an advanced calculator and mathematical tool that runs as part of the GNU Emacs environment, that i use for its capabilities in symbolic manipulation of matrices and symbolic derivation and integration. It's not Mathematica, and it's very different from Mathematica, but it's useful and free.
  • Emacs itself, the extensible, customizable, self-documenting real-time display editor.
  • Scipy, a library of scientific tools for the programming language Python, i prefer using a set of libraries from inside a full blown programming language (Python) than an ad hoc one (Matlab, Octave). Of course, Matlab has different assets... (toolkits, i.e.)
  • Python itself, an interpreted, interactive, object-oriented, extensible programming language.
  • Gnuplot, a command-line driven interactive data and function plotting utility, for 2- and 3-D graphs, Gnuplot does also parametric plots, model fitting and something more.

Giacomo Boffi