Links to lessons

You can access the material that i used in my classes following the links (in white) that I will post below.

  • 2013-06-11 Applications to Earthquake Engineering: Response Spectra, Design Spectra, Ductility Spectra.
  • 2013-06-04 Continuous systems with an infinite number of degrees of freedom.
  • 2013-05-28 Derived Ritz Vectors, Direct Numerical Integration, Multiple Support Excitation.
  • 2013-05-21:
    Matrix Iteration Repeat, Modal Contributions and Static Correction,
    • Recall onRitz-Rayleigh and Subspace Iteration
    • Modal Partecipation Factor
    • Modal contributions to the load vector
    • Modal contributions to pseudo-static response
    • Pseudo-displacements
    • Peak factors
    • Static correction
  • 2013-05-14:
    Superposition repeat, Matrix Iteration
    • a first approach to the issue with modal truncation errors
    • the idea of Matrix Iteration
    • convergence to 1st eigenvector/value
    • forcing convergence to higher mode, sweeping matrix
    • a first optimization, inverse iteration
    • the shifted eigenvalue problem
    • Rayleigh-Ritz procedure
  • 2012-05-07:
    Structural Matrices in multi DOF systems
    • further relationships of orthogonality
    • flexibility and stiffness
    • strain energy, symmetry
    • mass matrix, consistent or lumped>
    • damping matrix by linear combination
    • static condensation procedure
  • 2013-04-30:
    Multiple DOF systems
    • equations of dynamic equilibrium
    • vector equation of equilibrium, matrix formulation
    • homogeneous equation, eigenvalues and eigenvectors
    • vector orthogonality
    • modal expansion, uncoupled equations of motion
  • 2013-04-16:
    Generalized SDOF
    • articulated rigid bodies, generalised properties
    • separation of variables, deformable bodies
    • Rayleigh method
    • Rayleigh method's refinement
  • 2013-04-09:
    Step by step integration of the EOM
    • Piecewise exact integration
    • Explicit methods (central differences)
    • Implicit methods (Newmark Beta family)
    • Modified Newton-Raphson algorithm
  • 2013-03-26:
    Impulsive loads, intro to Step by Step methods
    • Impulsive Loads
    • definition, usual assumptions,
    • analytical solutions,
    • approximate analysis.
      •
    • Step by Step Methods
    • general discussion, pro"cons,
    • e.g., the piecewise linear method
      •
  • 2013-03-19:
    Response to Periodic and Non-Periodic Loading
    • Analysis in the frequency domain, Fourier Series and Fourier Transform, Discrete Fourier Transform and Aliasing, fast algorithm for DFT (FFT).
    • Analysis in the time domain, Duhamel integral, relationship between the two solutions.
  • 2013-03-12:
    Response to Harmonic Loading
    • undamped response, dynamic amplification factor, resonant response
    • damped response
    • accelerometer
    • vibration isolation
    • measuring equivalent damping ratio
  • 2013-03-05:
    Introduction - Free Vibrations
    • An introduction to dynamics of structures,
    • the single degree of freedom (SDOF) linear oscillator,
    • the free vibrations of SDOF oscillators.

The Third Homework

The text of the third homework is now available. This homework is due if you haven't submitted the first homework in due terms.

The Second Homework

The text of the second homework is now available. You must hand in your solutions, printed or nicely handwritten, the day of your oral exam.

The First Homework

2013-05-07
The text of the first homework is now available.
2013-06-04
The solutions of the first homework exercises are now available.

Homeworks explained

You have to present TWO homeworks, on different subjects, out of THREE homework assignments:

  • the FIRST or the THIRD, one of them, and
  • the SECOND one.
The FIRST assigment is about SDOF systems and a touch of MDOF, and is due on May 28. The SECOND will be released at the end of the classes, will be about MDOF systems and is due for the day of your oral examination.

The THIRD assignment will be about SDOF systems and a touch of MDOF's (that is, exactly the same subjects of the 1st one), will be released at the end of July and will be due at the end of August.
If you aren't ready for the first homework, if you plan to do the exam in September or in February, if you have other things to do in May, then you can do the THIRD assignment instead of the FIRST one.

Objectives

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,
  • the numerical methods for the eigen-analysis of multiple degrees of freedom systems and
  • earthquake engineering applications.

Organization

This year we'll have 14 or 15 weekly classes, inclusive of tutorials and computational exercises.

You will be evaluated on two homeworks and a final oral test.

All the slides used in classes will be (almost) immediately made available on this page after each class.

If you want to have a look at the slides before a class, you can: last year's slides are still available. Remember, however, that I'm still slowly changing the content and the organization of my lessons and that the reference material is only what I post here.

Recommended books

The first part of the course follows Clough and Penzien's book, the second part follows Chopra's. Should you prefer to buy a single book, my advice is buy Chopra's.

Note that a fair number of copies of Chopra's book (3rd ed.) are available from the campus library in Lecco, note also that Chopra's 2nd and 3rd editions are widely available at lower prices and are perfectly appropriate for my course.

Homeworks

Each homework comprises a set of exercises. While many of these exercises won't require more than paper, pencil and a hand-held calculator, the remaining ones will require plotting a time series or a bit of really elementary matrix algebra, i.e., things that every half-decent spreadsheet can do.
Of course specialized programs, let's say Mathematica, Matlab or Matlab's free clone Octave can be helpful.

A pleasant alternative to proprietary stuff is the IPython notebook, an example of which is the solution of an exercise I've assigned in 2012.


 

 

 

 

 

 

 

 

 

 

 

 

 

 
Giacomo Boffi