2011-04-19

MDOF Systems

Multiple degrees of freedom linear systems are very simple to study if we adopt a matrix notation for the equation of motion...

  • Vectorial equation of dynamic equilibrium.
  • Linear relationship between displacement, acceleration vector and elastic, inertial force vector are written in terms of a matrix product.
  • Homogeneous equation of motion, equation of frequencies, eigenvalues and eigenvectors, eigenvectors' properties.
  • Modal superposition.
  • A complete example of solution.
Material available for this class:
  • the slides i used for my lesson
  • a ready to print version of the slides,
  • a gnuplot script that you could use to produce the last two graphics in the slides (from the command line type "gnuplot response.gp"), or simply study to see a simple program that computes the response of a 2DOF system.
Giacomo Boffi