2012-06-07

Distributed Masses

Infinite number of DOF

When the problem leads to a model with lumped masses it is usually convenient to do a FE model and, using static condensation, a dynamic model with a cut down number of degrees of freedom.

When the structure is large, complex and the distributed nature of the masses does not allow for a reduced number of degrees of freedom, we have only the option of using most of the DOF of a refined FE model to perform the dynamic analysis.

When we face a relatively simple problem characterized by distributed masses, we have the alternative of using a continuous model, where the unknown is a function of time and position, leading to a formulation of the equation of motion in terms of partial differential equations.

It is possible to formulate and solve different problems of structural dynamics in terms of partial differential equations, but today we will study only the problem of transveral deflection of beams.

Equation of motion for an infinitesimal beam slice

Earthquake effective load

Free vibration problem

Eigenvalues and eigenfunctions

Forced response, modal superposition

Earthquake response

Material available for this class:



Giacomo Boffi