RamSeries manual


Modal Analysis

In dynamic analysis, the system of equations corresponding to a structure with n degrees of freedom is:

The corresponding free vibrations not dampened by the structural model are described by the following system of equations:

which corresponds to n eigenfrequencies and n eigenvectors. These are the solutions to the following homogeneous system of equations:

These eigenvectors are called modal forms and are orthogonal to the mass matrix and the stiffness matrix.

   Forming a complete base , can be writed

where is a scalar function of time, called generalized coordinate.

   Using the previous expressions and taking the orthogonality properties into account, we can transform one system with n degrees of freedom into a system of n equations with one degree of freedom each:

where :