RamSeries manual
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 :