In dynamic analysis, the system of equations corresponding to a structure with n degrees of freedom is:
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The corresponding free vibrations not dampened by the structural model are described by the following system of equations:
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which corresponds to n eigenfrequencies and n eigenvectors. These are the solutions to the following homogeneous system of equations:
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These eigenvectors are called modal forms and are orthogonal to the mass matrix and the stiffness matrix.
Forming a complete base
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where
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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 :
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