Mathematical Background |
 
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Mathematical Background |
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This section provides some of the mathematical background to the operation of Modes. Matrix algebra is used in the derivations that follow. A matrix quantity is denoted by bold typeface, for example w. An uppercase matrix variable, for example K, represents a rectangular array or tensor, that is an array comprised of m rows and n columns, where both m and n are greater than 1. A lowercase matrix quantity, for example v, represents a vector quantity that is a matrix comprising m rows and one column only.
The basic equation solved by Modes is:
where K is the total structure stiffness matrix; M is the total structure mass matrix; 
is the structure eigenvalue; and v is the associated eigenvector or mode shape. The corresponding structure natural frequency f is given by:
(2)
