The relationship between the real and imaginary parts of complex modes

It is shown that a simple relationship exists between the real and imaginary parts of complex modes of all systems which can be represented by real and symmetric mass, stiffness and damping matrices. The relationship is most simply expressed in those cases where all roots are complex and where the real parts of all roots have the same sign. In these cases, the relationship can be expressed in a form where the imaginary part of the modal matrix is equal to the real part of the modal matrix post-multiplied by a matrix which involves an arbitrary real orthogonal matrix and some diagonal matrices which are determined directly from the complex roots. In other cases, there remains a relationship between the real and imaginary parts, but this must be expressed in a different way. (C) 1998 Academic Press Limited.