The Relationship between the Real and Imaginary Parts of Complex Modes
SD Garvey, JET Penny (Aston University) & MI Friswell (University of Wales Swansea)
Journal of Sound and Vibration, Vol. 212, No. 1, April 1998, pp. 75-83
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.
This material has been published in the Journal of Sound and Vibration, Vol. 212, No. 1, April 1998, pp. 75-83, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Academic Press. This material may not be copied or reposted without explicit permission.
Please note that Elsevier Science has bought Academic Press. Although the original paper was published on IDEAL, in future access to this journal will be via ScienceDirect.
Download PDF file (166K)
Link to paper using doi:10.1006/jsvi.1997.1377
Journal of Sound and Vibration on ScienceDirect