THE ORTHOGONALITY AND NORMALIZATION RELATIONSHIPS WITH ITS APPLICATION OF COMPLEX MODES FOR NON-CONSERVATIVE SYSTEM

In the case of non-conservative system, a further study on orthogonality and normalization relationships of state vectors is firstly proposed in this paper．A new normalized technique about state vectors is presented accordingly．Secondly by using the orthogonality and normalization condition in sensitivity analysis of structural optimization, modal sensitivity expressions are derived．It could simultaneously avoid the effect on solving the coefficient of modal sensitivity, which is caused by the singular property．The expressions are concise and easy to be implemented．Finally the usefulness and effectiveness of the derived expressions are demonstrated by considering an example of a non-conservative damped four degrees-of-freedom system．