Guyader J.

Vibration modes are commonly used to represent behaviour of vibrating systems , however in medium and high frequency this representation is not well adapted because of the huge number of modes participating to the response . In this frequency range methods have been proposed to fit with phenomena and modal density is used instead of all modal information . In this paper a theoretical approach based on the eigen values of the so called G Matrix is presented . It permits to estimate the number of modes dominating the vibration response of systems excited in a frequency band and thus, to measure modal density. The response of the system can be approximated with corresponding eigen vectors . When modal overlap is achieved a very limited number of G matrix eigen element are sufficient to estimate the response . Applications to cars structures are presented to illustrate the approach.