On vibrations of a system with an eigenfrequency identical to that of one of Its subsystems

The free vibrations of a complex system with a natural frequency identical to that ofone of its subsystems is discussed. Such eigenvibrations need special considerationin many modal synthesis methods as the characteristic matrix (equation) does notexist. Particular emphasis has been placed on the case where a resonating subsystemis subjected to forces from other subsystems, which has not received sufficient attentionin the literature on substructure synthesis methods. Examples of such eigenvibrationsfor two simple systems are given. A general equation for system eigenfunctionscorresponding to eigenfrequencies of the isolated subsystems is presented anddiscussed.