A meta-modeling technique for the natural frequencies based on the approximation of the characteristic polynomial

Modal meta-models are used to approximate modal properties of structures when structural modifications are present. This paper proposes a viable meta-modeling approach which, based on the approximation of the coefficients of the characteristic polynomial, succeeds in accurately predicting the natural frequencies of the system under parameter variations in presence of veering. The obtained modal meta-model is used in combination with a procedure for efficient detection of veering and crossing phenomena without resorting to time-consuming mode tracking procedures. In this way it is possible to design a system which is safe against unexpected modal behavior.