An efficient meta-modeling approach for natural frequency approximation: The Q-method

The variability and uncertainty of structural parameters have a large impact on the modal properties and need to be considered for an adequate assessment of the dynamic response. Recently, so-called modal meta-models were used to approximate the natural frequencies of structures modeled with finite elements when structural modifications are present. The present 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 in presence of veering assuming stiffness variability. The meta-model is based on m^p+p finite element analyses, where m denotes the number of analyzed modes and p the number of parameters. The number of required analyses is independent of the model or of the complexity of the evolution of the modal parameters. Furthermore, 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.