A mode-based meta-model for the frequency response functions of uncertain structural systems

Frequency response functions (FRFs) play an important role in the assessment of the structural response of linear systems subjected to dynamic forces. In this work a functional relation (meta-model) between the uncertain structural parameters and the model properties is presented. The meta-model provides a computationally fast solution to approximate the eigenfrequencies and mode shapes needed thereafter for evaluating the FRFs. The meta-model circumvents the repeated solution of the eigenvalue problem for each set of uncertain structural input parameters. The provided relations can be helpful in the design stage to control the dynamic response within certain frequency bands. Moreover, the meta-model can be used for optimization and reliability assessments based on Monte Carlo sampling procedures. Numerical examples show the application of the method focusing mainly on the variability of the FRFs. The efficiency and accuracy of the meta-model to compute approximate FRFs is assessed by a comparison with the solution by Finite Element (FE) analyses.