Sensitivity analysis of piezoelectric material parameters using Sobol indices

Abstract The applicability of the method of Sobol to the non-smooth, resonant behavior of a vibrational eigenmode of a piezoelectric element is examined. The goal is to quantify the sensitivity of the system upon variation of the piezoelectric material parameters. The randomly distributed piezoelectric material parameters needed for this statistical approach are taken from a Latin Hypercube Sampling (LHS). A hybrid computational approach is applied: The LHS process, the creation of the simulation model, the extraction of the resonance frequencies, and the calculation of the Sobol indices is performed in MATLAB ® . The finite-element software COMSOL Multiphysics ® is used for the computation of the electrical and mechanical properties of the considered block-shaped piezoceramic test specimen. To this end, an eigenfrequency analysis as well as a frequency domain study are set up, combined with a parametric sweep using the LHS parameter combinations as input. The convergence of the calculated Sobol indices depending on the LHS sampling size is investigated. It is shown that the Sobol analysis successfully identifies the most influential material parameters.