Thermo-electro-mechanical vibration analysis of nonlocal piezoelectric nanoplates involving material uncertainties

This study aims to detect the influence of material uncertainties on the free vibration of nonlocal piezoelectric nanoplates under thermo-electro-mechanical loadings. The size-dependent governing equations are derived based on the nonlocal theory and Hamilton's principle, and Navier method is used for the solution. Considering inadequate experimental data, uncertain-but-bounded parameters are used to quantify the uncertain nanomaterial properties. Based on the interval analysis theory, a novel hull iterative algorithm (HIA) is proposed to evaluate the thermo-electro-mechanical vibration behavior of piezoelectric nanoplates. The presented method is compared with Monte Carlo method and sensitivity based interval analysis method, and well agreements are achieved. A sensitivity analysis is performed to identify the most dominant uncertain parameters. Using the HIA, parametric studies are carried out to explore the combined effects of material uncertainties and temperature change, external electric voltage, biaxial force as well as nonlocal parameter on the natural frequency of piezoelectric nanoplates.