Fuzzy Fractional Modeling of Piezothermoelastic Beams: A Hybrid FLHPA Approach for Uncertainty Quantification

This research aims to investigate the uncertainty in the dynamic response of piezothermoelastic (PTE) beams with fractional-order derivatives by incorporating fuzzy logic into the modeling framework. The governing equations of the beam are derived based on the fractional-order theory of thermoelasticity, and uncertainties are introduced through fuzzy initial conditions. To solve the resulting fuzzy partial differential equations, a hybrid Fuzzy Laplace Homotopy Perturbation Analysis (FLHPA) is developed, leading to recurrence relations for the approximate analytical solution. Two distinct fuzzy numbers, namely Triangular Fuzzy Number (TFN) and Gaussian Fuzzy Number (GFN), are employed to quantify and compare the influence of fuzziness on beam deflection, electrical potential, and temperature fields. The results show that GFN provides a wider range of uncertainty compared to TFN, capturing more realistic variations in system behavior. Numerical simulations on PZT-5A beams are presented with detailed graphical comparisons, highlighting the effect of fractional order and fuzzy type on uncertainty propagation. The proposed framework offers a robust approach for analyzing uncertain coupled thermo-electro-mechanical systems.