Dynamic analysis of piezoelectric beams under fuzzy initial conditions: A comparative study

Abstract

This study develops a fuzzy-based modelling framework to analyze the uncertain dynamic behaviour of cantilever piezoelectric beams by introducing fuzziness directly into the initial conditions, an aspect not addressed in existing literature. Two widely used fuzzy representations – Triangular Fuzzy Numbers (TFN) and Gaussian Fuzzy Numbers (GFN) – are employed to characterize imprecision in the excitation parameters. The Fuzzy Adomian Decomposition Method (FADM) is applied to derive semi-analytical solutions for the transverse deflection and induced electric potential, followed by an r-cut based uncertainty propagation procedure. Numerical investigations using PZT–5A material reveal that the choice of fuzzy number significantly influences the resulting uncertainty bounds. For mid-span deflection at t = 2 s, the GFN representation produces uncertainty widths approximately 1.8–2.0 times larger than TFN at r = 0.5, and around 1.4–1.6 times larger at r = 0.9. TFN yield compact intervals with lower computational cost, whereas GFN provide smoother and more conservative uncertainty envelopes. Additionally, the uncertainty width monotonically decreases with increasing r and converges to the deterministic response as r → 1. The findings demonstrate that the type of fuzzy number plays a crucial role in the fidelity and robustness of uncertainty modelling in piezoelectric structures. The proposed framework offers a computationally efficient tool for the dynamic analysis, design, and reliability assessment of intelligent piezoelectric devices operating under imprecise or partially known initial conditions.