Thermo-Electro-Mechanical Vibration Analysis of Microbeams with Non-Ideal Boundary Conditions

In this study, the vibration characteristics of microbeams subjected to thermal loads and electric field effects under non-ideal boundary conditions were investigated. The non-ideal boundary conditions are modeled as a linear combination of ideal fixed and simply supported boundary conditions. The weighting factor, k, is defined as a measure of deviation from the ideal boundary conditions. To determine the influence of the boundary conditions, both non-ideal fixed and non-ideal simply supported beams were examined. The equations of motion of the system are derived using Hamilton's principle, and the Method of Multiple Scales, a perturbation technique, is applied to obtain approximate analytical solutions for both linear and nonlinear vibration responses. The effects of thermal loads, electric field influence, and non-ideal boundary conditions on the natural frequencies were investigated. The results demonstrate that the natural frequencies vary significantly with changes in the weighting factor, k. To address operational reliability, a formal probabilistic sensitivity and uncertainty analysis using Monte Carlo simulations is integrated, quantifying how uncertainties in geometrical and thermal parameters propagate to structural instability. Furthermore, a theoretical framework for calibrating the abstract boundary parameter via Finite Element Model updating is introduced. These results indicate that idealized boundary condition assumptions may lead to significant inaccuracies in the design and reliability assessment of micro-electromechanical systems (MEMSs) operating under the combined effects of thermal and electric fields. Relying solely on idealized support assumptions may result in significant failure (damage) predictions owing to the underestimation of thermally induced buckling and electrical pull-in risks arising from assembly imperfections. Furthermore, a probabilistic sensitivity analysis is implemented to quantify how parameter uncertainties propagate through the system, bridging the gap between pure deterministic modeling and operational reliability.