Temperature-Controlled Frequency Adjustment of AFG Uniform and Symmetrically Doubly Tapered Microbeams based on the Nonlocal Modified Couple Stress Theory

This study explores the temperature-controlled frequency adjustment of axially functionally graded (AFG) symmetrically doubly tapered microbeams embedded in a three-parameter elastic foundation. The microbeam features a larger cross-section at its center, tapering linearly and symmetrically toward both ends. Utilizing the nonlocal modified couple stress theory and the Euler–Bernoulli beam model, size-dependent governing equations incorporating thermal effects are derived. A higher-order global residue harmonic balance method is employed to obtain a closed-form analytical expression for the nonlinear frequency. Parametric studies investigate the influence of material composition, taper ratios, temperature, initial amplitude, foundation parameters and small-scale effects on the nonlinear frequency. The results demonstrate that the ratio of the nonlocal parameter to the length scale parameter can be tuned to align frequencies with classical theory predictions, with this ratio being affected by the taper ratio, temperature and boundary conditions. Notably, temperature control enables precise tuning of the nonlinear frequency, allowing it to be increased or decreased relative to that of uniform microbeams. These findings provide valuable insights for the design and optimization of tapered microbeams in advanced micro-electromechanical systems.