Comparing the Modified Strain Gradient, Modified Couple Stress, and Classical Results for Vibration Dissipation of SMA-Wire-Reinforced Microplates with Nonidentical Size-Effect Coefficients

We focused here on evaluating the nonlinear time-dependent vibration dissipation of shape memory alloy (SMA) wires embedded in composite microplates. The nesting interatomic force field of the extremely small plate is accounted for in the framework of the modified strain gradient theory (MSGT) that affects the phase transformation events of the SMA wires as well. Brinson’s constitutive law which was modified by Shariyat and his co-authors is employed. The nonlinear governing equations with extra-differentiation orders due to using MSGT are derived based on Hamilton’s principle. The proposed solution algorithm and phase transformation tracing technique are quite different from those of macro-mechanics. The spatial variations are traced by a highly accurate sixth-order 48-degrees-of-freedom element in the natural coordinates to enable treating the extra-differentiation orders of the MSGT. Effects of the identical and nonidentical size-effect coefficients on the micro-dimension structural damping and direct and converse martensite–austenite phase transformations of the SMA are studied. Results show that MSGT leads to higher stiffness and less damping in comparison with modified couple stress theory (MCST) and classical plate theory (CPT), while the l 1 and l 2 size-effect coefficients have, respectively, the highest and least effects on the lateral deflection and phase transformation, and l 0 has the highest role in amplifying the higher vibration modes.