Free-vibration characteristics of micropolar thermoelastic plate immersed in viscous media

This study presents a rigorous analysis of free-vibration propagation in a homogeneous, isotropic micropolar generalized thermoelastic plate fully immersed in a viscous fluid on both surfaces. The formulation is developed within the frameworks of classical Fourier and non-Fourier (Lord–Shulman, LS) thermoelasticity to account for both diffusive and finite-speed thermal wave effects. By employing the Helmholtz decomposition technique, the coupled field equations are reduced to a tractable form, leading to compact secular equations under various mechanical boundary conditions. A detailed numerical investigation is carried out for a representative material to evaluate phase velocities and attenuation coefficients corresponding to symmetric and skew-symmetric vibration modes. The results are presented graphically to illustrate the influence of micropolar parameters, thermal relaxation, and viscous fluid loading on wave characteristics. In addition, analytical expressions for displacement, microrotation, and temperature fields are derived, and their spatial variations are analyzed to highlight key thermo-micropolar interactions. Several limiting cases are examined to validate the formulation and establish consistency with classical results. The findings of this study have practical relevance in defense and geophysical applications, particularly for understanding wave propagation and dynamic behavior in fluid-saturated geological layers.