This study presents a thermomechanical vibration analysis of novel doubly curved sandwich plates composed of a functionally graded metal foam core and hybrid metal–ceramic face layers. A refined four-variable sinusoidal higher-order shear deformation theory is employed to derive the governing equations, while the analytical solution is obtained using the Navier method. The proposed formulation is validated by comparing the present non-dimensional displacement and natural frequency results with available benchmark solutions, showing excellent agreement. Comprehensive parametric analyses are then conducted to examine the effects of foam distribution type, porosity coefficient, material grading index, foundation stiffness parameters, core thickness ratio, metal–ceramic volume fraction, temperature rise, and boundary conditions on the fundamental dimensionless frequency parameter. The results reveal that the frequency response exhibits a strongly nonlinear variation with increasing temperature difference, generally decreasing to a near-zero minimum value before increasing again after the critical thermal state. The critical temperature difference varies approximately between 120 and 500 depending on material and structural parameters. Increasing the foam porosity coefficient improves the residual frequency level, raising the minimum λ₁₁ from about 0–0.5 to nearly 1.0–2.0. The Winkler-type foundation parameter K₁ delays the critical thermal state from approximately 200 to 480, whereas the shear foundation parameter K₂ shifts it toward lower temperature ranges. Increasing the material grading index enhances the minimum frequency but reduces the critical temperature threshold. In contrast, increasing the metallic constituent ratio decreases the structural stiffness and lowers the initial frequency values, for example from approximately 10 to 6 under fully clamped boundary conditions. The fully clamped boundary condition provides 30–70
