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
This paper presents a robust mathematical framework for vibration control of functionally graded graphene origami (GOri)-reinforced annular stepped plates integrated with optimally distributed piezoelectric patches. The structural model is developed using a higher-order shear deformation theory (HSDT) with a mathematical exponential shape function, while the governing equations are discretized via the mathematical generalized differential quadrature method (GDQM). The effective properties of the GOri–copper composite are defined as functions of graphene weight fraction, folding degree, temperature, and four through-thickness distribution patterns (UD, FG-X, FG-O, FG-V). A systematic design-space exploration covering 2304 discrete actuator configurations is performed to identify layouts that balance modal controllability of the first three bending modes against added actuator mass. The results reveal a pronounced non-monotonic stiffening–softening response with respect to the graphene folding degree, with peak stiffness occurring near 0.6. Linear quadratic regulator (LQR) control is adopted as an idealized full-state feedback benchmark. While significant vibration attenuation is achieved under nominal conditions, the study demonstrates that the closed-loop performance is highly sensitive to uncertainties in graphene weight fraction and folding degree. In particular, parameter deviations can alter modal participation factors and degrade controllability. A Monte Carlo analysis (500 samples) with statistically defined material uncertainties shows that the vibration reduction remains positive across all realizations, with mean attenuation levels of 14–17 dB and standard deviations of approximately 4–5 dB.
