This study introduces an analytical framework that integrates the state-space method with generalized thermoelasticity theory to obtain exact solutions for the static and dynamic behaviors of laminated plates featuring imperfect interfaces and resting on a Winkler foundation. The model comprehensively accounts for the foundation-structure interaction, interfacial imperfection, and the coupling between the thermal and mechanical fields. A parametric analysis explores the impact of the dimensionless foundation coefficient, interface flexibility coefficient, and thermal conductivity on the static and dynamic behaviors of the laminated plates. The results indicate that a lower foundation stiffness results in higher sensitivity of structural deformation with respect to the foundation parameter. Furthermore, an increase in interfacial flexibility significantly reduces the global stiffness and induces discontinuities in the distribution of stress and temperature. Additionally, thermal conductivity governs the continuity of interfacial heat flux, while thermo-mechanical coupling amplifies the variations in specific field variables. The findings offer valuable insights into the design and reliability evaluation of composite structures operating in thermally coupled environments.

This paper investigates the free vibration behavior of functionally graded graphene-reinforced porous cylindrical shells with complex boundary conditions, resting on a visco-Pasternak foundation, by utilizing the differential quadrature method (DQM). First, an improved Halpin–Tsai micromechanical model is employed to determine the effective material properties of the functionally graded graphene-reinforced porous cylindrical shells. Subsequently, based on the first-order shear deformation theory and Hamilton’s variational principle, the governing equations of motion are established. Finally, the differential quadrature method (DQM) is applied to obtain the reduced ordinary differential governing equations under various complex boundary conditions, and the accuracy of the numerical method is verified by comparison with the analytical solution for simply supported boundary conditions derived via trigonometric functions. In the numerical examples, the effects of boundary conditions, material parameters, geometric parameters, and visco-Pasternak foundation parameters on the vibration behavior of cylindrical shells are also discussed in detail.