Transverse vibration of functionally graded prestressed beam on elastic foundation
This study investigates the transverse vibration behaviour of functionally graded prestressed beams resting on elastic foundations. The material properties are assumed to vary continuously through the beam thickness according to a power-law distribution. The governing equation is derived using Euler–Bernoulli beam theory and Hamilton's principle. The Galerkin method is employed to determine the natural frequencies and dynamic responses of the beam. Validation of the proposed model is performed through comparison with published results, showing excellent agreement with errors below 2%. Parametric analyses are conducted to examine the effects of prestressing force, foundation stiffness, power-law index, boundary conditions, slenderness ratio, and skin-to-core thickness ratio on vibration characteristics. The results indicate that increasing foundation stiffness and tensile prestress significantly increase natural frequencies, while increasing the power-law index decreases beam stiffness and lowers vibration frequencies. The study demonstrates that the combined effects of prestress and elastic foundation improve vibration performance and structural stability. The developed model provides useful information for the design of advanced engineering structures employing functionally graded materials.