Patil, M.A.Kadoli, R.2026-02-042023Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2023, 45, 7, pp. -16785878https://doi.org/10.1007/s40430-023-04272-0https://idr.nitk.ac.in/handle/123456789/21835A unified analytical approach is established to predict the frequency behaviour of symmetric functionally layer-wise graded beams with an integrated Terfenol-D layer under simply supported, clamped-clamped, and clamped-simply supported boundary conditions. In contrast to previous research, the analytical solution relies on transcendental equations. Terfenol-D layered functionally graded beam uses Reddy’s generalised beam theory as the basis for its governing equation. First-order shear deformation and rotating inertia were taken into consideration in the study. To ensure the accuracy of the analytical solution, comparisons are made with the current differential quadrature solution based on Euler–Bernoulli beam theory. The current analytical solution yields frequency results that are in good agreement with those obtained by the differential quadrature approach. The present analytical means is straightforward and easy to understand as compared to previous researcher’s work. © 2023, The Author(s), under exclusive licence to The Brazilian Society of Mechanical Sciences and Engineering.Beams and girdersBoundary conditionsDifferentiation (calculus)Vibration analysisDifferential quadratureDifferential quadrature methodDifferential quadrature methodsExact solutionFree vibrationFunctionally graded beamsSimply supportedSymmetricsTerfenol-DVibrationFunctionally graded materials