<p>Porous materials are increasingly utilized in sandwich structures due to their exceptional energy absorption. This paper develops a hierarchical beam element to predict the nonlinear vibration characteristics of sandwich beams with functionally graded material (FGM) face-sheets and a porous core. Several homogenization models, namely the Voigt, Reuss, Mori-Tanaka, and Hashin-Shtrikman, are employed to determine the effective properties of the FGM. The element formulation is based on Timoshenko beam theory, employing hierarchical interpolation functions to approximate the displacement field and eliminate shear-locking. The resulting nonlinear governing equations are solved for frequencies using a direct iterative method. Numerical results demonstrate that the proposed element is efficient, and it can provide accurate nonlinear frequencies with a small number of elements. Results show that increasing the porosity coefficient reduces the nonlinear frequency ratio, and this trend is amplified by higher vibration amplitudes but mitigated by higher material grading indices. While homogenization models significantly impact results at high amplitudes, their influence diminishes as porosity increases. It is also shown that the beam with more constraints exhibits lower sensitivity to both porosity and the choice of homogenization model.</p>