Engineers are aware of the need to account for uncertainties in their predictions in knowledge of the material and cross-section properties (e.g., Young's modulus, damping factor, section area). Furthermore, acousticians are often interested in the prediction of the maximum sound power that could be radiated by a given structure. But they face a numerical challenge due to the amount of input parameter combinations they must solve to compute the maximum response. In this context, a simple case of acoustic radiation in two dimensions---a simply supported beam in light fluid---is a good way to investigate the sensitivity of the acoustic power to the uncertainties of the input parameters. To study this case, an analytical method with a perturbation scheme up to the second order has been intensively used, and compared with a Monte Carlo method. In this presentation, it will be shown that the acoustic power is very sensitive to the variations of the structural parameters in the neighborhood of the beam eigenfrequencies, and that second-order perturbation techniques are not sufficient. Consequently, a hybrid method is proposed to improve the results locally.