The calculation of the vibrational responses of systems on frequency bands appears to be more and more important in engineering simulation. This is particularly true in medium frequency bands, where these responses have a strong sensitivity to the frequency. To find this, standard techniques usually involve many frequency fixed computations. In this work, we propose a novel technique that does not need the resolution of vibration problems at many different frequencies. It combines the use of the ”Variational Theory of Complex Rays” (VTCR), a mid frequency dedicated numerical strategy, and the ”Proper Generalized Decomposition” (PGD), a reduced order model technique. The VTCR uses exact solutions of the governing equation (propagative and evanescent waves) to find approximated solutions of the vibrational problem. The PGD expands the VTCR approximation over the frequency band thanks to a separated representation of the unknowns. Examples of such a strategy on complex structures will illustrate the efficiency of the proposed approach.