The properties of nonlinear systems have attracted a considerable interest these past years since they can be used to develop bio-inspired applications ranging from signal detection to image processing. Among these nonlinear signatures is Vibrational Resonance (V.R.) which expresses the ability of a nonlinear system to take benefit of a high frequency perturbation in order to enhance its response to a weak low frequency excitation . Since its introduction in mechanical systems and electronic devices, this effect has been widely reported in various systems and for different applications. Indeed, V.R can be used to detect subthreshold signals or to enhance the perception of subthreshold images. Among the systems which exhibits V.R., we can cite bio-inspired circuits, networks of coupled electronic neurons, as well as inhomogeneous and space-dependent nonlinear damped systems.These last mechanical systems constitute the subject of our communication which adresses more specifically the conditions of existence of V.R. The system under numerical investigation models a particle of mass m submitted to a multistable potential and a space dependent nonlinear damping. After showing that multiple resonances can be controlled by the system parameters, we show that the particle mass can allow or hinder V.R.. Indeed, V.R. ceases to exist for particles exceeding a critical mass. Keywords: Vibrational Resonance, nonlinear dynamics.