This paper aims at introducing nonlinear interactions in the sound synthesis of nonlinear resonators. Sound synthesis is performed using the formalism of Volterra series which is used to describe and simulate weakly nonlinear models using their Volterra kernels. Interactions are constraints imposed to the considered models and are used to excite (e.g. bowing a string or striking a plate) or connect resonators together (such as connecting a string to a bridge). This requires to resolve an inverse problem giving the interaction force as a function of a given velocity. In the case of Volterra series, kernels of the inverse problem have been defined by Schetzen. Using this definition, a structure of simulation of the direct and inverse problems at each time step will be defined. Application to the case of a Kirchhoff-Carrier string connected to a Berger plate will be presented including computation of the kernels (direct and inverse), structure of simulation and numerical results.