This paper introduces a simplified and controllable model for mode coupling in the context of modal synthesis. The model employs efficient coupled filters for sound synthesis purposes, intended to emulate the generation of sounds radiated by sources under strongly nonlinear conditions. Such filters generate tonal components in an interdependent way, and are intended to emulate realistic perceptually salient effects in musical instruments in an efficient manner. The control of energy transfer between the filters is realized through a coupling matrix. The generation of prototypical sounds corresponding to nonlinear sources with the filter bank is presented. In particular, examples are proposed to generate sounds corresponding to impacts on thin structures and to the perturbation of the vibration of objects when it collides with an other object. The sound examples presented in the paper and available for listening on the accompanying site illustrate that a simple control of the input parameters allows the generation of sounds whose evocation is coherent, and that the addition of random processes yields a significantly improvement to the realism of the generated sounds.