Several solutions for multimodal vibration damping of thin mechanical structures based on piezoelectric coupling have been developed over the years. Among them, piezoelectric network damping consists in using piezoelectric transducers to couple a structure to an electrical network, where the transferred electrical energy can be dissipated. In particular, the effectiveness of coupling rods, beams and plates to networks which are their electrical analogues has been proven. This work is the first step going towards more complex structures. After defining and experimentally validating a new electrical analogue of a simply-supported plate, the study is extended to the damping of a non-periodic plate. Experiments show that in this case, a broadband damping is achieved once the piezoelectric transducers are coupled to an adequate analogous network. A finite element model of the structure coupled to its analogous network is concurrently developed and validated.