For noise and vibration reduction, various approaches can be employed depending on the frequency range to attenuate. Generally, active or passive piezoelectric techniques are effective in the low frequency range, while dissipative materials, such as viscoelastic or porous treatments, are efficient for higher frequency domain. In this work, we develop reduced order models for the resolution of a fully coupled electro-mechanical-acoustic system using modal projection techniques. The problem consists of an elastic structure with surface-mounted piezoelectric patches coupled with an inviscid and compressible fluid. The piezoelectric elements, connected with a resistive or resonant shunt circuit, are used for the vibration damping of the coupled system. Numerical examples are presented in order to illustrate the accuracy and versatility of the proposed methodologies.