<p>Acoustic metamaterials incorporating membrane resonators strategically positioned along the path of acoustic waves have exhibited remarkable capabilities for enhancing sound attenuation in the low-frequency range. This paper presents an analytical model to investigate the sound transmission loss (STL) characteristics of an acoustic metamaterial composed of a plate structure integrated with shunted piezoelectric patches. By combining effective medium (EM) theory with circuit-based impedance modeling, the proposed method provides a rapid and accurate estimation of STL across various configurations without relying on extensive finite element (FE) method or experimental setups. The model offers design flexibility, allowing the STL to be tuned within a desired frequency range by changing the resistance and inductance of the shunt circuit. This provides a low-cost and scalable alternative to purely numerical approaches. The model is validated against FEM simulations, showing strong agreement and highlighting its potential for early stage design and optimization of sound insulation piezo-plate metamaterials.</p>