With the rapid advancement of industrialization and technology, vibration issues in mechanical engineering have become increasingly prominent, posing significant challenges to the stability and performance of various mechanical systems. Although traditional vibration control methods, such as damping and dynamic vibration absorbers, are widely used, they exhibit notable limitations in effectively mitigating these issues, particularly in complex and variable environments. Acoustic metamaterials, owing to their unique physical properties, have emerged as a promising solution, offering innovative approaches to vibration and noise control. While research on linear piezoelectric acoustic metamaterials is well-established, their nonlinear characteristics remain underexplored. This study endeavors to bridge the existing research gap by providing an in-depth theoretical and simulation-based investigation of the transmission properties of one-dimensional nonlinear piezoelectric metamaterials. Through detailed analysis and simulation, the study demonstrates significant bandgap properties within specific frequency ranges, highlighting their potential for practical applications. These findings not only enhance the theoretical understanding of nonlinear piezoelectric metamaterials but also offer a robust foundation for their future development and application in advanced vibration control technologies. By advancing this knowledge, the study contributes to the ongoing efforts to address the complex challenges posed by vibration in mechanical engineering.