Low- and medium-frequency noise transmits vibrations to the cabin structure, which subsequently radiates noise into the interior. In order to solve the vibration and noise optimization problem of stiffened thin plates, topology optimization is utilized to improve the vibration and noise reduction effects by optimizing the layout of stiffeners. This study focuses on four-edge clamped stiffened thin plates and employs density-based topology optimization method to maximize its first-order modal frequency. Under the constraint of constant mass, the optimal distribution of stiffeners on the plate is designed. Modal, stiffness, and sound transmission loss analyses are conducted for the stiffened thin plate before and after optimization. The results show that the optimized stiffened plate achieves an increase in its first-order modal frequency and improves sound transmission loss within a certain frequency range, without significantly reducing the overall stiffness. The study provides a reference for vibration and noise reduction optimization in the structural design of stiffened plates.