This paper studies the propagation process of vibrations and the characteristic vibration patterns in Chladni plates, and gives a detailed discussion on the regulation and synthesis methods of Chladni patterns. Firstly, the mathematical model of thin plate vibration problem is established theoretically, successfully revealing the reasons for the appearance of vibration modes, and exploring the changes in vibration patterns caused by modal superposition. Furthermore, the Chladni patterns predicted by the theoretical model are verified by numerical simulation. Finally, by laying small particles on the plate surface, the experiment successfully observed different Chladni patterns. This study not only helps deepen understanding of the special characteristics of wave propagation in plates, but also provides control and synthesis methods for vibration patterns, providing ideas for vibration visualization research, particle manipulation and other applications.