A Novel Approach to the Design of Distributed Dynamic Vibration Absorbers for Plates Subjected to Classical and Elastic Edge Conditions

Plate structures are the main components of offshore platforms and ships in engineering applications. The vibration control of the low-frequency mode of plate structures has always been a meaningful research object in marine science and engineering. Due to their low cost and good performance, dynamic vibration absorbers are widely used. To enhance the design efficiency of dynamic vibration absorbers, a mathematical model was developed for plates with dynamic vibration absorbers under different boundary constraints. To overcome the discontinuity of the displacement function, auxiliary series were introduced. In addition, the efficiency of resolving the plate structure’s equivalent mass was significantly improved compared with when using FEM software Abaqus 6.14. The validity of the proposed mathematical model was confirmed in comparison with related studies, the FEM results, and the experimental results. Considering the mathematical model and design approach proposed in the current paper, more research on the vibration control of plates subjected to clamped and elastic boundary conditions should be performed. The mathematical model and findings in the design process may have positive implications for the control of the vibration of plate structures in marine science and engineering.