| dc.description.abstract | This thesis establishes a theoretical analysis method to investigate the vibration characteristics and transient wave propagation behavior of plate structures under the influence of mass effects, including the differences in resonant frequencies and mode shapes of plates with arbitrarily added mass distributions, as well as the transmission paths and energy changes of flexural waves passing through mass arrays, thereby achieving the effect of a mass lens.
The theoretical model first derives an analytical solution for the free vibration of a plate with an attached mass array. After obtaining the vibration characteristics such as resonant frequency and mode shape using the Gorman superposition method, the transient wave propagation theoretical solution is obtained through normal mode method. The theoretical analysis results of vibration characteristics and transient wave propagation are verified by comparison with finite element simulation software. The theoretical analysis of resonant frequency, mode shape, transient displacement, strain, and other physical quantities is highly accurate, confirming that the theoretical method proposed in this study can accurately and effectively analyze the frequency domain and time domain dynamic behavior of plate structures with arbitrarily added mass.
Based on this theoretical model, the influence of the arrangement and distribution of the mass array on the vibration characteristics and transient wave propagation of the plate is investigated. By changing the dynamic behavior of the plate structure through the attached mass array, a wave propagation path analysis method applicable to plate flexural waves is developed. The relationship between the group velocity of flexural waves and the added mass is summarized to control the wave velocity difference to change the wave propagation direction, thereby forming a specific required wave propagation path, and establishing its corresponding mass array.
Finally, based on this design method, the content of the mass array that can form a specific effect, including focusing, divergence, and control of wave propagation direction, is calculated, successfully achieving the purpose of controlling the energy of flexural waves, which can provide significant benefits for energy recovery and vibration reduction. | en_US |