| 摘要(英) |
This study investigates the frequency response and transient wave propagation behavior of a rectangular plate induced by base excitation through theoretical analysis, finite element simulation, and experimental measurement. The frequency response includes vibration
characteristics and displacement field response. Additionally, the dynamic characteristics of
granular materials induced by plate vibration are explored using a two-way coupled finite
element method (FEM) and discrete element method (DEM) simulation, and the influence of
dimensionless acceleration on the formation of Chladni patterns in granular materials is
examined.
In this study, the theoretical model utilizes the superposition method to obtain the natural
frequencies and mode shapes. In experimental measurements, both steel ball impact and shaker
excitation are used to excite the plate′s dynamic behavior. The transient strain signals of the
plate are obtained through FFT transformation to acquire the resonant frequency and frequency
response. Simultaneously, the mode shapes at different frequencies are observed through the
Chladni patterns formed by the particles on the plate. Comparisons between theoretical,
experimental, and simulation results for vibration characteristics show a good correspondence
in both resonant frequencies and mode shapes. Furthermore, the nodal lines in the simulation
results coincide with the particle resting positions in the Chladni pattern experiments. The
results also indicate that the symmetry of the mode shape is related to the mechanism of specific
mode appearance.
Based on the vibration analysis results, the transient wave propagation analysis utilizes the
modal expansion method to construct a theoretical solution for the transient wave propagation
of the plate using mode shapes and time functions. The theoretical analysis in this study
considers the damping effect, and the short-time Fourier transform is applied to the transient
strain of the plate to obtain the frequency response decay trend of each mode. The damping
iii
ratios of each mode are calculated and input into the theoretical solution considering the
damping ratio effect to obtain the transient theoretical solution of the plate. In the experiment,
a shaker is used to excite the plate structure to generate transient strain signals during dynamic
vibration. By comparing the experimental measurement results with the finite element
simulation and theoretical analysis results, it is found that in the constant-frequency excitation
experiment, the simulated and theoretically calculated transient strains agree well with the
experimental results in terms of both waveform and magnitude. However, in the swept
frequency excitation experiment, there are some differences in the waveforms of the simulated
and theoretically calculated transient strains compared to the experiment, which is caused by the slight difference between the resonant frequency of the experimental system and the theoretical value. Finally, the accuracy of the transient wave propagation theoretical solution considering the damping effect is verified by applying different types of wave sources to the base of the structure.
Finally, this study explores the frequency response of a free-edge rectangular plate and the
dynamic behavior of granular materials induced by plate vibration. The finite element simulation is used to investigate the frequency response of the free-edge rectangular plate, and the mechanisms of Chladni patterns generated under different boundary conditions are compared. In this paper, a two-way coupled discrete element method (DEM) and finite element method (FEM) are used to simulate the dynamic behavior of granular materials on an elastic
rectangular plate. The particle aggregation under different dimensionless accelerations is investigated, and the simulation results are compared with the experiments to verify the accuracy of this method |
| 參考文獻 |
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