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ABSTARCTThin plate structures are widely used in dynamic platforms, such as aerospace, ships and high-speed trains. The artificial modulation of elastic waves in thin plates has always been one of the most important factors affecting the dynamic performance of devices. Dynamic platforms require vibration modulation of flexural waves to ensure the stability of the overall structural vibration characteristics, while also ensuring the comfort of the internal working environment. However, in the current research on flexural wave modulation, there are still some urgently problems that need to be investigated of the wave modulation in robustness, predictability, compactness and tunability. Here are achievements of this thesis to meet demands of abovementioned scientific problems:(1) This thesis first constructed chiral waveguides based on two functional unit cells with opposite chirality. The chiral waveguides, protected by the chirality of resonant frequencies of scatterers, show stronger robustness compared with the C6v waveguides.(2) Furthermore,constructed a robust and predictable cavity modes,which could allow us to capture the cavity modes at a fixed frequency with high-quality factor. The energy capture capability of the topological cavity mode is about 30 times that of the bare plate to achieve a high energy density topological cavity mode. It is also found that the frequency of the topological vortex peaks has a sensing effect on the mass and position of a normalized small mass near the vortex core.(3) To achieve the compact modulation of the flexural wave, we developed the reverse numerical design method of bound states in the continuum (BIC). The BIC based on high symmetry show highly robustness is robustness and compactness with frequency and modal predictability.(4) To solve the non-tunable in passive structures, this thesis constructs a real parameter theoretical model of gain and loss in the time-modulated scatterer. The effective elastic constant of the space-time scatterer generates positive and negative values of the imaginary part based on coupling resonance effects, which mean the gain and loss of an active system.