In traditional methods, the absorption of flexural waves in beams and plates is often achieved by incorporating complex and heavy structures with additional damping materials. In addition, new vibration reduction methods for beams and plates have emerged in recent years, such as phononic crystals and acoustic black holes. Among them, the research on absorbers based on continuous bound states, which can achieve near-100% absorption without the need for additional damping materials, has garnered extensive attention. However, this research is based on the time-domain coupled mode theory, which is not applicable to all models and results in a complex design process, making it difficult for widespread application in industrial engineering. Therefore, this paper proposes a research method for elastic absorbers based on the acoustic impedance matching theory. Theoretical calculations, numerical simulations, and experimental validations have demonstrated that this theory can accurately predict the absorption curve of the proposed absorbers and can quickly and easily realize the structural design of elastic absorbers, bringing new possibilities for the research on flexural waves absorption and vibration reduction design. The theoretical method and absorption structure proposed in this paper do not need additional damping materials, which is more conducive to meet the requirements of lightweight structures in aeronautical engineering. At the same time, it brings new possibilities for the field of vibration wave absorption, especially the design of efficient absorption and vibration reduction of curved waves.