**5. Conclusions**

In this paper, the novel dynamics plate model is completely based on the theory of three-dimensional elasto-dynamics theory, and the derivation of the dynamic equation is conducted without any prior assumption but in view of the partial differential operator theory and analytic theory of complex function. Therefore, the proposed dynamic equation is more exact. It is not only suitable for low-frequency vibration of the plate but also suitable for high-frequency vibration, which will not produce the phenomenon of high-frequency dispersion.

With the development of modern mechanics and mathematics, new research results and methods continue to appear. The research object develops toward high speed and high-frequency. The new development of mathematical and mechanics improves the ability to solve complex mechanical problems and plays a positive role in promoting the development of mathematics in mechanics and physics. It provides a new formulation and means for solving the dynamics and numerical calculation of solid structures more accurately. The governing equation of bending plate vibration proposed in this paper is expected to be used to analyze the vibration of thick plates, evaluate the applicable condition of the engineering plate theory and design the active vibration control of thick plates exactly in the research on the dynamics and stability for flexible spacecraft structures and broadband vibration frequency.

**Author Contributions:** Conceptualization, C.Z. and M.W.; validation, C.Z. and M.W.; investigation, X.H. and W.Z.; data curation, X.H. and H.X.; writing—original draft preparation, C.Z.; writing review and editing, M.W. and J.N.; funding acquisition, J.N. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the Key Laboratory of Underwater Acoustic Environment Institute of Acoustic Chinese Academy of Science SSHJ-KFKT-2020, the Key Research and Development Program of Zhejiang Province (No. 2021C03013), the National Key Research & Development Program of China (No. 2017YFB1301300), the Key Laboratory funding for Technology in Rural Water Management of Zhejiang Province and the Fundamental Research Funds for the Provincial Universities of Zhejiang (GK199900299012-026).

**Institutional Review Board Statement:** The study in this paper did not involve humans or animals.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The study did not report any data.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

