Aiming at the vibration analysis of irregular shape plates, a semi-analytical method for dynamic vibration analysis of arbitrary polygonal plate structures under elastic boundary conditions is proposed based on the Jacobi-Ritz method. Based on the Kirchhoff thin plate theory, the vibration theoretical model of polygonal plate is established. Aiming at the difficult problem caused by the complex integral region involved in the energy functional of polygonal plate system, the simplified form of the energy functional equation of polygonal plate system is derived by introducing the divergence theorem. The displacement tolerance function of the polygonal plate is constructed by using the Jacobi orthogonal polynomial, and the complex boundary conditions of the polygonal plate are simulated by the penalty parameter method. A vibration analysis method of the polygonal plate based on the Jacobi-Ritz method is proposed. Finally, the effectiveness of the proposed method is verified by comparing with the simulation results and the reference data.
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