Modeling and Analysis of Vibration Characteristics of Rectangular Plate with Circular Through Hole Under Complex Boundary Conditions

This paper presents a method to study the free vibration of a plate with circular holes. The circular hole is regarded as a virtual small plate in which the mass density and Young’s modulus are zero. Therefore，the free vibration problem of the circular hole plate can be transformed into the free vibration problem of the equivalent rectangular plate with non-uniform thickness. The model is derived from the spectral geometry method(SGM)，and the displacement of the plate with circular holes is expanded by the modified Fourier series. Virtual springs are added to the boundary of the plate to simulate the boundary conditions of simply supported and fixed supports. The accuracy of this method is verified by comparison with the finite element calculation results. The relationship between modal numerical solutions of plates with circular holes and boundary conditions and geometry of the plate is studied. © 2024 Nanjing University of Aeronautics an Astronautics. All rights reserved.