In this investigation, free vibration of stepped circular Mindlin plate with arbitrary boundary conditions is presented by an improved Fourier–Ritz method. Based on the locations of the step variations, the stepped circular plate can be divided into different concentric annular and circular plates. The first-order shear deformation plate theory is employed to establish the theoretical model. Once all the displacements of a stepped circular plate are expanded by an improved Fourier series expansion, an exact solution can be obtained based on the Rayleigh–Ritz procedure by the energy function of the current model. The convergence and accuracy of the proposed method are proved by several numerical examples. The effects of classical boundary conditions and geometrical parameters on the frequency parameters of a stepped circular plate are also analyzed.

Finger seals are a new type of seal with good sealing performance and long service life. The noncontacting feature relies on the gas film force. However, when the seal works in an unsuitable environment or its design parameters are not reasonable, the lifting pad may not be able to generate sufficient air film force. This causes contact between the fingers and the rotor, resulting in a reduced service life of the seal. In view of this situation, this paper proposes a method that can quickly determine whether there is enough gas film force to lift the sealing finger at the design stage. The aeroelastic coupling characteristics of the noncontacting finger seal are studied in conditions where contact exists between the fingers and the rotor. The influences of various environmental and key structural parameters on the number of contact fingers, leakage, bearing force, and friction moment are studied. The results show that the pressure difference, eccentricity, and key design parameters have important effects on the number of contact fingers. The effect of rotation speed is relatively small. This paper provides a time-efficient tool for the design of noncontacting finger seals, which can quickly predict the performance of the sealing system.