A novel method is proposed to analyze the vibration characteristics of a flexible rotor installed on a rectangular panel foundation with arbitrary positions and angles. Springs are introduced to simulate the boundary conditions of panel foundation and the connecting bearings. The vibration displacements in each degree of freedom of both the spinning shaft and panel foundation are constructed through the improved Fourier series expansion. By introducing additional terms into the general Fourier series, the discontinuities at the foundation boundaries and connection joints are effectively eliminated. The Rayleigh-Ritz method is employed to derive the system’s characteristic matrices. The accuracy and convergence of the proposed model are validated by comparing the results with those obtained from finite element method. The impact of boundary conditions, bearing stiffness, as well as the mounting positions, orientation angles, and spinning speed of the shaft on the coupling system are examined. The results demonstrate that the rotor’s installation configuration significantly affects the system’s characteristics. In this model, the boundary conditions of both the rotor and the panel foundation are general, allowing for arbitrary angles and positions of rotor installation on the panel foundation. This approach provides an efficient tool for analyzing the dynamic characteristics of such complex rotor-foundation engineering systems.
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