An extended Chebyshev spectral method for vibration analysis of rotating cracked plates

Abstract

A semi-analytical model for free vibration analysis of rotating plates with cracks is developed based on an extended Chebyshev spectral method. The displacement variables of the rotating plates modeled with thick plate theory are established by a new form of improved Chebyshev series expansions composed of a standard Chebyshev series and supplementary crack functions. The crack functions are derived from the Fourier cosine series and their antisymmetric counterparts to capture the stress singularity at the crack tip. The model systematically considers the rotating effects including the rotating stiffening, rotating softening, and Coriolis force effects. The penalty function method was used to simulate the boundary conditions, and the displacement components of the cracked plate were uniformly expressed in the form of a series expansion. The vibration governing equations of the rotating cracked plate are derived based on Hamilton principle. Experimental validation of dynamic modeling of a cracked plate is conducted. The efficiency and accuracy of the proposed method are further demonstrated by comparing results with reference data, FEM simulations, and experimental data. Numerical results show that the extended Chebyshev spectral method can accurately capture the complex geometries at crack locations while maintaining the rapid convergence characteristic of traditional Chebyshev spectral methods. Findings reveal that cracks increase modal coupling, resulting in more complex natural frequencies and mode shapes.