This article presents a cut spectral Bogner-Fox-Schmit (BFS) element for wave propagation analysis of thin isotropic plates of arbitrary shapes at high frequencies. The need for structured discretizations inherent to a recently proposed rectangular spectral BFS element based on \(\hbox {C}^1\) -continuous Gauss-Legendre-Lobatto interpolations is addressed by employing a fictitious domain approach, namely the finite cell method. A structured Cartesian mesh is used in place of the conventional geometry-conforming discretization, along with an advanced numerical integration of cut elements. This modification facilitates the analysis of more intricate geometries with non-rectangular shapes or those featuring holes, or inclusions. The free vibration analysis of circular plates demonstrates that this method offers excellent accuracy and convergence properties. Through transverse vibration analysis of a simply supported plate with a hole at the centre, it is shown that responses in low- and high-frequency ranges can be accurately resolved using this method. In this scenario, the numerical results are benchmarked against converged solutions calculated employing the S8R6 element in ABAQUS. The effectiveness of this method in wave propagation problems is verified by comparing its performance with the converged solutions obtained using the standard cut BFS element with a very fine mesh. Results confirm that this element achieves exceptional accuracy, faster convergence, and improved computational efficiency compared to its standard finite element counterpart. The present element, being the first \(\hbox {C}^1\) -continuous spectral plate element for general shapes, will facilitate the development of other spectral elements for wave propagation analysis of isotropic and laminated composite plates based on advanced higher-order theories requiring \(\hbox {C}^1\) -continuity.
