Modeling approach and experiments for the free vibration investigations of spatially coupled shell-plate systems with complex shapes

A general modeling approach is presented to analyze the free vibration behavior of the spatially coupled shell-plate system (SCSPS) with complex geometric shapes. The coupling mechanism established by the penalty function method can be applied not only to the SCSPS but also to other extensively studied shell-plate structures. The conventional method for irregularly-shaped plates involves the utilization of one-to-one mapping technology (OTOMT) to transform the two-dimensional plane domain of the plate into a square domain, aiming to fulfill the numerical solution requirement for integral calculation. However, since the OTOMT is a planar mapping technique that cannot be applied to shells, in this paper, we propose a coordinate transformation strategy to convert two-dimensional shells into plane geometry in order to address this limitation. The vibration problem is simultaneously resolved numerically using the Hamilton's principle and the Jacobi spectral method. The current method is validated for several key capabilities based on three case studies, as well as modal experiments and the commercial finite element software. Additionally, a series of model evaluations are employed to demonstrate the advantages of the current method. Moreover, the results of the parametric study illustrate the impact of several variables on the natural frequency of the structure.