Homogeneous Model in Finite Element Analysis for Natural Frequency Calculation of Axisymmetric Shells

Purpose. The article aims to provide practical recommendations for calculating natural frequencies in axisymmetric shells using finite element methods. It focuses on the need to develop a simplified model that can be used in any modern finite element software package. The study analyzes the impact of the simplified homogeneous model on the deviation and error of natural frequencies compared to real structures. Design / Method / Approach. The research is based on creating a simplified shell geometry by determining parameters such as shell thickness and density. These parameters are derived under the condition of equivalence in the moment of inertia and mass of the cross-sectional element. These parameters can vary along the height of the shell. Findings. The natural frequencies of the experimental shell with complex geometry were calculated and compared with those of the simplified model. The deviations and errors in the calculated frequencies were determined. It was demonstrated that the simplified model allows the calculation of natural frequencies with a deviation of no more than 1% from the experimental model, while significantly reducing computation time and the required computer resources. Theoretical Implications. The research expands the understanding of challenges in calculating the natural frequencies of complex objects using finite element methods under limited computational resources. Practical Implications. Practical recommendations are provided for engineers and designers when performing modeling tasks in the mechanics of deformable solid bodies. Originality / Value. The article presents an original analysis of a real case where a simplified model was implemented to determine the natural harmonics of a liquid rocket engine nozzle, making it a valuable tool for studying complex structures. Research Limitations / Future Research. The study is limited to the analysis of determining the natural frequencies of axisymmetric shells and does not cover all possible geometric features. Future research may focus on developing simplified models based on the equivalence of stiffness and mass parameters.