2025 Volume 2025 Pages 20250006
In this paper the development of natural vibration analysis method for two types of thin-walled shell structures using the isolated element method is presented. The shell elements are a generalized quadrilateral thin-walled shell element with two orthogonal curvatures and a cylindrical thin-walled shell. The isolated element method (IEM) proposed by the authors is a discretized analysis method with divided elements. It extends the minimum potential energy principle without using nodes between elements, Lagrange multiplier method and penalty method. The continuity is satisfied by natural boundary conditions at the element boundaries. The admissible function in the element includes rigid body displacements and rotations using the local coordinate system is used and can be defined arbitrarily to some extent. On the other hand, noise and acoustic problems require analysis over a wide frequency range from low frequencies to high frequencies, requiring a large number of degrees of freedom in the analysis. By taking advantage of the characteristics of the isolating element method, natural vibration analysis in these wide frequency ranges can be performed with high accuracy using a small number of elements compared to the conventional FEM. In this presentation the basic theory of shell is based on Flügge's theory (Flügge-Goldenveizer-Novozhilov equations) and using the previously reported results for the basic plane stress field and plate bending, the equations for the generalized quadrilateral shell elements and the cylindrical shell are described. Numerical examples of the cylindrical shell are shown.
