FREE VIBRATION OF THIN-WALLED ORTHOTROPIC CYLINDRICAL SHELL ON ELASTIC FOUNDATION

The semi-analytical solutions of the free vibration frequency of orthotropic cylindrical shell under elastic basis and the general boundary condition were obtained in this paper to provide a reliable theoretical basis for the parametric analysis and design of typical engineering structures. The proposed method contains three key parts:1) Differential equations of vibration of cylindrical shells with radial preloading on the elastic foundation were derived based on the Donnell-Mushtari shell theory and Hamilton principle; 2) It is pointed out that there are a total of nine different combinations of solutions for the differential equation, which clarifies the errors in the literature and avoids the possible omission of solutions; 3) The general solutions of the vibration frequency were obtained by the dichotomy, which were in good agreement with those of classical literature and validated the applicability of the proposed method. It is found that the influence of the spring stiffness and the internal pressure on the natural frequency is non-linear, while the method is applied to parametric analysis of the cylindrical shell with springs supported at both ends. The method developed in this paper is applicable to the vibration of cylindrical shell under general boundary conditions, which is accurate, reliable, can avoid omitted solutions with strong applicability, and provides a reliable method for vibration analysis of such structures.