A simple tool to forecast the natural frequencies of thin-walled cylinders

Abstract

Abstract. This paper presents an approximate method to predict the natural frequencies of thin-walled cylinders. By taking inspiration from a previous work of one of the authors, the starting point of the proposed approach is a proper construction of reasonable eigenfunctions. However, a new simple tool based on the principle of virtual work has been developed to estimate the natural frequencies and the amplitude of vibration without complex numerical resolution. Moreover, the applicability of the model is extended to all the most common constraint conditions. The identification of the natural frequencies of a continuous cylinder is reduced to an eigenvalue problem based on a matrix whose elements depend only on the geometric characteristics of the cylinder, the mechanical properties of the material and known numerical parameters. The latter are precalculated for given boundary conditions, covering clamped or pinned end constraints. Although the proposed formulation can address any constraints combination, only a pinned-pinned cylinder is analyzed here for brevity. The reliability of the model was tested against FEM analysis results. These comparisons showed that the maximum error versus the exact solutions for the lowest natural frequency is around 2% for all the mode shapes of the pinned-pinned case, offering an excellent trade-off between accuracy and ease of use.

A Dynamic Matrix for the Study of Free Vibrations of Thin Circular Cylindrical Shells under Different Boundary Conditions

“…The simplifying assumptions can concern the formulation of the equations of motion for thin cylinders [8,9,[45][46][47][48][49] or the approach for solving the partial differential equations by using energetic methods such as Rayleigh-Ritz's [50,51] or Hamilton's principle [46,48,52] and introducing the beam flexural vibrations in the displacements eigenfunctions for thin cylinders [10,14,15,20,21,[45][46][47][53][54][55]. However, despite the simplification, a closed-form solution is not always ensured [48,51].…”