Fundamental frequency of a sandwich cylindrical panel with clamped edges

A novel solution of the free vibration problem formulated for a shallow sandwich cylindrical panel with fully clamped edges is presented in the paper. Based on this solution, an analytical formula for the fundamental frequency is derived. The panel vibrations are modelled using the engineering theory of laminated cylindrical shells taking into account the transverse shear deformations. The governing equations derived in terms of the panel displacements, deflections and angles of rotation of the normal element, are solved using the Galerkin method. The functions approximating the shape of the vibrating panel are obtained based on the analysis of the bending deformation of clamped-clamped sandwich beam subjected to a uniformly distributed inertial load. The analytical formula is applied to calculations of the fundamental frequencies for sandwich panels with various structural parameters. The results of these calculations have been successfully verified using the finite element method and implemented in the design analysis of sandwich panels considering a constraint imposed on the value of their fundamental frequency.

Automated summary

This paper presents a novel solution to the free vibration problem of a shallow sandwich cylindrical panel with fully clamped edges, and derives an analytical formula for the fundamental frequency. The panel vibrations are modeled using engineering theory and solved using the Galerkin method, with approximate functions for the shape of the vibrating panel obtained from analysis of bending deformation of a clamped-clamped sandwich beam. The analytical formula is applied to calculate fundamental frequencies of sandwich panels with various structural parameters, successfully verified using the finite element method and implemented in the design analysis of sandwich panels.