Comparison of modal parameters of isotropic shell structures using beam and shell models considering slenderness ratio with various boundary conditions

Abstract

Modal parameters namely frequency, mode shape and generalized mass are required to determine the forced response of structures using mode summation method. The structure may be thin shell element of aircraft, rocket, submarine, pipeline and pressure vessel. The initial estimates are generally carried out using Euler-Bernoulli (EB) beam theory or classical beam theory since it provides reasonable engineering solution to the slender beams only as it introduces significant error for the calculation of modal parameters for short beams and also for higher modes. The predictions are improved by using Timoshenko Beam (TB) model which is based on First Order Shear Deformation Theory (FSD T). The accurate prediction of model parameters for thin isotropic shells shall be carried out by using shell equations based on Flügge formulations and Finite Element Analysis (FEA). The objective of the present paper is to compare the modal parameters of the first three beam type modes (n = 1) of thin isotropic shells using both beam and shell models considering the slenderness ratio for various boundary conditions. The results shall be useful for the selection of suitable model for the estimation of modal parameters of beam type modes for shell structures. The errors in modal parameters predicted by EB beam theory for the general assumption of slender beam (L/D = 10) is also reported.