Optimization of the Ritz method to calculate axisymmetric natural vibration frequencies of cylinders

Abstract

A straightforward accurate technique is presented for calculating natural frequencies for axisymmetric vibration of cylinders of any aspect ratio. The Ritz variational method is applied by using algebraic polynomials in the form of power series in the axial and radial coordinates. The adequate choice of the maximum exponents for each coordinate is important factor in order to achieve better accuracy, compatible with an admissible time of calculation. A computational model is developed that provides the optimum selection of exponents by following an automatic iterative process. This leads to a precise calculation of frequencies in a minimum time of calculation. The method is tested by comparing numerical and experimental results and a good agreement is obtained. The common hypothesis on the number of terms in the radial and axial coordinates is not sufficiently justified, as is proved.