The Enhanced Spline-Method for Numerical Results of Natural Frequencies of Beams

There are many cases in engineering practice when it is necessary to know values close to exact for natural modes of beam and framing vibrations. This paper devoted to enhance the accuracy of calculations of natural frequencies of a beam, which is realized on the basis of an extrapolation of numerical results obtained by spline functions of 5th degree.This paper shows that proposed spline-method has the second order of convergence This method has the minimum relative error less than 1·10-8 for the first five natural frequencies at number of elements M = 512, and for the following five frequencies the method has an error less than 1·10-6. Therefore, the realized method of extrapolation shown itself as very effective instrument to improve the accuracy of the spline-method for determining the natural frequencies for the beam under various fixing conditions, and in future it may allow to achieve the calculation results for many practical problems with high accuracy.