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# Accession Number:

## AD0831130

# Title:

## CONVERGENCE OF APPROXIMATE NATURAL FREQUENCIES OF OSCILLATIONS OF A FREE BEAM WITH VARIABLE PARAMETERS TO THE EXACT FREQUENCIES OF THE PROBLEM,

# Descriptive Note:

# Corporate Author:

## FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OH

# Report Date:

## 1967-09-20

# Pagination or Media Count:

##
10.0

# Abstract:

## The problem of determining the natural frequencies of flexural and torsional vibrations of a beam with variable and with concentrated loads is analyzed. The essense of the method proposed consists in partitioning the beam into a certain number of segments in which it is assumed that variation of parameters is smooth. To determine the modes of vibrations and the natural frequencies in each segment, differential equations with constant coefficients obtained by averaging variable parameters are set up whose solutions can be obtained by means of electronic computers. By applying the theory of Fredholm integral equations with a symmetrical kernel and the Weil theorem concerning the eigenvalues of completely continuous self-adjoint operators in Hilbert space it is proven that approximate natural frequencies converge to the exact natural frequencies when the number of conditional segments increases without bound. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#