A GENERAL ALGORITHM FOR COMPUTING NATURAL FREQUENCIES OF ELASTIC STRUCTURES

Abstract

This paper presents and proves an algorithm for determining the natural undamped frequencies of vibration of any linearly elastic structure if its dynamic stiffness matrix K(ω0) corresponding to any finite set of displacements D is known. In general K(ω) is not a linear function of ω², and methods which are available for solving linear eigenvalue problems are inapplicable. The algorithm is valid for systems with either a finite or infinite number of degrees of freedom. It enables one to calculate how many natural frequencies lie below any chosen frequency, without determining them, and hence to converge on any required natural frequency to any specified accuracy. Coincident natural frequencies, and exceptional ones which correspond to D = 0 and not to det K (ω) = 0, are automatically accounted for.