Compact computation of natural frequencies and buckling loads for plane frames

Abstract

AbstractExisting theory is assembled to give a method which needs only the core of a mini‐computer to calculate the eigenvalues of large rigidly jointed plane frames with certainty, the eigenvalues being natural frequencies and critical load factors in free vibration and buckling problems, respectively. The method is illustrated by annotated listings of vibration and buckling programs, each involving under two hundred Fortran statements and with low number storage requirements (see Table I). The use of the programs as ‘black boxes’ is fully explained, with illustrative examples.The member theory used is the ‘exact’ classical Bernoulli‐Euler uniform member theory. Possible applications include: evaluation of answers from approximate methods; calculation of critical loads for substitution in the modified Merchant‐Rankine formula to estimate collapse loads of frames; and calculation of shifts in natural frequencies caused by structural damage, in connection with structural integrity monitoring of inaccessible structures.