A compact method for computing the eigenvalues and eigenvectors of plane frames

Abstract

Two Fortran computer programs are presented which calculate the eigenvalues and eigenvectors of rigidly jointed plane frames. The eigenvalues are natural frequencies and critical load factors in vibration and buckling problems, respectively, while the eigenvectors are the corresponding mode shapes. The theory is based on the stiffness method of analysis and uses classical (exact) member equations together with an algorithm which ensures that the required eigenvalues are found with certainty. The corresponding eigenvectors are then retrieved by a simple technique which offers improved accuracy over more established methods. The programming style is specifically aimed towards minicomputer application and this is illustrated by annotated listings of the programs, each of which contains just over two hundred Fortran statements. The use of the programs as ‘black boxes’ is fully explained with illustrative examples.