The Normal Modes of Beam-Like Structures by a Lanczos-Stodola Method.

A method of finding the flexural and torsional normal modes of structures which have straight stiffness axes and which are mounted as cantilevers is given. The Lanczos method of minimised iterations is used to obtain intermediate modes using the integro-differential equations and the mass and stiffness distributions. The inertia matrix appropriate to the intermediate modes is tridiagonal and the stiffness matrix is unit. The dominant eigenvalues and vectors of the inertia matrix give good approximations to the graver normal bodies. Results of test calculations using a computer program which also allows for the presence of discrete masses are given.