Vibrations of slack cables with discrete masses

This paper describes a new method for obtaining the natural frequencies and mode shapes of arbitrarily slack cables which may contain concentrated masses as well as distributed mass and tensile stiffness. The method of imaginary reactions is used to perform the static calculation and Stodola's method is applied to do the dynamics. Integral formulas for the required influence functions appropriate to both fixed-fixed and fixed-forced boundary conditions are included. Solutions to sample problems, obtained with a program implemented on Naval Research Laboratory's Advanced Scientific Computer, are presented. The efficiency of this method is believed to exceed that of available finite element programs when the required number of integration intervals is large: that is, when numerous masses are present and/or high order modes are required.