A method of determining the extraneous unknowns in problems of the stability and vibrations of rods

An approximate method of determining the critical loads in problems of the stability of compressed rods has been extended to statically indeterminate systems. For this purpose, a method has been developed for solving stability problems when there are extraneous unknowns defined by the stationarity condition for the potential energy of the system. It is shown that, combined with Grammel's method and Hamilton's variational principle, the method described for determining the extraneous unknowns in statically indeterminate systems can also be used in problems of finding the natural frequencies of vibrations of rods.