Contribution to the Determination of Natural Frequencies and Shapes of Vibrations of Bar-Shaped Systems.

It is shown that when solving a bar-shaped system with the aid of the deformation method and if all natural frequencies and shapes of vibration have to be determined, the condition of zero value of the determinant of the structure's dynamic rigidity matrix is not sufficient so that a triaxial solution of a system of conditional equations has to be admitted. The article suggests that the second condition may be neglected by inserting another joint into the various bars; however, in this case the number of unknowns will increase. Several examples are presented to illustrate the problem.