Numerical solution for the differential equations governing the free vibrations of space helicoid al bars

Abstract EN

This paper presents an alternative numerical procedure for the analysis of free vibrations of three dimensional bars.

First, for a specified geometry the twelve governing differential equations of equilibrium and deformations are presented within the framework of linear elasticity.

Then the method of variation of parameters and the method of dynamic stiffness matrix are outlined as two alternative methods for solving the resulting equations.

Finally, the dynamic stiffness matrix procedure is introduced as a more practical numerical procedure to solve the boundary value problem.

The procedure is developed starting from the dynamic transport matrix and is used to develop a true helicoidal finite element.

This procedure is outlined by performing the analysis of free vibrations of helicoidal circular bars and the results are compared to those of a general finite element code.