NUMERICAL-SOLUTION FOR THE DIFFERENTIAL-EQUATIONS GOVERNING THE FREE-VIBRATIONS OF SPACE HELICOIDAL BARS

This paper presents an alternative numerical procedure for the analysi s of free vibrations of three dimensional bars. First, for a specified geometry the twelve governing differential equations of equilibrium a nd deformations are presented within the framework of linear elasticit y. Then the method of variation of parameters and the method of dynami c stiffness matrix are outlined as two alternative methods for solving the resulting equations. Finally, the dynamic stiffness matrix proced ure 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 fini te element. This procedure is outlined by performing the analysis of f ree vibrations of helicoidal circular bars and the results are compare d to those of a general finite element code.