TORSIONAL FREE VIBRATION OF A CYLINDER WITH VARYING CROSS-SECTION AND ADHESIVE MASSES

The natural vibration frequency of a torsion cylinder with varying cross section and an adhesive mass is investigated in this paper. From the numerical solution of the governing equation under the relevant boundary conditions we can define a function which is called the target function in this paper. It is proved that the problem for evaluating the natural vibration frequencies is equivalent to finding the zeros of the target function. An improvement formulation of the target function is suggested in this paper. Without regard to the number of the adhesive masses, the target function is obtained from a solution of one particular initial boundary value problem of the ordinary differential equation. The zeros of target function can be easily evaluated by the well known half-division technique. The suggested method depends significantly on the computer computation. It is proved that the target function approach provides one more effective method in this field. Many numerical results are carried out in this paper. The given numerical examples generally show that the adhesive masses influence by lowering the vibration frequency of torsion cylinder in general.