INVESTIGATION OF PARAMETERS AFFECTING FREE VIBRATION FREQUENCY OF HELICAL SPRINGS

A set of 12 partial differential equations pertaining to helical springs is solved for free vibrations by the transfer matrix method. The dynamic transfer matrix including the axial and the shear deformations and the rotational inertia effects for any number of coils is numerically determined up to any desired precision in an efficient way. It is proved that the coefficients of the characteristic determinant of the dynamic differential matrix, [D], with odd-numbered subscripts are equal to zero which is based on the peculiarity that the traces of the same matrix with odd powers are all equal to zero. This important property of [D] has been the essence of the developed solution algorithm. The validity of the computer program coded in Fortran-77 has been verified by means of comparisons with the results given in literature. Next, the effects of the helix angle, the boundary conditions, the number of coils, and the ratio of (cylinder diameter/wire diameter) on the free vibration frequencies are investigated