Page 403 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

390 Classical Methods Chap. 12

Figure 12.4-4.

12.5 DIGITAL COMPUTER PROGRAM FOR THE
TORSIONAL SYSTEM

The calculations for the Holzer problem can be greatly speeded up by using a
high-speed digital computer. The problem treated is the general torsional system
of Fig. 12.5-1. The program is written in such a manner that by changing the data,
it is applicable to any other torsional system.
The quantities of concern here are the torsional displacement 6 of each disk
and the torque T carried by each shaft. We adopt two indexes: N to define the
position along the structure and I for the frequency to be used. For the computer
program, some notation changes are required to conform to the Fortran language.
For example, the stiffness K and the moment of inertia J of the disk are
designated as SK and SJ, respectively.
The equations relating the displacement and torque at the N\h and {N + l)st
stations are
0(7, TV + 1) = 0(7, N) - T{I, N ) / S K{N ) (12.5-1)

T {I ,N -h 1) = T {I, N) + \ { I ) * S J ( N + 1)*(9(7, TV+ 1) (12.5-2)

where A = SU, 1) = 1, T(7,1) = A(7)* 5/(1).

By starting at N = 1, these two equations are to be solved for 6 and T at
each point N of the structure and for various values of A. At the natural
frequencies, 6 must be zero at the fixed end or T must be zero at the free end.