Page 133 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

120 Transient Vibration Chap. 4
or
z = F{x, y,t)
Thus, this vector equation is identical in form to the equation in one variable and
can be treated in the same manner.
Example 4.8-2
Solve the equation 2x + 8i + IOOjc = fit) using RUNGA, with fit) vs. r, as shown
in Fig. 4.8-1.

t Figure 4.8-1.

Solution: The eomputer program RUNGA, available in the disk aecompanying the book,
is essentially the same as the one presented in See. 4.8. It ineludes damping, and the
exeiting foree is approximated linearly between several time points.
The use of the program RUNGA is illustrated here for Example 4.8-2. The
program solves the differential equation
d^x dx
~dF dt
The eomputer asks for the numerieal values of m, c, k and the defining values
of fit) which for Example 4.8-2 are obtained from the given figure for fit) vs. t. The
force is defined by the four points of the following table.
t fit)
0 0
0.25 1.0
0.50 0.50
1.0 0
It then asks for the initial values, which for this problem are x(Q) = i(Q) = 0. With
this input the computer calculates the natural period, r = 27ry and the time
interval h, and proceeds with the computation for the solution.
The results presented are the displacement xit) and the velocity xit). At this
point the program asks whether a printout is desired and also presents a choice for
the rough plot.
Presented are the solution for Example 4.8-2 and its rough plot for the
displacement.