The treatment was performed with the following parameters:

amplitude of oscillation A = 5 mm; frequency of oscillations f = 24 Hz; working tool mass m = 3.5-7.5 kg; treatment time [tau] = 12-36 min; and eccentricity [epsilon] = 10 mm.

An analytical solution in the complex form for the dimensionless shear stresses in the fluid is presented in terms of the Hartmann number, the suction/injection velocity parameter, the Reynolds number, the dimensionless velocity

amplitude of oscillation in the x- and y- directions, the ratio of the frequency of oscillation to the angular velocity of the disks, and the dimensionless time.

Therefore, compared with the other two control schemes, fuzzy-sliding mode control has the advantage in reducing the period and

amplitude of oscillation and the peak value of machining force.

As we can see from (1) and (2), when the frequency of the disturbing force a and the DD natural frequency [[omega].sub.d] are coincided, the amplitude of the mass oscillation M goes to zero [x.sub.M] [right arrow] 0, and the

amplitude of oscillation DD, respectively, proportional to the ratio of springs elasticity coefficients of main and auxiliary mass

The softening response consists of a frequency decrease as the

amplitude of oscillation increases, whereas the hardening response consists of a frequency increase of the structure as the

amplitude of oscillation increases [16].

It is seen that the

amplitude of oscillation of velocity increases and the required time to reach the steady state also increases as l increases.

The exact model has

amplitude of oscillation of 0.002, the single averaged model of 0.001, and the double averaged model has zero

amplitude of oscillation.

Not only the period of oscillation and

amplitude of oscillation can be correctly estimated but also the guaranteed convergence rate can be accurately calculated.

In the following section, the values of m and [[tau].sub.1] are determined simultaneously by the government and the Central Bank, so that income's constant

amplitude of oscillation around its intertemporal equilibrium value is minimized.

During sliding itself, the

amplitude of oscillation is lower.

Under some conditions non-linear oscillators may display irregular and really complex oscillations, being it impossible to detect its period and

amplitude of oscillation, in other words, the oscillation becomes aperiodical (it never exactly repeats).

It is evident that for the initial 1 min the screw rotated without oscillation, and then the

amplitude of oscillation gradually increased to about 100[micro]m.