In Section 2, the conditions of fractional damped systems being in critical damping case are given first.
Critical Damping of the System with Fractional Derivative Damping
(16.) The galvanometer which was considered most suitable for precise comparisons of standard cells, and which has been kept in mind during the design of the comparator, has the following constants: Complete period, 9 seconds; external resistance for critical damping
, 1,200 ohms; sensitivity with 1,200 ohms in series, 4 mm/[micro]v with a scale distance of 1 m.
Second, under critical damping
where [[zeta].sub.1] = 1 and [alpha] = 1, [tau] is transmitted to the drill bit, indicating loading.
From the structural dynamics point of view, the structural vibrations damp in the lowest possible time if the structure behaves in the critical damping
Here, [[zeta].sub.3] is the critical damping
ratio of the vibration isolation system and [[omega].sub.3n] is the natural frequency.
B(s) equal to zero (note that minus sign correspond to the complex conjugate pole of transfer function)--with [[sigma].sub.i] denote the modal damping coefficient, [[tau].sub.i]is the natural frequency, [[omega].sub.i] = [square root of [[sigma].sup.2.sub.i] + [[tau].sup.2.sub.i]] is the resonant frequency and [[xi].sub.i] = [[sigma].sub.i]/[[omega].sub.i] is the percent of critical damping
The critical damping
coefficient [C.sub.c] is found to be
al., 2002) resuming two original non-linear complex models of both types of bearings, studying their dynamical behavior, finding some values of critical damping
coefficient and some zones of chaotic behavior.
Dynamic behavior of three-parameter system was studied by Brennan ; he pointed out that the system had critical damping
if additional stiffness was at least eight times that of the main stiffness; the isolator afforded no advantages if the system was excited by white noise.
These peaks tend to indicate an equivalent damping ratio of 1, which is true considering the definition of critical damping
as the system no longer possesses oscillation.