where [xi] is the fraction of

critical damping in the highest mode.

D in this study was defined as the ratio of the actual damping coefficient to the

critical damping coefficient as shown in Equation (2), where AL is the area of the hysteresis loop and AT is the area of the shadow triangle as shown in Figure 11.

For a given mode i, the

critical damping ratio [[xi].sub.i] in Rayleigh damping is expressed in terms of damping coefficients [alpha] and [beta] as

Before adding the signal, the damping coefficient ratio is adjusted to make the Duffing oscillator system in the chaotic critical state, and the

critical damping coefficient is expressed as [k.sub.c].

Critical damping is defined as the threshold between overdamping and underdamping.

Additionally a theoretical model that assigns a percent

critical damping value to a given set of shock absorber damping values, estimated suspension inertia, stiffness, and geometry was used.

Further the baseline analysis configuration has a mechanical trail of zero ([l.sub.t] = 0m) and lateral damping for both the trailing wheel with lateral fexibility and the LG-Shimmy model represents 5%

critical damping.

In simplified seismic response analysis procedures, like the SELF procedure, the effect of the dissipated energy produced by yielding of the material and by viscous damping on the reduction of the structural response is taken into account by considering an equivalent amount of viscous damping (usually 5% of

critical damping).

The damping loss factor is defined as the ratio of energy dissipated per cycle of oscillation to the total dynamic energy in a subsystem and can be related to other commonly used damping parameters like the

critical damping ratio.

Because of difficulties in obtaining data values, particular case heuristic

critical damping based approach developed by Tsuji et al.

In the relation (1), [zeta] = c/[c.sub.cr] represents the fraction of the

critical damping, whose values, compared to unity, give important indications about the damping of structure.

The damping values are kept constant at 8% to 10% of the

critical damping value.