T1-17 Figure 22    Shock Effect at Different                     Damping Values 5 4 3 2 x = 0.2 3 = 1.26 x = 0.1 3 = 0.63 x = 0 3 = 0 1 1 2 3 4 = 5 d_max dst amax g V3 g Figure 22 illustrates Equation (18). When the damp- ing is small, maximum force transmitted to equipment is very nearly kd_max. 3.3.2    Sudden Impact on Equipment [3] Sudden impact, or a sharp blow is characterized by a large force (F_o) acting for a short period of time (t_o) as shown in Figure 23(a). For practical purposes, suddenness is taken to mean that t_o is small in comparison with the natural period of vibration of the system in Figure 23(b). The impulse, I, is defined as the area under the force-time curve; i.e., I = F_o t_o  lb-sec or kg m/sec                                                                                                                                             (19) Application of impulse I results in a sudden downward velocity V of the object, V = Ig/W.                                                                                                                                                                         (20) The maximum isolator deflection and the maximum acceleration of the object can be obtained by substituting V into Equation (18). 4.0    NONLINEARITIES The equations previously given for transmissibilty (Section 3.1) make certain assumptions which may not always be valid. For example, it is assumed that the damping is viscous or linear (resistance to relative motion is proportional to the relative velocity). The assumption greatly simplifies the analysis. However, the damping provided by wire mesh is a combina- tion of localized frictional losses by individual wires and hysteresis in the cushion itself. Damping in elastomeric materials has similar characteristics. In practical terms, this means that the damping is a function of displacement in addition to velocity, and the terms describing the damping in the equations of motion are nonlinear. At resonance, where the displacement is large, the damping is high. In the isolation band, where displacement is small, the damping is negligible. This condition gives the best of both worlds as damping is only desirable under resonance conditions. Thus, the idealized curves in Figure 10 are on the conservative side since they show deterioration of isolation in the high frequency (after resonance) range. Figure 23    Vibration Isolation System of Object W (b) Subjected                     to Sudden Impact on the Object with Time History (a) W x I Object Vibration Isolator k c Damping constant Sudden impulse (large force F_o acting over very short time (t_o): I = F_ot_o). Base (b) SYSTEM (a) FORCE TIME CURVE OF AN IMPULSE Impulse to Time