Consider the microgravity isolation suspension system shown

Consider the microgravity isolation suspension system shown below to be used for isolating sensitive experiments in space. The system consists of an outer frame of mass M = 10 kg and an inner experiment box of mass m = 4 kg. The inner box can slide vertically inside the frame without friction and its motion is isolated by 4 springs of stiffness k = 500 N/m. The outer frame is excited by a vertical disturbance force f(t). Write the equations of vertical motion of the outer frame of mass M and the inner experiment box of mass m. Find the transfer function from the disturbance force f(t) to the vertical displacement x(t) of the inner box. Consider a sinusoid disturbance input force Determine the steady-state amplitude of the inner box displacement |x|.

Solution

Hello,

if outer frame was experienced f(t) force vertically displace the system by x(t).

1. As frame moves below two springs will be compressed sd inner experimental box is independent of frame and it will roll.

transfer fuction is related to control engineering.

2. be cause of this upper springs will be expnaded. so displacement in upper and lower springs will be different.

so governing equation is.

(M+m)a1-ma2) + K2 (-x2) + 4k(x1) +4Cv1- 2Cv2 = f(t)

x1 displacement due to movement of mass M due to force f.

x2 displacement due to movement ofmass m (internal distarbunce).

x = displacement.

v= veleocity.

a = Acceleration.

if experimental system of mas m, to be in equilibrium when x2=0.

rewriting equation.

(M+m)a1 + 4Kx1 + 4cV1 = f(t)