1 how to design isolator with the customer requirement with

1) how to design isolator with the customer requirement with the data given above?

A shipping company need to design an umdamped isolator, for a printed circuit board. The mass of the board is 2 kg and during shipping, it is expected that the ship base is subjected to 8.1 Hz and amplitude of 2 mm. The isolator design has to fulfill the customer requirement whereby the displacement transmitted to the printed circuit board should be no more than 2 % of the base motion. Write your answer in N/m up to 2 decimal points.

Solution

Isolator has to be undamped (given)

Transmissibility ratio(T) = 1/(r²-1)²

r= w/w_n where w= frequency of ship and w_n is natural frequency.

T= 0.02 ( 2percent is given)

therefore 0.02= 1/(r²-1)²

r² -1 = 7.07

r=2.84

w/w_n =2.84

w= 2*pi*f

f= 8.1 Hz (given)

w= 50.9 rad/s

w_n= w/r

w_n= 50.9/2.84= 17.91 rad/s

w_n²= k/m

k= w_n² * m (m=2 kg)

k= 641.54 N/m is the required value of spring stiffness for isolation of vibration.