1. Elastic Mountings
Main engines or auxiliaries in which there are out of balance forces or couples transmit them to the seating and so to the hull structure which may cause a forced vibration of unacceptable amount depending on the characteristics of the seating and the surrounding hull structure. The condition will be worst when the frequency of the distributing force close to the natural frequency of the seating or hull structure.
When such vibration occurs, or to avoid the risk of it in advance, one method available is to mount the engine on elastic or spring supports which will absorb the energy before it is transmitted to the structure. This practice is mainly confined to small high speed engines.

2. Elastic Mountings (Contd..)
Let,
=The weight of the machine/engine
=Angular velocity of the machine in rad/sec
=Centrifugal force due to unbalance in the machine for 1 rad/sec
Therefore the centrifugal force=
For a particular machine ‘m’ and ‘r’ is fixed. Therefore the centrifugal force is proportional to the square of angular frequency. Therefore at a speed of rad/secd ,the total centrifugal force will be The vertical component of the total centrifugal force will be

3. Elastic Mountings (Contd..)
When the machine attached directly to the foundation, there will be no relative movement between them, and the whole force will be transmitted directly to the seating. But if the machine is mounted on vertical springs, and is at the same time prevented from sideways motion then it will be free to move vertically on the seating within the limits allowed by the spring system. So the machine of weight W will be subjected a periodic disturbing force and will execute forced vertical vibration.

4. Elastic Mounting (Contd..)
We already know that the amplitude of the forced vibration for periodic disturbing force is given by:
So we can write,
The pulsating force in the springs at any instant will be equal to the deflection at that instant multiplied by the spring constant ‘k’ . So the maximum pulsating force is given by the following equation:

5. Elastic Mounting (Contd..)
So we obtain,
But is the maximum force transmitted to the seating when the connection is rigid.

6. Elastic Mountings (Contd..)
Thus the force transmitted through the spring mounting will be less than that transmitted through a rigid mounting if
numerically (i.e. both signs will hold good)
So the natural frequency of the machine on the springs must be less than 70%of the forcing frequency.

7. Elastic Mountings (Contd..)
The effects of damping have been so far neglected. This can be assumed to be approximately true if the mountings consists only of soft springs. However if rubber, cork or other similar materials are used in the design of the seating, considerable damping is introduced, and must be taken into account.
The amplitude of forced vibration under the influence of a periodic disturbing force and in the presence of damping is given by the following equation

8. Elastic Mountings (Contd..)
Here in this case, the amplitude due periodic disturbing force Therefore the amplitude will be:
The vertical force transmitted by them will be:
If C is the damping force per unit velocity, the force due to damping will be,

9. Elastic Mountings (Contd..)
These two forces are 90 degree out of phase. Therefore, the resultant force is given by:

10. Elastic Mountings (Contd..)
But
Now putting the value of ‘A’