# Vibration Isolation Study Notes for Mechanical Engineering

By Akhil Gupta|Updated : November 23rd, 2021

1.Vibrations Causing Unbalanced Forces in a Mechanical Running System

1.1. Rotating Unbalance: (Rotors, whose C.G. is not coinciding with the axis of shaft).

At time, t

fun in a particular direction ,

fun = (MRotor2)

where, f0 = (mRotor2)—max volume of unbalanced force.

ω—force frequency or excitation.

1.2. Reciprocating Unbalance: (in Piston-crank)

[mR—mass of Reciprocating Ports]

(mass of Piston + mass of crosshead + mass of connecting Rod)

Where, ω = forced frequency and m = machine mass (whole) which is under vibrations.

1.3. Forced-Damped Systems (Perfect Reality)

Fig.1: Forced vibrations of a damped spring mass system

After some time, CF = 0

Were,  A = Amplitude of steady state vibrations (independence of time) (forced vibrations)

Running system vibrations will never stop.

Every machine/mechanical running system must have one running life.

1.4. Magnification factor (M.F.):

Fig.2: magnification factor

• As Underdamping Increases

1.5. Phase Diagram or forced-Damped system:

• Spring and damping force’s max values are perpendicular to each other.
• Inertia force lies exactly opposite (At 180°) To the spring force’s max value.

1.6. Vibration Isolations:

It is used to isolate the ground from the vibrations of the Running machine so as to save other stationary m/cs from these vibration effects.

Fig.3: vibration isolation

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