Vibration Isolation MCQ Quiz in मल्याळम - Objective Question with Answer for Vibration Isolation - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Explanation:
The amplitude ratio and transmissibility of a vibration isolator is unity when the frequency of exciting force is √2 times the natural frequency.

• For any damped system, the damping ratio (ξ) is defined as the ratio of the damping constant to the critical damping constant.
• Logarithmic decrement is used to obtain damping in free vibration.
• Dampers absorb the energy and do not allow the vibration amplitude to reach the infinity in the resonance phase, while in conservative systems without any damper; the amplitude reaches infinity when resonance happen.

i.e. at ω = ω_n

Resonance occurs

Amplitude → ∞

• Transmissibility of vibration

\(T_r=\frac{\sqrt{1+\left(2 \xi \frac{\omega}{\omega_n}\right)^2}}{\sqrt{\left(1-\frac{\omega^2}{\omega_n^2}\right)^2+\left(2 \xi \frac{\omega}{\omega_n}\right)^2}}\)

Put \( \frac{\omega}{\omega_n}=\sqrt{2}\)

T_r = \(\frac{\sqrt{1+4 \xi^2 \cdot 2}}{\sqrt{(1-2)^2+4 \xi^2 \cdot 2}}=\frac{\sqrt{1+8 \xi^2}}{\sqrt{1+8 \xi^2}}\) = 1

Concept:

Vibration Isolation: 

• The purpose of vibration isolation is to control the transmission of the vibration to the base upon which the machines are installed.
• It is done by mounting the machines on the spring, dampers, or other vibration isolation material.
• In a vibration isolation system, transmissibility is also known as the isolation factor. 
  • Force transmissibility is defined as the ratio of force transmitted to the foundation that impressed on the system.
  • For a viscous damped system with impressed force F0 and transmitted force FT, transmissibility is given as 

\(\frac{{{F_T}}}{{{F_0}}} = {\rm{\;Transmissibility\;}} = \frac{{\sqrt {1 + {{\left( {2ξ r} \right)}^2}} }}{{\sqrt {{{\left( {1 - {r^2}} \right)}^2} + {{\left( {2ξ r} \right)}^2}} }}\)

Where, ω = speed of the exciting source, rad/s, ωn = natural frequency of system, rad/s, ζ = damping ratio

The transmissibility curve for different values of the damping ratio is shown below

Conclusions:

• Independent of the value of the damping ratio, the transmissibility of the mechanical system tends to zero as the value of the frequency ratio is above √2. T
• The section beyond frequency ratio √2 is known as the Isolation part of the transmissibility curve,

\(\frac{{{F_T}}}{{{F_0}}} <1 \)

⇒ ϵT < 1

• If the frequency ratio (ω/ωn) is less than √2 then the transmitted force is always greater than the exciting force.

\(\frac{{{F_T}}}{{{F_0}}} >1 \)

⇒ ϵ_T > 1

So, the best answer is option 3

• If the frequency ratio (ω/ωn) is equal to √2 then the transmitted force is equal to the exciting force.

ϵT = 1

Concept:

At resonance (ω = ω_n), phase angle ϕ is 90°.

When ω/ω_n ≫ 1; the phase angle is very close to 180°. Here inertia force increases very rapidly, and its magnitude is very large.

Explanation:

Vibration may be caused by instability in the media flowing through the rotating machine.

A damper is a device that is used for damping vibration. Damping is the dissipation of energy from a vibrating structure. And dissipation means a transformation of energy into another form of energy and therefore removal of energy from the vibrating system.

Accumulator: An accumulator is a device to store sufficient energy in case of machines that work intermittently to supplement the discharge from the normal source. 

The objective of a damper and an accumulator is opposite to each other.

Concept:

In the vibration isolation system, the ratio of the force transmitted to the force applied is known as the isolation factor or transmissibility ratio.

\(T = \frac{{{F_T}}}{{{F_O}}} = \frac{{\sqrt {1 + {{\left( {2\zeta \frac{\omega }{{{\omega _n}}}} \right)}^2}} }}{{\sqrt {\left[ {1 - {{\left( {\frac{\omega }{{{\omega _n}}}} \right)}^2} + {{\left( {2\zeta \frac{\omega }{{{\omega _n}}}} \right)}^2}} \right]} }}\)

• When ω/ωn = 0 ⇒ TR = 1, (independent of ζ)
• When ω/ωn = 1 and ξ = 0 ⇒ TR = ∞, (independent of ζ)
• When frequency ratio ω/ωn = √2, then all the curves pass through the point TR = 1 for all values of damping factor ξ.
• When frequency ratio ω/ωn < √2, then TR > 1 for all values of damping factor ξ. This means that the force transmitted to the foundation through elastic support is greater than the force applied.
• When frequency ratio ω/ωn > √2, then TR < 1 for all values of damping factor ξ. This shows that the force transmitted through elastic support is less than the applied force. Thus vibration isolation is possible only in the range of ω/ωn > √2. Here the force transmitted to the foundation increases as the damping is increased.

Explanation:

Since the natural frequency of R (128 Hz) is closest to the frequency produced by the instrument (144 Hz), therefore Sample 'R' will show the most perceptible induced vibration.

When frequency of two vibration close near or matched then their amplitude get maximum. 

Concept:

Vibration Isolation: 

• The purpose of vibration isolation is to control the transmission of the vibration to the base upon which the machines are installed.
• It is done by mounting the machines on the spring, dampers, or other vibration isolation material. 
  • Force transmissibility is defined as the ratio of force transmitted to the foundation that impressed on the system.
  • For a viscous damped system with impressed force F0 and transmitted force FT, transmissibility is given as 

\(\frac{{{F_T}}}{{{F_0}}} = {\rm{\;Transmissibility\;}} = \frac{{\sqrt {1 + {{\left( {2\xi r} \right)}^2}} }}{{\sqrt {{{\left( {1 - {r^2}} \right)}^2} + {{\left( {2\xi r} \right)}^2}} }}\)

Where, ω = speed of the exciting source, rad/s, ωn = natural frequency of system, rad/s, ζ = damping ratio

The transmissibility curve for different values of the damping ratio is shown below

Conclusions:

• Independent of the value of the damping ratio, the transmissibility of the mechanical system tends to zero as the value of the frequency ratio is above √2. The section beyond frequency ratio √2 is known as the Isolation part of the transmissibility curve.
• If the frequency ratio (ω/ωn) is less than √2 then transmitted force is always greater than the exciting force.
• If the frequency ratio (ω/ωn) is equal to √2 then transmitted force is equal to the exciting force.

Concept:

In the vibration isolation system, the ratio of the force transmitted to the force applied is known as the isolation factor or transmissibility ratio.

\(T = \frac{{{F_T}}}{{{F_O}}} = \frac{{\sqrt {1 + {{\left( {2\zeta \frac{\omega }{{{\omega _n}}}} \right)}^2}} }}{{\sqrt {\left[ {1 - {{\left( {\frac{\omega }{{{\omega _n}}}} \right)}^2} + {{\left( {2\zeta \frac{\omega }{{{\omega _n}}}} \right)}^2}} \right]} }}\)

• When ω/ωn = 0 ⇒ TR = 1, (independent of ζ)
• When ω/ωn = 1 and ξ = 0 ⇒ TR = ∞, (independent of ζ)
• When frequency ratio ω/ωn = √2, then all the curves pass through the point TR = 1 for all values of damping factor ξ.
• When frequency ratio ω/ωn < √2, then TR > 1 for all values of damping factor ξ. This means that the force transmitted to the foundation through elastic support is greater than the force applied.
• When frequency ratio ω/ωn > √2, then TR < 1 for all values of damping factor ξ. This shows that the force transmitted through elastic support is less than the applied force. Thus vibration isolation is possible only in the range of ω/ωn > √2.

Therefore, from the figure, we can say that higher damping reduces the transmissibility in the region where ω/ω_n <√2 and in the region ω/ω_n > √2, higher damping increases the transmissibility.

Explanation:

In the vibration isolation system, the ratio of the force transmitted to the force applied is known as the isolation factor or transmissibility.

\(\varepsilon = \frac{{\sqrt {1 + {{\left( {\frac{{2c\omega }}{{{c_c}.{\omega _n}}}} \right)}^2}} }}{{\sqrt {{{\left( {\frac{{2c\omega }}{{{c_c}.{\omega _n}}}} \right)}^2} + {{\left( {1 - \;\frac{{{\omega ^2}}}{{{\omega _n}^2}}} \right)}^2}\;} }}\)

Concept:

Vibration Isolation: 

• The purpose of vibration isolation is to control the transmission of the vibration to the base upon which the machines are installed.
• It is done by mounting the machines on the spring, dampers, or other vibration isolation material. 
  • Force transmissibility is defined as the ratio of force transmitted to the foundation that impressed on the system.
  • For a viscous damped system with impressed force F0 and transmitted force FT, transmissibility is given as 

\(\frac{{{F_T}}}{{{F_0}}} = {\rm{\;Transmissibility\;}} = \frac{{\sqrt {1 + {{\left( {2\xi r} \right)}^2}} }}{{\sqrt {{{\left( {1 - {r^2}} \right)}^2} + {{\left( {2\xi r} \right)}^2}} }}\)

Where, ω = speed of the exciting source, rad/s, ωn = natural frequency of system, rad/s, ζ = damping ratio

The transmissibility curve for different values of the damping ratio is shown below

Conclusions:

• Independent of the value of the damping ratio, the transmissibility of the mechanical system tends to zero as the value of the frequency ratio is above √2. The section beyond frequency ratio √2 is known as the Isolation part of the transmissibility curve.
• If the frequency ratio (ω/ωn) is less than √2 then transmitted force is always greater than the exciting force.
• If the frequency ratio (ω/ωn) is equal to √2 then transmitted force is equal to the exciting force.