Mechanical Vibrations MCQ Quiz in தமிழ் - Objective Question with Answer for Mechanical Vibrations - இலவச PDF ஐப் பதிவிறக்கவும்

Explanation:-

Critical or whirling speed of a shaft

• When the rotational speed of the system coincides with the natural frequency of lateral/transverse vibrations, the shaft tends to bow out with a large amplitude. This speed is termed as critical/whirling speed.
• Whirling speed or Critical speed of a shaft is defined as the speed at which a rotating shaft will tend to vibrate violently in the transverse direction if the shaft rotates in the horizontal direction.
• In other words, the whirling or critical speed is the speed at which resonance occurs.
• Hence we can say that whirling of the shaft occurs when the natural frequency of transverse vibration matches the frequency of a rotating shaft.
• It is the speed at which the shaft runs so that the additional deflection of the shaft from the axis of rotation becomes infinite is known as critical or whirling speed.

Explanation:

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 

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 the frequency ratio   is known as the Isolation part of the transmissibility curve i.e., For effective vibration isolation, the frequency ratio  must be less than 
• If the frequency ratio (ω/ωn) is less than then the transmitted force is always greater than the exciting force.
• If the frequency ratio (ω/ωn) is equal to  then the transmitted force is equal to the exciting force.

Explanation:

Vibration

Vibration is a periodic motion of small magnitude. But for sake of simplicity, we can assume it as a simple harmonic motion of small amplitude.

Transverse vibrations

• When the particles of the shaft or disc move approximately perpendicular to the axis of the shaft, then the vibrations are known as transverse vibrations.

• In this case, the shaft is straight and bent alternately and bending stresses are induced in the shaft.

• Rotating shafts tend to vibrate violently in Transverse direction at critical speeds.

Longitudinal vibrations

• When the particles of the shaft or disc move parallel to the axis of the shaft, then the vibrations are known as longitudinal vibrations.

• In this case, the shaft is elongated and shortened alternately and thus the tensile and compressive stresses are induced alternately in the shaft.

Torsional vibrations

• ·When the particles of the shaft or disc move in a circle about the axis of the shaft, then the vibrations are known as torsional vibrations.

• ·In this case, the shaft is elongated and shortened alternately and thus the tensile and compressive stresses are induced alternately in the shaft.

Critical or whirling speed of a shaft

The speed, at which the shaft runs so that the additional deflection of the shaft from the axis of rotation becomes infinite, is known as critical or whirling speed.

Explanation:

Damping ratio:

The ratio of the actual damping coefficient (c) to the critical damping coefficient (cc) is known as damping factor or damping ratio.

Transmissibility:

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

If  then ϵ = 1 for all values of damping factor c/cc.

Magnification factor:

The ratio of the amplitude of forced vibration by the harmonic force Focos(ωt) to the static deflection produced by force Fo is known as the magnification factor.

Explanation:

Damped vibration:

When the energy of a vibrating system is gradually dissipated by friction and other resistance, the vibrations are said to be damped vibration.

Damping ratio:

The ratio of the actual damping coefficient (c) to the critical damping coefficient (cc) is known as damping factor or damping ratio.

• Overdamped System: ζ > 1
• Underdamped: ζ
• Critical Damping: ζ = 1: The displacement will be approaching to zero in the shortest possible time. The system does not undergo a vibratory motion. 

Concept:

The natural frequency is given by:

Calculation:

Given:

L₁ = L, 

For cantilever beam:

{\omega _1} \end{array}\)

Concept

Critical speed

Whirling speed or Critical speed of a shaft is defined as the speed at which a rotating shaft will tend to vibrate violently in the transverse direction if the shaft rotates in horizontal direction. In other words, the whirling or critical speed is the speed at which resonance occurs.

Critical speed of the shaft:

Calculation:

Given:

Δ =  25 mm

  rad/sec

Concept:

Peak amplitude 

Where, ω_n = Natural frequency, ω = forced frequency

ξ = Damping factor or damping ratio

Calculation:

 ξ = 0 given

F₀/m = a

∴ A = 10.00 mm

Concept:

Critically damped system never executes a cycle, it approaches equilibrium with exponentially decaying displacement, because the system returns to equilibrium in fastest time without any oscillations and in critically damped free vibrations, the damping force is just sufficient to dissipate the energy within one cycle of motion. The value of Damping Factor () is 1.

Eg. AK 47 gun

Explanation:

Magnification Factor:

where .

Thus M.F = f(r, ξ)

During resonance, the amplitude of vibration is maximum i.e Magnification factor is maximum and for an underdamped harmonic oscillator i.e. (ξ ≠ 0) it happens just before the frequency ratio reaches unity as can be seen from the graph given below.

Thus for an underdamped oscillator, resonance or rather point of maximum amplitude occurs when the excitation frequency is less than the undamped natural frequency.

Mistake PointsOption 2 is correct, At multiple places, option 3 has been given as the correct answer, which is wrong, because irrespective of the amount of damping, the maximum amplitude occurs before the ratio  reaches unity, which is evident from the plot of magnification factor against the ratio of frequency . Option 3 is correct for no damping, but the question is for underdamped harmonic oscillator.