Vibrations QUESTION BANK f
Short Answer Questions (2 Marks) f f f f
(1) Define critical speed of a shaft. Why is critical speed encountered?
f f f f f f f f f f
Ans:
The speed at which resonance occurs is called critical speed of the shaft. In ot
f f f f f f f f f f f f f f
her words, the speed at which the shaft runs so that the additional deflection
f f f f f f f f f f f f f f
of the shaft from the axis of rotation becomes infinite is known as critical spe
f f f f f f f f f f f f f f
ed.
The critical speed may occur due to one or more of the following reasons:
f f f f f f f f f f f f f
1) Eccentric mountings like gears, flywheels, pulleys, etc.,
f f f f f f
2) Bending of the shaft due to self-weight f f f f f f
3) Non-uniform distribution of rotor material, etc. f f f f f
(2) What are the causes of vibrations?
f f f f f
Ans:
1) Unbalanced forces in the machine: Produced within the machine itself.
f f f f f f f f f
2) Dry friction between the two-mating surface: Self-
f f f f f f
excited vibration produced.f f
3) External excitations: These excitations may be periodic, random or the nat
f f f f f f f f f f
ure of an impact produced external to the vibrating system.
f f f f f f f f f
4) Earthquakes: These are responsible for the failure of many buildings, da f f f f f f f f f f
ms.
5) Winds: These are cause the vibration of transmission and telephone line un
f f f f f f f f f f f
der certain conditions.
f f
(3) Write about the terms: free vibrations, forced vibrations and damped vibr
f f f f f f f f f f
ations.
Ans:
Free or natural vibrations: When no external force acts on the body, after givi
f f f f f f f f f f f f f
ng it an initial displacement, then the body is said to be under free or natural vi
f f f f f f f f f f f f f f f f
brations.
Forced vibrations: When the body vibrates under the influence of external fo
f f f f f f f f f f f
rce, then the body is said to be under forced vibrations.
f f f f f f f f f f
Damped vibrations: When there is a reduction in amplitude over every cycle of
f f f f f f f f f f f f f
vibration, then the motion is said to be damped vibration.
f f f f f f f f f
R.fSyamfSudhakarfRao,fAssociatefProfessor,fGurufNanakfInstitutionsfTechnicalfCampus,fIbrahimpatnam
,Vibrations QUESTION BANK f
(4) Write the formula for natural frequency ‘ f ’ and static deflection ‘ δ ‘ of t
f f f f f f f f f f f f f f f f
he cantilever beam loaded at free end and shaft having negligible mass.
f f f f f f f f f f f
Ans:
Natural frequency, 𝑓𝑛 = 1 𝑔 f f f ff f
2𝜋 √ f
𝛿
Static deflection, δ = f f f
𝑊𝑙3
f
3𝐸𝐼
W = Load at the free end, in Newton l
f f f f f f f f f f
= Length of the beam in meter
f f f f f f
E = Young’s modulus for the material of the beam in N/m2
f f f f f f f f f f f
I = Moment of inertia of the beam in m4
f f f f f f f f f
(5) What is a torsionally equivalent shaft? f f f f f
Ans:
A shaft having diameter for different lengths can be theoretically replaced by
f f f f f f f f f f f
an equivalent shaft of uniform diameter such that they have the same total an
f f f f f f f f f f f f f f
gle of twist when equal opposing torques are applied at their ends. Such a theo
f f f f f f f f f f f f f f
retically replaced shaft is known as torsionally equivalent shaft.
f f f f f f f f
(6) Explain briefly, the longitudinal, transverse and torsional free vibra f f f f f f f f
tions.
Ans:
Longitudinal vibrations: When the particles of the shaft or disc moves parallel f f f f f f f f f f f f
to the axis of the shaft, then the vibrations are known as longitudinal vibrations.
f f f f f f f f f f f f f
In this case, tensile and compressive stresses induced in the shaft.
f f f f f f f f f f f
Transverse vibrations: When the particles of the shaft or disc move approxim
f f f f f f f f f f f
ately perpendicular to the axis of the shaft, then the vibrations are known as tr
f f f f f f f f f f f f f f
ansverse vibrations. Bending stresses are induced in the shaft.
f f f f f f f f
Torsional vibrations: When the particles of the shaft or disc move in a circle ab
f f f f f f f f f f f f f f
out the axis of the shaft, then the vibrations are known as torsional vibrations
f f f f f f f f f f f f f
. Torsional shear stresses are induced in the shaft.
f f f f f f f f
R.fSyamfSudhakarfRao,fAssociatefProfessor,fGurufNanakfInstitutionsfTechnicalfCampus,fIbrahimpatnam
, Vibrations QUESTION BANK f
(7) Write about Rayleigh’s method of finding the natural frequency of
f f f f f f f f f
transverse vibrations. f
Ans: Consider a shaft is loaded with point loads W1, W2, W3 and W4 etc. and y1, y2
f f f f f f f f f f f f f f f f f
, y3, y4 etc. be total deflection made under these loads.
f f f f f f f f f f
According to Rayleigh’s method, the maximum potential energy is equal to
f f f f f f f f f f
maximum kinetic energy. f f
½ Σ m g y = ½ 𝜔2 Σ m𝑦2 ; ω=
√𝑔 𝛴 𝑚𝑦2
f f f f f f f f f f f f f
𝛴f𝑚f𝑦
Natural frequency of transverse vibration, 𝑓𝑛 = 𝜔
f f f f f f ff f = f
1f
f
𝑔f𝛴f𝑚𝑦
2𝜋 2𝜋f f √
𝛴f𝑚f𝑦2
(8) What is node? f f
Ans: The point or the section of the shaft whose amplitude of torsional vibrati
f f f f f f f f f f f f f
on is zero is known as node. At node, the shaft remains unaffected by the vibrat
f f f f f f f f f f f f f f f
ion.
(9) What are the methods to eliminate or reduce the undesirable vibra
f f f f f f f f f f
tions.
Ans:
1) Removing the causes of vibrations. f f f f
2) Putting the screens if noise is objectionable. f f f f f f
3) Placing the machinery on proper isolators. f f f f f
4) Using shock absorbers. f f
5) Using dynamic vibration absorbers. f f f
10) Explain the terms Periodic motion, Time period, Frequency, Amplitude of
f f f f f f f f f f
motion, Resonance and Cycle f f f
Ans:
Periodic motion: A motion which repeats itself after equal interval of time. Time
f f f f f f f f f f f f f
period: Time taken to complete one cycle.
f f f f f f
Frequency: Number of cycles per unit time. f f f f f f
Amplitude of motion: The maximum displacement of a vibrating body from the
f f f f f f f f f f f f
mean position. f
Resonance: The vibration of the system when the frequency of the external for
f f f f f f f f f f f f
ce is equal to the natural frequency of the system.
f f f f f f f f f
Cycle: Motion completed during one time period.
f f f f f f
R.fSyamfSudhakarfRao,fAssociatefProfessor,fGurufNanakfInstitutionsfTechnicalfCampus,fIbrahimpatnam
Short Answer Questions (2 Marks) f f f f
(1) Define critical speed of a shaft. Why is critical speed encountered?
f f f f f f f f f f
Ans:
The speed at which resonance occurs is called critical speed of the shaft. In ot
f f f f f f f f f f f f f f
her words, the speed at which the shaft runs so that the additional deflection
f f f f f f f f f f f f f f
of the shaft from the axis of rotation becomes infinite is known as critical spe
f f f f f f f f f f f f f f
ed.
The critical speed may occur due to one or more of the following reasons:
f f f f f f f f f f f f f
1) Eccentric mountings like gears, flywheels, pulleys, etc.,
f f f f f f
2) Bending of the shaft due to self-weight f f f f f f
3) Non-uniform distribution of rotor material, etc. f f f f f
(2) What are the causes of vibrations?
f f f f f
Ans:
1) Unbalanced forces in the machine: Produced within the machine itself.
f f f f f f f f f
2) Dry friction between the two-mating surface: Self-
f f f f f f
excited vibration produced.f f
3) External excitations: These excitations may be periodic, random or the nat
f f f f f f f f f f
ure of an impact produced external to the vibrating system.
f f f f f f f f f
4) Earthquakes: These are responsible for the failure of many buildings, da f f f f f f f f f f
ms.
5) Winds: These are cause the vibration of transmission and telephone line un
f f f f f f f f f f f
der certain conditions.
f f
(3) Write about the terms: free vibrations, forced vibrations and damped vibr
f f f f f f f f f f
ations.
Ans:
Free or natural vibrations: When no external force acts on the body, after givi
f f f f f f f f f f f f f
ng it an initial displacement, then the body is said to be under free or natural vi
f f f f f f f f f f f f f f f f
brations.
Forced vibrations: When the body vibrates under the influence of external fo
f f f f f f f f f f f
rce, then the body is said to be under forced vibrations.
f f f f f f f f f f
Damped vibrations: When there is a reduction in amplitude over every cycle of
f f f f f f f f f f f f f
vibration, then the motion is said to be damped vibration.
f f f f f f f f f
R.fSyamfSudhakarfRao,fAssociatefProfessor,fGurufNanakfInstitutionsfTechnicalfCampus,fIbrahimpatnam
,Vibrations QUESTION BANK f
(4) Write the formula for natural frequency ‘ f ’ and static deflection ‘ δ ‘ of t
f f f f f f f f f f f f f f f f
he cantilever beam loaded at free end and shaft having negligible mass.
f f f f f f f f f f f
Ans:
Natural frequency, 𝑓𝑛 = 1 𝑔 f f f ff f
2𝜋 √ f
𝛿
Static deflection, δ = f f f
𝑊𝑙3
f
3𝐸𝐼
W = Load at the free end, in Newton l
f f f f f f f f f f
= Length of the beam in meter
f f f f f f
E = Young’s modulus for the material of the beam in N/m2
f f f f f f f f f f f
I = Moment of inertia of the beam in m4
f f f f f f f f f
(5) What is a torsionally equivalent shaft? f f f f f
Ans:
A shaft having diameter for different lengths can be theoretically replaced by
f f f f f f f f f f f
an equivalent shaft of uniform diameter such that they have the same total an
f f f f f f f f f f f f f f
gle of twist when equal opposing torques are applied at their ends. Such a theo
f f f f f f f f f f f f f f
retically replaced shaft is known as torsionally equivalent shaft.
f f f f f f f f
(6) Explain briefly, the longitudinal, transverse and torsional free vibra f f f f f f f f
tions.
Ans:
Longitudinal vibrations: When the particles of the shaft or disc moves parallel f f f f f f f f f f f f
to the axis of the shaft, then the vibrations are known as longitudinal vibrations.
f f f f f f f f f f f f f
In this case, tensile and compressive stresses induced in the shaft.
f f f f f f f f f f f
Transverse vibrations: When the particles of the shaft or disc move approxim
f f f f f f f f f f f
ately perpendicular to the axis of the shaft, then the vibrations are known as tr
f f f f f f f f f f f f f f
ansverse vibrations. Bending stresses are induced in the shaft.
f f f f f f f f
Torsional vibrations: When the particles of the shaft or disc move in a circle ab
f f f f f f f f f f f f f f
out the axis of the shaft, then the vibrations are known as torsional vibrations
f f f f f f f f f f f f f
. Torsional shear stresses are induced in the shaft.
f f f f f f f f
R.fSyamfSudhakarfRao,fAssociatefProfessor,fGurufNanakfInstitutionsfTechnicalfCampus,fIbrahimpatnam
, Vibrations QUESTION BANK f
(7) Write about Rayleigh’s method of finding the natural frequency of
f f f f f f f f f
transverse vibrations. f
Ans: Consider a shaft is loaded with point loads W1, W2, W3 and W4 etc. and y1, y2
f f f f f f f f f f f f f f f f f
, y3, y4 etc. be total deflection made under these loads.
f f f f f f f f f f
According to Rayleigh’s method, the maximum potential energy is equal to
f f f f f f f f f f
maximum kinetic energy. f f
½ Σ m g y = ½ 𝜔2 Σ m𝑦2 ; ω=
√𝑔 𝛴 𝑚𝑦2
f f f f f f f f f f f f f
𝛴f𝑚f𝑦
Natural frequency of transverse vibration, 𝑓𝑛 = 𝜔
f f f f f f ff f = f
1f
f
𝑔f𝛴f𝑚𝑦
2𝜋 2𝜋f f √
𝛴f𝑚f𝑦2
(8) What is node? f f
Ans: The point or the section of the shaft whose amplitude of torsional vibrati
f f f f f f f f f f f f f
on is zero is known as node. At node, the shaft remains unaffected by the vibrat
f f f f f f f f f f f f f f f
ion.
(9) What are the methods to eliminate or reduce the undesirable vibra
f f f f f f f f f f
tions.
Ans:
1) Removing the causes of vibrations. f f f f
2) Putting the screens if noise is objectionable. f f f f f f
3) Placing the machinery on proper isolators. f f f f f
4) Using shock absorbers. f f
5) Using dynamic vibration absorbers. f f f
10) Explain the terms Periodic motion, Time period, Frequency, Amplitude of
f f f f f f f f f f
motion, Resonance and Cycle f f f
Ans:
Periodic motion: A motion which repeats itself after equal interval of time. Time
f f f f f f f f f f f f f
period: Time taken to complete one cycle.
f f f f f f
Frequency: Number of cycles per unit time. f f f f f f
Amplitude of motion: The maximum displacement of a vibrating body from the
f f f f f f f f f f f f
mean position. f
Resonance: The vibration of the system when the frequency of the external for
f f f f f f f f f f f f
ce is equal to the natural frequency of the system.
f f f f f f f f f
Cycle: Motion completed during one time period.
f f f f f f
R.fSyamfSudhakarfRao,fAssociatefProfessor,fGurufNanakfInstitutionsfTechnicalfCampus,fIbrahimpatnam
