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INSTITUTE OF AERONAUTICAL ENGINEERING
Dundigal, Hyderabad - 500 043
MECHANICAL ENGINEERING QUESTION BANK
Department : MECHANICAL ENGINEERING Course Code : 57027
Course Title : MECHANICAL VIBRATIONS Course Category : CORE
Course Structure : Lectures Tutorials Practical’s Credits
4 1 - 4
Course Coordinator : Prof.VVSH Prasad
OBJECTIVES:
S. No. Question
Blooms Taxonomy
Level
Course Outcome
s UNIT-I
1 a. Discuss the response of under damped , critically damped and over damped systems using respective response equations and curves
b. A machine part of mass 2.5 Kgs vibrates in a viscous medium. A harmonic exciting force of 30 N acts on the part and causes resonant amplitude of 14mm with a period of 0.22sec. Find the damping coefficient. If the frequency of the exciting force is changed to 4Hz, determine the increase in the amplitude of forced vibration upon removal of the damper.
Understanding , Analyzing
1
2 a. Explain the term Vibration and deals with which kind of bodies.
b. Give some typical examples of vibration system.
c. What are the three elementary parts of Vibration system? Understanding 1 3 a. A damped system has following elements :
Mass = 4 kg; k = 1 kN/m; C = 40 N-sec/m
Determine: (a) damping factor, & natural frequency of damped oscillation.
b. Logarithmic decrement, and number of cycles after which the original amplitude is reduced to 20.
Analyzing 1,5
4 a. What is Simple Harmonic Motion?
b. Define Degrees of freedom.
c. What is Free Vibration? Give one example.
Understanding 1,5 5 a. Draw the diagram ,write the dimension less amplitude ratio equation and
plot the response curves MF vs ω/ωn ,Φ vs ω/ωn incase of following forced damped vibrations
i. Forced vibration with constant harmonic excitation
ii. Forced vibration with rotating and reciprocating unbalance a. iii) Forced vibration due to base excitation.
b. In a particular case of a large canon, the gun barrel and recoil mechanism have a mass of 500kg with recoil spring stiffness 10,000N/m.The gun
Analyzing 1,5
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recoils 0.4m upon firing. Find i) Critical damping co efficient of the damper ii) initial recoil velocity of the gun
6 a. What is Forced Vibration? Give one example.
b. Write equation of motion for simple vibration system.
c. What is natural frequency?
Understanding 1,5 7 a. Derive an expression for the transmissibility and transmitted force for a
spring- mass-damper system subjected to external excitation. Draw the vector diagram for the forces.
b. A metal block, placed on a rough surface, is attached to a spring and is given an initial displacement of 10cmfrom its equilibrium position. After five cycles of oscillation in 2s, the final position of the metal block found to be 1cm from its equilibrium positions. Find the coefficient of friction between the surface and the metal block.
Evaluating,
Analyzing 1,5
8 a. Define damping.
b. What is resonance?
c. What is damping ratio. Understanding 1
9 a. What is the difference between a vibration isolator and a vibration absorber?
b. Does spring mounting always reduce the vibration of the foundation of a machine?
c. What is the function of a vibration isolator?
Understanding , Remembering
1,3,5
10 Determine the frequency of oscillations for the system shown in fig. Also determine the time period if m = 4 kg and r = 80 mm.
Analyzing 1,5
11 a. What is a vibration absorber?
b. Why is it important to find the natural frequency of a vibrating system c. What happens to the response of an undamped system at resonance?
Understanding 1,3 12 Find the equivalent stiffness, frequency and time period for the system shown
in figure below
If k1= 200 N/m k2 = 100 N/m, m = 20 Kg L = 2000 mm, A = 100 mm2 density is 7200 kg/mm3
Analyzing 1,2,3
13 a. Define the flexibility and stiffness influence coefficients
b. What is the difference between a vibration absorber and a vibration isolator?
c. Give two examples each of the bad and good effects of vibration.
Understanding 1,4
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14 A circular cylinder of mass m and radius r is connected by a spring of stiffness k as
shown in fig. If it is free to roll on the rough surface which is horizontal without slipping, determine the natural frequency.
Analyzing 1,5
15 a. What is meant by logarithmic decrement?
b. Define the term magnification factor Understanding 1
16 A wheel is mounted on a steel shaft ( 8 3 1 09 N2) G
m
of length 1.5m and 0.80 cm. The wheel is rotated 50 And released. The period of oscillation is observed as 2.3s.
Determine the mass moment of inertia of the wheel.
Analyzing 1
17 Determine the natural frequency of spring mass system as shown in the figure.
Analyzing 1
18 Find the natural frequency of system in the figure 2.20 assuming the bar CD to be Weightless and rigid.
Analyzing 1
UNIT-II
1 Indicate some methods for finding the response of a system under non
periodic forces. Applying 1,2
2 Derive the convolution integral for a single degree of freedom subjected to an Evaluating 1,2
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impulse.
3 In the vibration testing of a structure ,an impact hammer with a load cell to measure the impact force is used to cause excitation. Assuming m=5kg,
k=2000n/m, c=10Ns/m and F=20 Ns.Find the response of the system. Analyzing 1,2 4 Explain the terms generalized impedance and admittance of a system. Understanding 2 5 What is a response spectrum? And what are engineering applications? Understanding 2 6 Find the undamped response spectrum for the sinusoidal pulse force using
initial conditions x(0)=0,dx/dt (0)=0 Analyzing 1,2
7 How is the Laplace transform of a function x(t) defined. And advantages of
this transform method. Understanding 4
8 A compacting machine modeled as a single d.o.f system. the force on the mass m due to a sudden application of pressure can be idealized as a step force. Determine the response of the system.
Analyzing 3 9 Use the convolution integral to determine the response of an undamped 1-
degree-of-freedom system of natural frequency n
and
m when subject toa constant force of magnitude
F0. The system is at rest in equilibriumat t=0.
Analyzing 3
10 Use the convolution integral to determine the response of an under damped 1-degree-of-freedom system of natural frequency n
damping ratio
,and mass m when subject to a constant force of magnitude F
0. The system is at rest in equilibrium at t=0.
Analyzing 3
11 Use the convolution integral to determine the response of an undamped-1- degree-of-freedom system of natural frequency n
and mass
m whensubject to a time-dependent excitation of the form F(t)=F
0e
-αt. The system is at rest in equilibrium at t=0.
Analyzing 3
12 Use the convolution integral to determine the time-dependent response of an undamped 1-degree-of-freedom system of natural frequency n
and mass m when subject to a harmonic excitation of the form F(t)=F
0sin
twith
n
Analyzing 3
13 Use the convolution integral to determine the response of an undamped 1- degree-of-freedom system to the excitation of Fig.
Analyzing 3
14 Use the Laplace transform method to determine the response of an under- damped 1-degree-of-freedom system of damping ratio
,
natural frequencyn and mass m, initially at rest in equilibrium and subject to a series of applied impulses, each of magnitude I, beginning at t=0, and each a time t0
apart.
Analyzing 3
UNIT-III
1 How do you differentiate displacement pick up, velocity pick up and
acceleration pick up? Explain with a sketch. Analyzing 3
2 A seismic instrument is fitted to measure the vibration characteristics of a Analyzing 3 F0
t0
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machine running at 120 rpm. If the natural frequency of the instrument is 5 Hz and if it shows 0.004 cm determine the displacement, velocity and acceleration assuming no damping.
3 Describe Frahms reed tachometer. Understanding 3
4 A vibrometre having a natural frequency of 4 rad/s and ζ =0.2 is attached to a structure performs a harmonic motion.. If the difference between the maximum and minimum recorded values is 8 mm, find the amplitude of motion of the vibrating structure when its frequency is 40 rad/s.
Analyzing 3 5 Explain the seismic instrument and how it will be used to measure
displacement and acceleration. Understanding 3
6 A simple model of a motor vehicle can vibrate in the vertical direction while travelling over a rough road. The vehicle has a mass of 1200kg.The suspension system has a spring constant of 400KN/m and a damping ratio of ζ=0.5.If the vehicle speed is 20km/hr,determine the displacement amplitude of the vehicle mounted with vibrometre.The road surface varies sinusoiallywith amplitude Y=0.05 and wave length of 6m.
Analyzing 3
7 What is an accelerometer? Sketch the dimensionless amplitude vs frequency curves of vibration – measuring instrument. Explain in what region it can be used as an accelerometer.
Applying 3,5 8 A commercial type vibration pick up has a natural frequency of 6cps and a
damping factor ζ=0.6.calculate the relative displacement amplitude if the instrument is subject to motion x=0.08sin 20t.
Analyzing 3,5 9 A seismic instrument is mounted on a machine running at 1000 rpm. The
natural frequency of the seismic instrument is 20 rad/sec. The instrument records relative amplitude of 0.5 mm. Compute the displacement, velocity and acceleration of the machine. Damping in seismic instrument is neglected.
Analyzing 3,5 10 Seismic instrument has natural frequency of 6 Hz. What is the lowest
frequency beyond which the amplitude can be measured within 2% error.
Neglect damping.
Analyzing 3,5 11 A seismic instrument has a natural frequency of 6 Hz and damping factor
0.25. What is the lowest frequency beyond which the amplitude can be measured with 2% error?
Analyzing 3,5 12 It is desired to measure maximum acceleration of a machine part, which
vibrates violently with a frequency of 700 cycles/min. An accelerometer with negligible damping, 0.5 kg mass and 18 kN/m spring constant is attached to it. The total travel of the indicator is found to be 8.2 mm, find the maximum amplitude and maximum acceleration of the part.
Analyzing 3,5
UNIT-IV
1
a.
Obtain the frequency equation for the two DOF spring mass system.b.
Also determine the natural frequencies and mode shapes.Assume m1 ,m2 ,k1 and k2 for governing equations.
Analyzing 1,3 2 a. Obtain the frequency equation for the two DOF torsional system.
b. Also determine the natural frequencies and mode shapes.
Assume J1 ,J2 ,k t1 and k t2 for governing equations.
Analyzing 1,3 3 a. What is the main disadvantage of a dynamic vibration absorber? Show
that for such an absorber ,its natural frequency should be equal to the applied frequency.
b. A vibratory system performs the motions as expressed by the following eqations,find the frequency ratios and mode shapes
Analyzing 1,3
4 a. A diesel engine ,weighing 3000 N is supported on a pedestal mount. It has been observed that the engine induces vibration into the surrounding area through its pedestal mount at an operating speed of 6000rpm.Determine the parameters of the vibration absorber that will reduce the vibration when mounted on the pedestal. The magnitude of
Analyzing,
Evaluating 1,3
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the exciting force is 250 N and the amplitude of the auxiliary mass is to be limited to 2mm.
b. What is meant by static and dynamic coupling ?How can coupling of the equations of motion be eliminated. Derive the governing equations thro Lagrange energy approach.
5 Determine the natural frequency of torsional vibrations of a shaft with two circulariscs of uniform thickness at the ends. The masses of the discs are M1
= 500 kg andM2 = 1000 kg and their outer diameters are D1 = 125 cm and D2 = 190 cm. The length of the shaft is l = 300 cm and its diameter d = 10 cm as shown in fig
G = 0.83 x 1011N/m2.
Analyzing 1,3
6 A slender rod of length L and mass m is pinned at O as shown in figure below. A spring of stiffness K is connected to the rod at point P while a dashpot of damping coefficient c is connected to the rod at point Q.
Assuming small displacements; Derive a linear differential equation governing the free vibration of this system. Use the displacement of the point P, measured from the systems equilibrium position as the generalized coordinate.
Evaluating 1,3
7 Solve the problem shown in figure. m1=10kg, m2=15kg and k = 320 N/m.
Applying 1,3
8 Two pendulums of different lengths are free to rotate y-y axis and coupled together by a rubber hose of torsional stiffness 7.35 X 103 Nm / rad as shown in figure. Determine the natural frequencies of the system if masses m1 = 3kg, m2 = 4kg,
L1 = 0.30 m, L2 = 0.35 m.
Applying 1,3
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9 Determine the modes of vibrations for the system shown in figure
Analyzing 1,3
10 The equations of motion of a two degree of freedom system is given by
The eigen vectors for the above system are given by
Calculate the principal coordinates of the system.
Analyzing 1,3
UNIT-V
1 a. Obtain natural frequency equation in matrix form for system shown in Fig. using Eigen value method 2
b. Find modal vectors and mode shapes of the system shown using Eigen value method 3
Analyzing 2,4,5
2 a. How can we make a system to vibrate in one of its natural made?
b. Name a few methods for finding the fundamental natural frequency of a multi degree offreedomsystem
Remembering 2,4,5 3 The schematic diagram of a marine engine connected to a propeller thro
gears as shown in fig.
The moment of inertia of the flywheel =9000kg-m2,engine=1000kg- m2,gear1=250 kg-m2,gear2=150 kgm2,propeller=2000kg-m2.find the natural frequencies and mode shapes of the system in torsional vibration. 3
Considering inertia of the gears Considering inertia of the gears aa
a. Considering inertia of the gears
b. Without considering the inertia of the gears
Analyzing 2,4,5
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4 a. What is Rayleigh s principle?
b. State whether we get a lower bound or an upper bound to the fundamental natural frequency. If we use Rayleigh’s method
Understanding 2,4 5 a. Obtain the stiffness co-efficient of the system shown below.
b. Obtain the flexibility co-efficient of the system shown above
Analyzing 2,4,5
6 a. What is Rayleigh s quotient?
b. What is the matrix iteration method? Understanding 2,4
7 a. Can we use any trial vector in the matrix iteration method to find the largest natural frequency?
b. What is the difference between the matrix iteration method and Jacobi’s method?
Applying 2,4 8 Using the matrix iteration method, how do you find the intermediate natural
frequencies? Applying 2,4
9 The arrangement of the compressor, turbine and generator in thermal power plant is shown in fig. Derive the equations of the motion of the system as θi is the generalized co-ordinate.
Evaluating 2,4,5
10 a. Explain principle of orthogonality of modal vectors
Applying 2,4
UNIT-VI
1 Determine the frequency of vibrations for the system shown in figure using Analyzing 2,4,5
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stodola method.
2 Explain the procedure to find out natural frequency of vibrations by Dunker leys method for simple supported beam subjected to three point loads at equidistance along the span.
Understanding 2,4,5 3 A solid steel shaft of uniform diameter, which carries two discs of weights
600N and 1000 N is represented by a SSB 10 cm and 20 cm from the left support of 30cm length shaft made of steel with density 7800 kg/m3.
Determine the frequency of oscillation using Dunkerleys method by considering the weight of the shaft. E =19.6 x106 N/cm2 and I = 40 cm4
Analyzing 2,4,5
4 A shaft of negligible weight 6 cm diameter and 5 meters long is simply supportedat the ends and carries four weights 50 kg each at equal distance over the lengthof the shaft as shown in Figure. Find the frequency of vibration by Dunkerley'smethod.
Take E = 2 x 106 kg / cm2 if the ends of the fixed.
Analyzing 2,4,5
5 Determine the frequency of vibrations for the system shown in figure using Stodola
method.
Analyzing 2,4,5
6 Explain the procedure to find out natural frequency of vibrations by Dunker leys method for simple supported beam subjected to three point loads at equidistance along the span
Understanding 2,4,5 7 Using matrix method determine the natural frequencies of the system shown
in Fig. Analyzing 2,4,5
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8 Determine the natural frequencies of the system shown in Fig. 6.2. using matrix method.
Analyzing 2,4,5
9 Determine the fundamental frequency and first mode of the system shown in Fig. 6.3 using matrix Iteration method.
Analyzing 2,4,5
10 Find the lowest natural frequency of vibration for the system shown in Fig.
6.6 by Rayleigh’s method Analyzing 2,4,5
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11 Briefly explain the approximate methods for frequency analysis? Understanding 2,4,5 12 Explain the Rayleigh ritz method for vibration analysis ? Understanding 2,4,5 13 a. Estimate the fundamental frequency of a simply supported beam carrying
three identical equally spaced masses as shown in fig using Dunkerly method. Use flexibility Co efficient
b.
Derive the Rayleigh’s quotient for the above beam and write the deflections in terms of flexibility coefficients
Analyzing 2,4,5
14 a. Estimate the approximate fundamental natural frequency of the system shown in Fig. using Rayleigh’s method. Take: m=1kg and K=1000 N/m.
b. Define and derive Maxwell reciprocal theorem.
Evaluating 2,4,5
15 a. Find first natural frequency using matrix Iteration method (use flexibility influence co-efficient)
b. Determine the modal vectors of above system Analyzing 2,4,5
16 a. For system shown in above fig, determine the lowest natural frequency
by “stodolas” method.(carry out two iterations) Evaluating,
Analyzing 2,4,5
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b. Deduce the governing equation for semi definite torsional vibratory multi DOF System
Using Holzars method. Assume j1=j2=j3 =1, kt1=kt2 =1 (as shown above) UNIT-VII
1 a. How does a continuous system differ from a discrete system in the nature of its equation of motion?
b. How many natural frequencies does a continuous system have?
Applying 1,2,4,5 2 a. State the possible boundary conditions at the ends of a string.
b. What is the main difference in the nature of the frequency equations of a discrete system and a continuous system?
Understanding 1,2,4,5 3 a. Derive the governing equation for continues vibration of a slender axial
bar of length L, cross- sectional area A and density ρ.
b. Derive the solution for wave equation of torsional vibration and give the displacement boundary conditions for various end conditions
Evaluating 1,2,4,5 4 Show that the equation of transverse vibrations of a beam at a distance x
withdeflection `y' is given by d4y/d4x + ρA/EI d2y/dt2 = 0. Evaluating 1,2,4,5 5 A bar of uniform cross-section having length l is fixed at both ends as shown
in figure 7.8. The bar is subjected to longitudinal vibrations having a constant velocity at all points. Derive suitable mathematical expression of longitudinal vibration in the bar.
Evaluating 1,2,4,5
6 A bar fixed at one end is pulled at the other end with a force P. The force is suddenly released. Investigate The vibration of the bar.
Analyzing 1,2,4,5
7 Derive the governing equation for continues vibration of a slender axial bar
of length L, cross- sectional area A and density ρ. Evaluating 1,2,4,5 8 a. Determine the natural frequencies and mode shape of a bar/rod when
both the ends are free in a continuous system
b. Derive the 1D wave equation for lateral vibrations of a string.
Analyzing,
Evaluating 1,2,4,5 9 a. What is a continuous system? How many natural frequencies does a
continuous system have? How does a continuous system differ from a discrete system in the nature of its equations of motion?
b. Derive an expression for the longitudinal vibration of a uniform bar of length L, one end of which is fixed and the other end is free.
Applying,
Evaluating 1,2,45 10 a. Derive the 1d equation of Torsional vibration of circular shaft (subjected
to continuous system)
b. Write notes on( i) longitudinal vibration of rods/bars (ii)difference
Evaluating,
Understanding 1,2,4,5
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between discrete system to continuous system of vibrations 11 State the possible boundary conditions at ends of a string.
Mention the velocity of wave propagation constant i. Torsional vibration of a shaft
ii. Transverse vibration of a string iii. Longitudinal vibration of a bar
a. Derive the equation δ2y/δx2 =1/a2 *δ2y/δt2
Understanding , Evaluating
1,2,4,5
17 Obtain a general expression for the lateral vibration of string. Understanding
1,2,4,5 18 What is the speed of torsional waves in a solid steel (G=80 x 109 N/m2,
7 8 0 0k g /m3
) shaft of 20 mm diameter?
Understanding
1,2,4,5 19 Derive the partial differential equation governing free longitudinal vibrations
of a uniform bar. Evaluating 1,2,4,5
20 Determine the natural frequencies and mode shapes of torsional oscillation of a uniform shaft of length L, mass density
, and cross-sectional polar moment of inertial J. The shaft is fixed at one end and free at the other end.
Analyzing 1,2,4,5
21 Determine the characteristic equation for longitudinal oscillation of a bar of length L, elastic modulus E, and mass density p that is fixed at one end and has a particle of mass m attached to the other end.
Analyzing 1,2,4,5 22
A ship/s propeller is a 20m steel
(E 2 1 01 09N /m, 7 8 0 0k g /m3)shaft of diameter 10cm. The shaft is fixed at one end with a 500kg propeller attached to the other end. What are the three lowest natural frequencies of longitudinal vibration of the propeller shaft system?
Analyzing 1,2,4,5
UNIT-VIII
1 a. What are the various methods available for vibration control?
b. What is single-plane balancing?
Understandin
g 1,2,5
2 a. Describe the two-plane balancing procedure.
b. What is whirling?
Understandin
g 1,2,5
3 a. What is the difference between stationary damping and rotary damping?
b. How is the critical speed of a shaft determined?
Understandin
g 1,2,5
4 a. What causes instability in a rotor system?
b. What considerations are to be taken into account for the balancing of a reciprocating engine?
Understandin
g 1,2,5
5 Find the whirling speed of a 50 mm diameter steel shaft simply supported at the ends in bearings 1.6 m apart, carrying masses of 75 kg at 0.4 m from one end, 100 kg at the center and 125 kg at 0.4 m from the other end. Ignore the mass of the shaft. Assume the required data.
Analyzing 1,2,5 6 A shaft 1600 mm long and diameter 40 mm has a rotor of mass 5kg at its
midspan. It is observed that the deection of the shaft at mid span is 0.4 mmunder the weight of the rotor. Find the critical speed of the shaft.
Analyzing 1,2,5 7 A disc of mass 5 kg is mounted midway between bearings which may be
assumed to be simple supports. The bearing span is 48 cm. the steel shaft, which is horizontal, is 9 mm in diameter. The C.G of the disc is placed 3 mm from the geometric center. The equivalent viscous damping at the center of the disc – shaft may be taken as 48 N-s/m. if the shaft rotates at 675 rpm, find the maximum stress in the shaft and compare it with dead load stress in the shaft. Also find the power required to drive the shaft at this speed.
Analyzing 1,2,5
8 A shaft 40 mm diameter and 2.5 m long has a mass of 15 kg per meter length. It is simply supported at the ends and carries three masses 90 kg, 140 kg and 60 kg at 0.8 m, 1.5 m and 2m respectively from the left support. E = 200 GN/m2.Find the whipping speed of the shaft.
Analyzing 1,2,5
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9 A shaft 1600 mm long and diameter 40 mm has a rotor of mass 5kg at its midspan. It is observed that the deection of the shaft at mid span is 0.4 mm under the weight of the rotor. Find the critical speed of the shaft.
Analyzing 1,2,5 10 Find the whirling speed of a 50 mm diameter steel shaft simply supported at
the ends in bearings 1.6 m apart, carrying masses of 75 kg at 0.4 m from one end, 100 kg at the center and 125 kg at 0.4 m from the other end. Ignore the mass of the shaft. Assume the required data.
Analyzing 1,2,5 11 A shaft 1600 mm long and diameter 40 mm has a rotor of mass 5kg at its
midspan. It is observed that the deection of the shaft at mid span is 0.4 mm under the weight of the rotor. Find the critical speed of the shaft.
Analyzing 1,2,5 12 a. A disk of mass 4 kg is mounted midway between the bearings
Which may be assumed to be simply supported? The bearing span is 48 cm.The steel shaft is 9 mm in diameter. The c.g. of the disc is displaced 3 mm from the geometric centre .the equivalent viscous damping at centre of the disc- shaft may be taken as 49 N-s/m. If the shaft rotates at 760 rpm, find the maximum stress in the shaft and compare it with the dead load stress in the shaft when the shaft is horizontal. Also find the power required to drive the shaft at this speed. Take E=1.96×1011 N/m2.
b. Explain &deduce the secondary critical speed of rotating shaft with diagram
Analyzing 1,2,5
13 a. Derive an expression for the critical speed of a light shaft having a single disc without damping.
b. A rotor has a mass of 12 Kg and is mounted midway on a horizontal shaft of 24 mm Supported at the ends by two bearings. The bearings are 1 m apart. The shaft rotates at 1200rpm. The mass centre of the rotor is 0.11 mm away from the geometric centre of the rotor due to certain manufacturing errors. Determine the amplitude of steady state vibrations
and dynamic force transmitted to the bearings if E = 200 GN/m2.
Evaluating,
Analyzing 1,2,5
14 What do you understand by critical speed? With reference to explain (i) heavy side
a. Light side. At what phase angle amplitude is infinite? (Sketching the phenomenon)
b. A rotor has a mass of 9.5 Kg and is mounted midway on a horizontal shaft of 12 mm
Supported at the ends by two bearings. The bearings are 0.6 m apart. The shaft rotates at 690rpm. The mass centre of the rotor is 6 mm away from the geometric centre of the rotor due to certain manufacturing errors. Determine the amplitude of steady state vibrations and dynamic force transmitted to the bearings if E = 200 GN/m2.take damping factor as 0.1.also find power required to rive the shaft at this speed.
Analyzing 1,2,5
15 a. prove the statement “if the shaft is running at half its critical speed, the variation of the vertical force occurs at natural frequency which causes large amount of vibration”
b. Derive the dimension less equation
d/e= r2/ {1-r2} where r=frequency ratio ,d=amplitude ,e=eccentricity
Evaluating,
Analyzing 1,2,5
Prepared by: Prof.VVSH Prasad
HOD, MECHANICAL DEPARTMENT
