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t0N{E72
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Seventh Semester B.E. Degree Examination, Dec.2015 lJan.20l6
Mechanical Vibrations d_. .9
I rme: 3 hrs.
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Note: Answer any FIVE
€la. () !
Qa
questions, selecting atleust TWO questions
from
PART - A Add the following harmonic motion and check the solution graphically : xr : 2cos (wt + 0.5) xz : 5sin (wt + 1.0). Represent the periodic motion given in the following fig.Q1(b) by harmoni.
x) +h
each
parl
(10 Marks)
r.rr.r,r,
.=N 6S OP
Marks)
lo
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Fig.Q1(b)
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Es bd
-L O.d boi
w
U.
Determine the natural frequency of undamped free vibration system using energy method. (06 Marks) Determine the natural frequency of the system shown in fig. Q2(b). (07 Marks)
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a=
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ia
Fig.Q2(b)
=(€ o-X a
9E 5o ot-
A semicircular disc of radius 'R' and mass 'm' is pivoted freely about the center as shown in fig. Q2(c). Dltermine its natural frequency of oscillation for small displacement. Use
ed
6d oj .i5 k.i
energy methsd.
trbo
EE Et or
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m
full
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h
Max. Marks:100
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a.
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O"r > -3|'.
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D.
-
10 oscillations,
the
b.
I
(10 Marks) sec/m. A spring mass damper system is having a mass of 1Okg and a spring of such stiffness which causes a static deflection of 5mm. The amplitude of vibration reduces to t/+ the initial value
in
4a.
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Fig.Q2(c)
A spring mass damper system consists of a spring of stiffiress 343N/m. The mass is 3.43kg. The mass is displaced 20mm beyond the equilibrium position and released. Find the equation of motion for the system, if the damping coefficient of the dash pot is 13.72N
E'
(07 NIarks)
system
iii)
determine
i)
Logarithmic decrement
ii)
Actual damping present in
Damped natural frequency.
(10 Marks)
Define "transmissibility". Derive an expression for motion transmissibility. (10 Marks) A machine of mass 500kg is supported on spring of stiffrress 106N/m. if the machine has a rotating unbalance of 0.25 Kg-m, determine i) The force transmitted to the floor at 1200 (10 Marks) rpm ii) The dynamic amplitude at this speed iii) The phase angle. 1
of2
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For More Question Papers Visit - www.pediawikiblog.com L0N.IE72 PART - B Mention the instruments used to measute displacement and acceleration. Discuss the (10 Marks) relevant frequency response curves. horizontal shaft supported_at on a25mm midway diameter 12 kg is mounted A rotor of mass b. the ends by two bearings. The span between the bearing is 900mm. Because of sotiie, manufacturing defect the Cg of the rotor is 0.02mm away from geometric centre of rotor. If the system rotates at 3000 rpm, determine the amplitude of steady state vibrations and (l0,Marks) dlmamic force on the bearing. Take E:200Gpa.
a. For the system shown in fig. Q6(a), i) Derive
the equation of
co
m
a.
motion
ii;
g.
Sitr,rp'frequency equation and obtain natural frequencies of the system iii) Obmin:modal vectors iv) Draw mode shapes. Neglect the inertia of wheels and friction between wheel and (12 Marks) surface.
ro, main mass
X"
,nd
X' for absorber x"
mass.
ik
It a.
ib
Explain the principle of undamped dynamic vibration absorbers. Obtain an expression for (08 Marks)
Find the lowest natural frequency of vibration for the system shown in Fig. Q7(a), by (08 Marks) Rayleigh's method. E - L96 x 1orr N/m2 )' .r:4 x 10-7 ma.
w
b.
lo
Fie.Q6(a)
'fn,= toDkq ct
Using Stodola's method, determine the fundamental mode of vibration and its natural (12 Marks) frequency ofthe spring mass system shown in fig. Q7(b).
Fig.Q7(b)
w
w w
.p
b.
ed
ia
Fig.Q7(a)
Explain the rold of i) Exciter ii) Transducer iii) Signal conditioner and iv) Analyzer used in experimental modal analysis. (08 Marks) (04 Marks) b. Explain briefly dlmamic testing of machines. Describe the three types of maintenance schemes given below : i) Break down maintenance ii) Preventive maintenance iii) Condition based (08 Marks) maintenance. **:k**
2
of2
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iv) Analyzer used in experimental modal analysis. (08 Marks). Explain briefly dlmamic testing of machines. (04 Marks). Describe the three types of maintenance ...
Expiain static and dynamic characteristics of sensors. Explain workirlg principle of Hall effect sensor. Deftne following terms: i) Hysteresis error. ii) Repeatability.
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