Download mcese 104 structural dynamics

M.TECH. DEGREE EXAMINATION
Branch : Civil Engineering
Specialization – Computer Aided Structural Engineering
Model Question Paper - I
First Semester
MCESE 104 STRUCTURAL DYNAMICS
(Regular – 2011Admissions)
Time : Three Hours
Maximum : 100 marks
Answer all questions.
Any data, if required may be suitably assumed and clearly indicated.
1 (a) What is D Alemberts principle? Explain how the principle is employed in vibration
problems.
(6 marks)
(b) Write short notes on :
1 Degree of freedom ; 2 Hamilton’s principle
(6 marks)
(c) Write the differential equation of the inverted pendulum and determine its natural
frequency.( Fig. 1.)
(13 marks)
m
k
l
Fig. 1.
OR
2 (a) Discuss the importance of dynamic analysis in Civil Engineering structures
(5 marks)
(b) Write the equation of motion for torsional vibration of a suspended rigid disc on flexible
bar.
(10 marks)
(c) Determine the natural frequency for horizontal motion of a steel frame in Fig. 2.
(10 marks)
m
L
L
[P.T.O]
Fig. 2.
L
3. (a) Show that the displacement of a critically damped system due to initial displacement u0
and velocity u0.
(8marks)
(b) Derive the equation of motion for the vibration of a SDOF system for >1
(12 marks)
(c) Explain Coulomb damping.
(5 marks)
OR
4. (a) Derive an expression for the force transmitted to the foundation and phase angle for a
damped oscillator idealized as a SDOF system subjected to harmonic force.
(8 marks)
(b) Compare the decay curves for various types of damping.
( 5 marks)
(c) A machine of weight 1,000 kg. is mounted on a steel beam of negligible weight at
centre. The rotor in the machine generates a harmonic force of 3,000 kg. at a frequency
60 rad/sec. Assume 10% damping, calculate amplitude of motion of machine, force
transmitted to supports and phase angle. Span of beam 3m ,E – 2 x 105 Mpa and I of
beam 5000 cm4.
(12 marks)
5
Determine the amplitude of motion of three masses shown in fig.3 when a harmonic
force F(t) = Fo Sin ωt is applied . Take m=1.5kg K= 1500N/m Fo = 10N ω= 10 rad/s .
Use mode superposition method.
fig.3
(25 marks)
OR
6
(a)
Calculate the first three frequencies of axial vibration of a bar fixed at one end.
(15 marks)
(b) Derive the orthogonality condition of natural modes of vibration in axial direction.
(5 marks)
(c) Discuss the modal analysis method.
7
(5marks)
(a) Determine the first two frequency by Rayleigh-ritz method , assuming
1 
1

   0.8  0.8
0.4  1.2 


 2k
K    2k
 0


 2k
4k
 2k
0 

 2k 
5k 

m 0 0 
M    0 m 0 
 0 0 m


(15 marks)
(b) Explain Dunkerley’s equation. Estimate the fundamental frequency of torsional
vibration for the system having two discs fixed to the shaft shown in fig.4
(10 marks)
I
10I
L
θ1
θ2
10L
fig.4
OR
8. For the multistory building shown in fig.5. Obtain frequencies and modes of vibration
using Stodolla’s method. Assume m = 5 x 104 kg, k= 5 x 104 kN/cm.
m/2
2k
2k
m
2k
2k
2m
2k
2k
fig.5
(25 marks)