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.

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)

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 L

[P.T.O]
Fig. 2.
3. (a) Show that the displacement of a critically damped system due to initial displacement u 0
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 F o = 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. (5marks)

7 (a) Determine the first two frequency by Rayleigh-ritz method , assuming

 1 1   2k  2k 0  m 0 0
   0.8 
 K    2k 
 M    0 

 0.8 4k  2k  m 0
0.4  1.2   0  2k 5k  0 0 m
     

(15 marks)

(b) Explain Dunkerley’s equation. Estimate the fundamental frequency of torsional

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

2k 2k
2m

2k 2k

fig.5

(25 marks)