F.Y. M.Tech. (Civil-Structural Engineering) (Semester (New CBCS)
Examination, 2018
Structural dynamics
Day and Date Saturday, 8-12-2018 Total Marks 70
Time 10.00 a.m. to 2.00 p.m.
Instructions Solve any 5 questions from each Section.
Figures to the right indicate full marks.
Assume suitable data if necessary and assume it
clearly.
1. From first principle derive the governing differential equation for undamped free
vibration. Obtain the solution if SDOF is given an initial displacement xo and
initial velocity Vo. 14
2. A structure modelled as a damped spring mass system with mass 1150 kg,
k 1548465.1 N/m and C 15.3 N sec./mm is subject to a harmonic exciting
force with frequency of 30 rad/sec. Determine The natural frequency
The damping ratio The amplitude of the existing force when the amplitude
of the vibrating mass is measured to be 8.398 mm. 14
3. A SDOF system is subjected to a transient force as shown in the following
figure 1. Derive the expression for magnification factor for the forced as well
as free vibration phases. 14
4. Write note of
Static condensation
Orthogonality conditions
Eigen value problem 14
5. Determine fundamental Frequency of vibrations using rayleigh method for the
system shown in figure 2.
Take K 1000 KN/M Assume Fundamental mode as 1.00 2.25 2.97} 14
6. Perform free vibration analysis of a simply supported beam and determine its
first three natural frequencies and mode shapes. 14
7. Write note on any two 14
Dunkerly's Method
Mode superposition Method
Duhamal's integral