Hall Ticket No Question Paper Code: BST004
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
M.Tech II Semester End Examinations (Supplementary) January, 2019
Regulation: IARE-R16
STRUCTURAL DYNAMICS
(Structural Engineering)
Time: 3 Hours Max Marks: 70
Answer ONE Question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
UNIT I
1. Obtain the expression for equation of motion x of an under damped SDOF system subjected
to free vibration.
Define
i. Damped and Undamped vibration.
ii. Continuous system and discrete systems
2. Explain the concept of Lumped mass idealization in detail.
Define the following
i. Natural frequency
ii. Damped frequency
iii. Time Period
iv. Damping ratio
v. Critical damping
UNIT II
3. What are the various methods for solving the differential equation of motion? State the conditions
under which these are preferred.
Give the explanation with their statements for the following.
i. Principle of virtual work.
ii. Hamilton's Principle.
4. Derive an expression for the steady state response of an under damped SDOF system subjected
to a harmonic excitation F FoSin!t applied to mass.
Obtain the direct equilibrium equation using Newton's second law of motion.
UNIT III
5. Explain the modal superposition procedure in case of multi degree of freedom system.
Explain the concept of mathematical modeling of a multi degree of freedom system.
Page 1 of 3
6. Derive the governing differential equation and undamped free vibration solution for two storey
shear building frame modelled as oscillators.
For the Figure obtain the mode shapes of the shear building.
M1 110x103kgs;M2 160x103kgs;M3 30x103kgs
K1 40x106N/m;K2 100x106N/m;K3 100x106N/m
Figure 1
UNIT IV
7. Mention the assumptions made in the flexural vibrations of uniform beams.
State and explain the procedure involved in vibration analysis using Hozler's method.
8. Find the natural frequencies and mode shapes for a beam with one end fixed and other end is
free.
For the multi storey building shown in Figure obtain the natural frequencies using Stodolla's
method.
M 5x103kgsandK 100x106N/m
UNIT V
9. A Harmonic motion has an amplitude of 0.05m and a frequency of 25Hz. Find the time period,
maximum velocity and maximum acceleration.
Explain the lumped mass approach as applied to SDOF systems and MDOF systems.
10. Explain the I.S code methods of analysis for obtaining the response of multi storied buildings
shown in Figure 3.
Distinguish between under damped, critically damped and over damped systems with suitable examples.