Hall Ticket No Question Paper Code: BST004
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
M.Tech II Semester End Examinations (Supplementary) January, 2018
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 response in terms of displacement for a SDOF system subjected to Undamped forced
vibration.
Explain
i. Vectorial representation simple harmonic motion.
ii. Oscillatory motion
2. What are the types of dynamic loads? What are the uncertainties of dynamic analysis?
Define logarthmic decrement and obtain the expression for logarithmic decrement.
UNIT II
3. Obtain the equation of motion using D Alembert's principle.
Obtain the expression for dynamic magnification factor for an under damped SDOF system
subjected to harmonic load F F0Sin!t.
4. Explain Duhamel integral method and write the expressions for displacement for damped and
undamped condition using Duhamel integral.
Explain the necessity of mathematical modeling in structural dynamics and mention the objectives
of dynamic analysis.
UNIT III
5. Differentiate with an example coupled and uncoupled equation of motion.
Derive the expression for orthogonality relationship between normal modes.
Page 1 of 2
6. Explain the concept of mathematical modeling of a multi degree of freedom system.
For the Figure write the equation of motion and determine the natural frequencies and mode
shapes.
Figure 1
UNIT IV
7. Explain the mode shapes of simple beams with different ends.
Analyze the undamped free vibration of beams in flexure.
8. Derive the natural frequency and mode shape for simple supported beam.
For the multi storey building shown in Figure obtain the natural frequencies and mode shapes
using Stodolla's method. M=10x103kgs and K=50x106 N/m.
Figure 2
UNIT V
9. Explain the concept of excitation by rigid base translation for earthquake analysis.
Define transmissibility and derive the expression for it.
10. Explain the lumped mass approach in MDOF systems.
Explain the procedure to find the lateral forces and storey shears in multi-storey building for
dynamic analysis.