Hall Ticket No Question Paper Code: BST004
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
M.Tech II Semester End Examinations (Regular) July, 2017
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. Classify the different types of vibrations in structural system. Explain with neat sketches.
Define the degrees of freedom and explain the types with example of singly storey and multi
storey shear buildings.

2. Explain Simple Harmonic motion with vectorial representation. Also explain the examples of
Simple Harmonic Motion.
Find the amplitude of the sum of the two harmonic motions,
x1 3 cos(2t x2 4 cos(2t
UNIT II
3. Determine the differential equation of a classical spring-mass system and its natural frequency by
using
i. D'Alembert's principle
ii. Energy method
iii. Rayleigh's method.

4. A machine of 20 kg mass is mounted on a spring and dashpot (SDOF). The total spring stiffness is
10N/mm and the total damping is 0.15N/mm/s. If the system is initially at rest and a velocity of 100
mm/s is imparted to the mass, then determine
i. Displacement and velocity of the mass as function of time
ii. Displacement and velocity at time equal to one second.
UNIT III
5. An undamped two DOF system shown in Figure 1 has mass m1= m2= m and stiffness k1= k2= k.
Determine its frequencies and mode shapes.
Page 1 of 2
Figure 1

6. Explain the mode superposition methods to combine the modes in response spectra method of
analysis.
Explain the orthogonality condition of mode shapes for multi degree freedom system.What is its
significance in dynamic analysis.
UNIT IV
7. Explain the iterative method of frequency of vibration of Multi-degree of freedom spring mass system
using Holtzer method.

8. Derive the first three natural frequency and mode shapes for cantilever beam by solving the governing
differential equation of flexural vibrations for continuous systems.
UNIT V
9. Derive the response of a Single-degree of freedom system due to base excitation by solving the governing
differential equation of motion.

10. Explain the IS code procedure for response of multi storey building to earthquake excitation using
Response spectra method.