Hall Ticket No Question Paper Code: BST004
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
M.Tech II Semester End Examinations (Regular/Supplementary) July, 2018
Regulation: IARE-R16
STRUCTURAL DYNAMICS
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. Explain clearly the rectilinear or longitudinal vibration, lateral or transverse vibrations and
torsional vibrations.
Define the following terms: undamped, damped, free and forced vibrations; resonance; phase
difference; periodic motion; time period; amplitude and degrees of freedom.
2. Derive the work done by a harmonic force on a harmonic motion of the same frequency.
A harmonic motion is given by 10 mm, where is in seconds and phase angle
in radians. Determine frequency and period of motion, and maximum displacement, velocity and
acceleration.
UNIT II
3. Derive the response of SDOF for damped free vibration case.
Discuss fundamentals of dynamic analysis with suitable simple examples.
4. An undamped SDOF system is subjected to a ramp impulse as shown in Figure 1. Find the stead
state response in the forced and free vibration states using Duhamel integral.
Figure 1
Formulate the equation of motion of a simple one storey shear building whose mass is lumped at
the floor.
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UNIT III
5. Derive the response to two degree freedom system shown in figure. Give the expression for natural
frequency and mode shape.
Figure 2
Describe two examples with neat sketches of the two degree of freedom systems.
6. Determine the natural frequencies and mode shapes of the 2 DOF systems shown in fig. and
verify the orthogonality of modes. The beams in each floor are assumed to be rigid.
Figure 3
Formulate the equation of motion of a simple two storey shear building whose masses are lumped
at the floors.
UNIT IV
7. Explain Stodola method to determine the fundamental frequency of the system.
Explain holzer method and basic procedure in the dynamics of a system.
8. Derive the natural frequency and mode shape for simply supported beam.
Derive governing differential equation of motion in continuous systems.
UNIT V
9. Define Transmissibility and derive the expression for it.
Enumerate the basic aspects of seismic design with a neat sketch, explain the strategy of earthquake
resistant design.
10. Explain the procedure to find the lateral forces and storey shears in multi-storey building for
dynamic analysis.

Explain the Indian Standard code method of analysis for obtaining response of multi storied
reinforced frame buildings.