Download VTU BE 2020 Jan ECE Question Paper 15 Scheme 7th Sem 15C744 Structural Dynamics

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Seventh Semester B.E. Degree Examination, 1 = i 9/Jan.2020
Structural Dynamics
Time: 3 hrs. Max. Marks: 80

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Note: Answer FIVE full questions, choosing ONE full question from each module.
Module-1
1 a. Define the following terms:
(i) Amplitude (ii) Damping (iii) Resonance (iv) Free vibration
(04 Marks)

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b.
Derive equation of motion for a freely vibrating undamped SDOF system and obtain its
solutions. (12 Marks)
OR
2 a. Define logarithmic decrement and derive an expression for logarithmic decrements.

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(09 Marks)
b.
An SDOF system having mass of 2.5 kg is subjected to free vibration with viscous damping.
The frequency of oscillation is found to be 20 Hz and measurement of the amplitude of
vibration shows two successive amplitudes to be 6 mm and 5.5 mm. Determine the damping

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coefficient. (07 Marks)
Module-2
3 a. Derive the expression for Duhamel's integral for the response of SDOF system subjected to
arbitrary excitation. (08 Marks)
b. An SDOF system consists of a mass of 20 kg, a spring of stiffness 2200 N/m and a dashpot

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with a damping coefficient of 60 N.S/m is subjected to a harmonic excitation of
F = 200sin5t. Write the complete solution of the equation of motion. (08 Marks)
OR
4 Derive an equation of motion for a damped harmonic excitation of a SDOF vibrating system
and obtain its complete solution. (16 Marks)

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Module-3
5 a. Explain the concept of shear building.
b. Determine the natural frequencies of the system shown in Fig.Q5 (b).
2 m WAr-
Fig. Q5 (b)

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(06 Marks)
(10 Marks)
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Seventh Semester B.E. Degree Examination, 1 = i 9/Jan.2020
Structural Dynamics
Time: 3 hrs. Max. Marks: 80
Note: Answer FIVE full questions, choosing ONE full question from each module.

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Module-1
1 a. Define the following terms:
(i) Amplitude (ii) Damping (iii) Resonance (iv) Free vibration
(04 Marks)
b.

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Derive equation of motion for a freely vibrating undamped SDOF system and obtain its
solutions. (12 Marks)
OR
2 a. Define logarithmic decrement and derive an expression for logarithmic decrements.
(09 Marks)

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b.
An SDOF system having mass of 2.5 kg is subjected to free vibration with viscous damping.
The frequency of oscillation is found to be 20 Hz and measurement of the amplitude of
vibration shows two successive amplitudes to be 6 mm and 5.5 mm. Determine the damping
coefficient. (07 Marks)

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Module-2
3 a. Derive the expression for Duhamel's integral for the response of SDOF system subjected to
arbitrary excitation. (08 Marks)
b. An SDOF system consists of a mass of 20 kg, a spring of stiffness 2200 N/m and a dashpot
with a damping coefficient of 60 N.S/m is subjected to a harmonic excitation of

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F = 200sin5t. Write the complete solution of the equation of motion. (08 Marks)
OR
4 Derive an equation of motion for a damped harmonic excitation of a SDOF vibrating system
and obtain its complete solution. (16 Marks)
Module-3

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5 a. Explain the concept of shear building.
b. Determine the natural frequencies of the system shown in Fig.Q5 (b).
2 m WAr-
Fig. Q5 (b)
(06 Marks)

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(10 Marks)
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OR
6 Determine the natural frequencies and mode shapes for the structure as shown in Fig. Q6.
?4- CC.,

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K
1
=600 kN/m
K2 = 1200 kN/m
= 1800 kN/m

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/ AAA
Fig. Q6

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(16 Marks)
Module-4
7 a. What do you mean by decoupling of equations? Explain the concept of modal superposition
method_ (08 Marks)
b. Explain orthogonality principle. (08 Marks)

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OR
8 Determine the natural frequencies an
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,7ode
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tat
shapes for the given system.

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1
c

Fig. Q8
(16 Marks)

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Module-5
9 a. Explain proportional damping in detail. (08 Marks)
b. Calculate the natural frequencies, mode shapes and damping ratio's for a proportionally
damped system given by:
- I

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[M]=
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-
9
1

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1
1
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3

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1

1
; [C]= [K = 49
- 1 -2 2

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(08 Marks)
OR
10 a. Explain consistent and Lumped mass matrices. (08 Marks)
b. Estimate the first 3 natural frequencies of a clamped free bar of length 9 in torsional
vibration by using a lumped mass model and 4 elements. (Element length = 4 ). (08 Marks)

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