Vibrations - Applied Mechanics and Structures - Naval Architecture & Marine Engineering Previous Year Questions

1

2022 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Vibrations

Naval Architecture & Marine Engineering (NM) 2022

Let \(\omega_f\) be the excitation frequency of a sinusoidal load and \(\omega_n\) be the natural frequency of a single degree of freedom system. Then the dynamic response of the system is highly affected by the stiffness of the system when

A

\(\omega_f = \omega_n\)

B

\(0 < \omega_f < \omega_n\)

C

\(0 < \omega_n < \omega_f\)

D

\(\omega_f = 0\)

Open complete paper

2

2022 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Vibrations

Naval Architecture & Marine Engineering (NM) 2022

If the maximum static deflection of a shaft is 5 mm, then the estimated critical speed using Rayleigh-Ritz method is __________ RPM (rounded off to nearest integer).

Check answer

Open complete paper

3

2022 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Vibrations

Naval Architecture & Marine Engineering (NM) 2022

An under-damped single degree of freedom system is freely oscillating with an initial amplitude \(A\). The initial velocity of the system is zero. After five cycles of oscillation, the amplitude reduces to \(A/2\).
Then the damping ratio of the system is ______% (rounded off to one decimal place) of critical damping.

Check answer

Open complete paper

4

2022 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Vibrations

Naval Architecture & Marine Engineering (NM) 2022

A system with two degrees of freedom, as shown in the figure, has masses \( m_1 = 200 \text{ kg} \) and \( m_2 = 100 \text{ kg} \) and stiffness coefficients \( k_1 = k_2 = 200 \text{ N/m} \).
Then the lowest natural frequency of the system is _____ rad/s (rounded off to one decimal place).

Check answer

Open complete paper

5

2023 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Vibrations

Naval Architecture & Marine Engineering (NM) 2023

For a given time varying load applied on a single degree of freedom system, the dynamic response amplitude is always less than the static response amplitude if

A

the applied loading frequency is greater than 1.5 times the natural frequency of the system

B

the damping is greater than 70% of critical damping

C

the damping is exactly 1/3rd of critical damping

D

the applied loading frequency is less than the natural frequency of the system for an undamped system

Check answer

Open complete paper

6

2024 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Vibrations

Naval Architecture & Marine Engineering (NM) 2024

Which one of the following reduces the ratio of vibratory response amplitude to the forcing amplitude, in large stationary engine shaft design?

A

Reduction in axial vibrations of the rotating shaft

B

Increase in the fundamental frequency of the rotating shaft

C

Decrease in the rotational speed of shaft

D

Operating the shaft at a speed exceeding the critical speed

Open complete paper

7

2024 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Vibrations

Naval Architecture & Marine Engineering (NM) 2024

A single degree of freedom system has a mass, stiffness and damping of 200 kg, 20 N/m and 62 N-s/m respectively. For a forced oscillation system, if the excitation frequency is equal to the undamped natural frequency, then the dynamic magnification factor is _______ (rounded off to three decimal places).

Check answer

Open complete paper

8

2025 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Vibrations

Naval Architecture & Marine Engineering (NM) 2025

The dynamic response amplitude \(|H(\omega)|\) of a single degree of freedom system subjected to support motion is given by the following expression.\n\n\[|H(\omega)| = \sqrt{\frac{1 + 4 \zeta^2 \left(\frac{\omega}{\omega_n}\right)^2}{\left[1 - \left(\frac{\omega}{\omega_n}\right)^2\right]^2 + 4 \zeta^2 \left(\frac{\omega}{\omega_n}\right)^2}}\]\n\n\(|H(\omega)|\) increases with an increase in damping ratio (\(\zeta\)) if the excitation frequency (\(\omega\)) is __________ the natural frequency (\(\omega_n\)) of the system.

A

equal to

B

0.75 times

C

\(\frac{\sqrt{3}}{2}\) times

D

greater than \(\sqrt{2}\) times

Open complete paper

9

2025 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Vibrations

Naval Architecture & Marine Engineering (NM) 2025

A single degree of freedom system is undergoing free oscillation. The natural frequency and damping ratio of the system are 1 rad/sec and 0.01 respectively.

The reduction in peak amplitude over three cycles is ______ % (rounded off to one decimal place).

Check answer

Open complete paper

10

2026 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Vibrations

Naval Architecture and Marine Engineering (NM) 2026

A ship undergoing harmonic oscillation has an uncoupled heave motion, \(\eta_3(t)\), governed by the following equation
\((M + A_{33}) \ddot{\eta}_3(t) + B_{33} \dot{\eta}_3(t) + K_{33} \eta_3(t) = f_3(t)\)
If \(F_3(\omega)\) is the Fourier transform of \(f_3(t)\), then the response in the frequency domain can be written as ______.

A

\(\frac{F_3(\omega)}{-\omega^2(M + A_{33}) + i\omega B_{33} + K_{33}}\)

B

\(\frac{iF_3(\omega)}{-\omega^2(M + A_{33}) + i\omega B_{33} + K_{33}}\)

C

\(\frac{F_3(\omega)}{\omega^2(M + A_{33}) - i\omega B_{33} + K_{33}}\)

D

\(\frac{F_3(\omega)}{\omega^2(M + A_{33}) + \omega B_{33} + K_{33}}\)

Open complete paper

11

2026 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Vibrations

Naval Architecture and Marine Engineering (NM) 2026

For a dynamic system with single degree of freedom, choose the CORRECT statement(s).

A

Damped natural frequency is greater than the undamped natural frequency.

B

Dynamic response is always greater than static response at all excitation frequencies.

C

Damping ratio can be estimated using logarithmic decrement method.

D

A non-zero phase lag is always observed between the excitation and response for a damped system.

Check answer

Open complete paper

12

2026 · Naval Architecture & Marine Engineering · Applied Mechanics and Structures · Vibrations

Naval Architecture and Marine Engineering (NM) 2026

A box shaped pontoon of length 100 m, breadth 12 m and draft 10 m is floating in water of density 1 tonne/m³. The roll radius of gyration is 1% of the ship’s length and the roll added mass moment of inertia is 20% of the roll mass moment of inertia. The vertical centre of buoyancy is located at half of the draft, and the vertical centre of gravity is at 6 m from the keel.
The roll natural frequency of the pontoon is ______ rad/s (rounded off to two decimal places).
Assume g = 10 m/s².

Check answer

Open complete paper