Structural Dynamics - Structures - Aerospace Engineering Previous Year Questions

1

2007 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2007

The number of natural frequencies of an elastic beam with cantilever boundary conditions is

A

1

B

3

C

1000

D

Infinite

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2

2007 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2007

The boundary conditions for an Euler-Bernoulli column are given in column X and the critical buckling loads are given in column Y. Match the boundary condition of the column to its corresponding buckling load. \(P_{cr}\) is the critical buckling load, \(E\) is the Young's modulus of the column material, \(I\) its sectional moment of area, and \(L\) is the length of the column.

A

X1-Y4, X2-Y3, X3-Y1, X4-Y2

B

X1-Y4, X2-Y2, X3-Y3, X4-Y1

C

X1-Y4, X2-Y1, X3-Y2, X4-Y3

D

X1-Y4, X2-Y3, X3-Y2, X4-Y1

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3

2008 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2008

A thin walled tube of circular cross-section with mean radius r has a central web which divides it into two symmetric cells as shown. A torque M is acting on the section. The shear flow q in the central web is

A

\(q = \frac{M}{2 \pi r^2}\)

B

\(q = 0\)

C

\(q = \frac{M}{4 \pi r^2}\)

D

\(q = \frac{M}{\pi r^2}\)

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4

2008 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2008

An engineer is asked to test a system which can be idealized as SDOF (single degree of freedom) with viscous damping. A frequency response test was conducted and it is found that the quality factor \(Q\) is equal to 10. What will be the logarithmic decrement if a free vibration test is performed?

A

\(\pi/40\)

B

\(\pi/20\)

C

\(\pi/10\)

D

\(\pi/5\)

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5

2008 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2008

The equation of motion of a uniform slender beam of length L in flexural vibration is given as \(EI \frac{\partial^4 w}{\partial x^4} + \rho A \frac{\partial^2 w}{\partial t^2} = 0\), where \(EI\) is the flexural rigidity, \(w\) is the lateral displacement and \(\rho A\) is the mass per unit length. The beam is simply supported at the two ends \(x = 0\) and \(x = L\). Assuming the mode shape in fundamental mode to be \(\sin \left( \frac{\pi x}{L} \right)\), the natural frequency in fundamental mode is

A

\(0.5 \sqrt{\frac{EI}{\rho A L^4}} \pi^2\)

B

\(\sqrt{\frac{EI}{\rho A L^4}} \pi^2\)

C

\(2 \sqrt{\frac{EI}{\rho A L^4}} \pi^2\)

D

\(4 \sqrt{\frac{EI}{\rho A L^4}} \pi^2\)

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6

2009 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2009

For the thin walled beam cross section as shown in the figure, the shear centre lies at

A

Mid point of AB, i.e. at point E

B

Mid point of BD, i.e. at point F

C

Junction point B

D

at a point G lying within the area ABC

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7

2009 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2009

A uniform rigid bar of mass \(m = 1\) kg and length \(L = 1\) m is pivoted at \(A\). It is supported by a spring of stiffness \(k = 1\) N/m and a viscous damper of damping constant \(C = 1\) N-s/m, with \(a = \frac{1}{\sqrt{3}}\) m as shown below. The moment of inertia of the rigid bar is \(I_A = \frac{mL^2}{3}\).
The system is

A

overdamped

B

underdamped with natural frequency \(\omega_n = 1\) rad/s

C

critically damped

D

underdamped with natural frequency \(\omega_n = 2\) rad/s

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8

2009 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2009

If the shaft is fixed at both ends, the boundary conditions are:

A

\(\frac{\partial \theta}{\partial x}\Big|_{x=0} = 0\) and \(\frac{\partial \theta}{\partial x}\Big|_{x=L} = 0\)

B

\(\theta(0)=0\) and \(\theta(L)=0\)

C

\(\frac{\partial \theta}{\partial x}\Big|_{x=0} = 0\) and \(\theta(L)=0\)

D

\(\theta(0)=0\) and \(\frac{\partial \theta}{\partial x}\Big|_{x=L} = 0\)

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9

2010 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2010

A horizontal cantilevered steel beam of rectangular cross-section having width b and depth d is vibrating in the vertical plane. The natural frequency of bending vibration is highest when

A

\(b = 10, d = 10\)

B

\(b = 20, d = 5\)

C

\(b = 5, d = 20\)

D

\(b = 25, d = 4\)

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10

2011 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2011

A statically indeterminate frame structure has

A

same number of joint degrees of freedom as the number of equilibrium equations

B

number of joint degrees of freedom greater than the number of equilibrium equations

C

number of joint degrees of freedom less than the number of equilibrium equations

D

unknown number of joint degrees of freedom, which cannot be solved using laws of mechanics

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11

2012 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2012

In a semi-monocoque construction of an aircraft wing, the skin and spar webs are the primary carriers of

A

shear stresses due to an aerodynamic moment component alone.

B

normal (bending) stresses due to aerodynamic forces.

C

shear stresses due to aerodynamic forces alone.

D

shear stresses due to aerodynamic forces and a moment component.

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12

2012 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2012

Buckling of the fuselage skin can be delayed by

A

increasing internal pressure.

B

placing stiffeners farther apart.

C

reducing skin thickness.

D

placing stiffeners farther and decreasing internal pressure.

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13

2012 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2012

The internal pressure \(p_y\) at yield, based on the von Mises yield criterion, if the vessel is floating in space, is approximately

A

500 MPa

B

250 MPa

C

100 MPa

D

20 MPa

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14

2016 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2016

The governing differential equation of motion of a damped system is given by
\(m \frac{d^2x}{dt^2} + c \frac{dx}{dt} + kx = 0\). If m = 1 kg, c = 2 Ns/m and k = 2 N/m then the frequency of the damped oscillation of this system is ____ rad/s.

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15

2017 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2017

A 2-DOF undamped spring-mass system with two masses and two springs has natural frequencies \(\omega_1 = 0.79\) rad/s and \(\omega_2 = 1.538\) rad/s. The mode shapes for the system are given by \(\phi_1 = [0.732 \; 1]^T\) and \(\phi_2 = [-2.73 \; 1]^T\). If the first mass is displaced by 1 cm, the minimum displacement in cms to be given to the second mass to make the system vibrate in first mode alone is ________ (in three decimal place).

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16

2017 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2017

A single degree of freedom spring-mass system of natural frequency 5 Hz is modified in the following manners:
Case 1: Viscous damping with damping ratio \(\zeta = 0.2\) is introduced in parallel to the spring.
Case 2: The original undamped spring-mass system is moved to a surface with coefficient of friction, \(\mu = 0.01\).
The ratio of the damped natural frequency for the cases 1 and 2 is given by ________ (in three decimal places).

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17

2017 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2017

The natural frequency of the system suspended by two identical springs of stiffness k as shown in the figure is given by ω_n = α√(k/m) for small displacement. Both the springs make an angle of 45° with the horizontal. The value of α is ______ (in two decimal places).

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18

2018 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2018

For a damped single degree of freedom system with damping ratio of 0.1, ratio of two successive peak amplitudes of free vibration is ______ (accurate to two decimal places).

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19

2018 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2018

The natural frequency (in rad/s) of the spring-mass system shown in the figure below is ______ (accurate to one decimal place).

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20

2018 · Aerospace Engineering · Structures · Structural Dynamics

Aerospace Engineering (AE) 2018

A 1 m long massless cantilever beam oscillates at 2Hz, while a 60 kg mass is attached at the tip of it. The flexural rigidity of the beam (in kN·m²) is ________ (accurate to two decimal places).

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