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Document Title
Fundamentals of Stress and Vibration 2. Engineering Mechanics Chapter
[A Practical guide for aspiring Designers / Analysts]

Taking ratio of ‘I composite ’ and ‘mr 2 composite ’, we get:

4
2
ρ πr ∗ L ∗ r 2 + ρ 2πr ∗ t ∗ L ∗ r ρ πr ∗ L + ρ 2πr ∗ t ∗ L
3
c
c
2
I composite 2 h 2 h

mr 2 = ρ πr ∗ L ∗ r + ρ 2πr ∗ t ∗ L ∗ r = ρ πr ∗ L + ρ 2πr ∗ t ∗ L
3
2
2
4
2
composite c h c h

4
Dividing the numerator and denominator by the common terms (r πL), we get:
I ρ c + 2ρ ∗ t
h
composite 2 r - - - - (2.55)
mr 2 composite ρ + 2ρ ∗ t
h
c r
I
It can be observed that, is a function of the densities of materials in the composite cylinder.
mr 2
Therefore, the acceleration ‘a’ is also a function of densities and so is the time of travel ‘t’.
As long as the hoop thickness remains small, the time of travel does not alter significantly. However,
as the thickness increases, it significantly changes the time of travel.

2.8 Curvilinear Motion

In a curve, every parameter changes from point to point, such as:

ü Radius of curvature
ü Direction of path
ü Speed of travel

[Fig 2.66: Curvilinear motion]

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QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries, Page 77 age 77
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