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Fundamentals of Stress and Vibration
[A Practical guide for aspiring Designers / Analysts] 1. Mathematics for Structural mechanics
2
3
: if θ = 90 then, we get πR , which is the volume of a hemisphere
1
3
4
3
if θ = 180 then,we get πR , which is the volume of a sphere
1
3
ͳǤͶǤͷ –ƒ†ƒ”† –‡‰”ƒŽ•

( ) ( )

x x n+1
+ c
n + 1
n
x (when( n = −1)) log e x + c
x e e x + c

e ax
e ax + c
a

sin x − cos x + c

cos x sin x + c

x + c
tan x log sec
e
log e x (log x + 1)x + c
e

a 2 x x x 2
2
a 2 − x sin −1 + 1 − + c
2 a a a 2

f x ∗ g(x) [integr ation by parts] g x f x − f x ∗ g x dx
′

ͳǤͶǤ͸ ͳ ‘”†‡” ‹ˆˆ‡”‡–‹ƒŽ “—ƒ–‹‘•
•–
Š‡ ‘”†‡” ‘ˆ ƒ †‡”‹˜ƒ–‹˜‡ †‡–‡”‹‡• –Š‡ ‘”†‡” ‘ˆ –Š‡ †‹ˆˆ‡”‡–‹ƒŽ ‡“—ƒ–‹‘Ǥ šƒ’Ž‡ǡ ‹ˆ ‘”†‡” ‘ˆ –Š‡
†‡”‹˜ƒ–‹˜‡ ‹• Ǯ͵ǯǡ –Š‡ǡ ‹– ‹• ƒ ͵ ‘”†‡” †‹ˆˆ‡”‡–‹ƒŽ ‡“—ƒ–‹‘Ǥ
Ӡ
ˆ –Š‡ ‘”†‡” ‘ˆ –Š‡ †‡”‹˜ƒ–‹˜‡ ‹• Ǯǯǡ –Š‡ǡ ‹– ‹• ƒ  ‘”†‡” †‹ˆˆ‡”‡–‹ƒŽ ‡“—ƒ–‹‘Ǥ Š‡ †‡‰”‡‡ ‘ˆ –Š‡
–Š
†‹ˆˆ‡”‡–‹ƒŽ ‡“—ƒ–‹‘ ‹• –Š‡ ’‘™‡” ‘ˆ –Š‡ †‡”‹˜ƒ–‹˜‡Ǥ

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