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Fundamentals of Stress and Vibration 1. Mathematics for Structural mechanics
[A Practical guide for aspiring Designers / Analysts]
ͳǤͶǤʹ ‡”‹˜ƒ–‹˜‡ –‘ ϐ‹† ƒš ƒ† ‹ ‘ˆ ƒ ˆ— –‹‘

‘•‹†‡” –Š‡ ˆ‘ŽŽ‘™‹‰ ‰”ƒ’Š•ǣ

[Fig 1.5: slope at peaks]
dy
The . helps us conclude that, is zero when the curve is either at maximum or
dx

minimum value

‘ ƒ• ‡”–ƒ‹ –Š‡ ƒš ‘” ‹ ˜ƒŽ—‡•ǡ –Š‡ ˆ‘ŽŽ‘™‹‰ ‘†‹–‹‘• ƒ’’Ž›ǣ

2
d y
1) when < 0 , the value of y is maximum
dx 2
2
d y
2) when > 0 , the value of y is minimum
dx 2
2
d y
3) when = 0 , this is called a saddle point stationary point , where the rate of change
dx 2

‘ˆ •Ž‘’‡ ‹• œ‡”‘ǡ ‡ƒ‹‰ǡ –Š‡ †‹”‡ –‹‘ ‘ˆ •Ž‘’‡ Šƒ‰‡ ‘—Ž† „‡ ’‘•‹–‹˜‡ ‘” ‡‰ƒ–‹˜‡Ǥ Š‹• ‹• ƒŽ•‘
ƒŽŽ‡† –Š‡ •–ƒ–‹‘ƒ”› ‘” •ƒ††Ž‡ ’‘‹–ǡ ƒ• •Š‘™ ‹ ȏ ‹‰ ͳǤ͸ȐǤ

[Fig 1.6: max, min and saddle points]

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