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Fundamentals of Stress and Vibration
[A Practical guide for aspiring Designers / Analysts] 1. Mathematics for Structural mechanics
Šƒ’–‡” ͳ - ƒ–Š‡ƒ–‹ • ˆ‘” –”— –—”ƒŽ ‡ Šƒ‹ •

ͳǤͳ –”‘†— –‹‘
ƒ–Š‡ƒ–‹ • ‹• ‡••‡–‹ƒŽ –‘ “—ƒ–‹ˆ› ƒ› ‡‰‹‡‡”‹‰ •‹–—ƒ–‹‘•ǡ „‡ ‹–ǡ ϐ‹†‹‰ –Š‡ ”ƒ–‡ ‘ˆ Šƒ‰‡ ‘ˆ
ƒ ‰‹˜‡ ’ƒ”ƒ‡–‡”ǡ ϐ‹†‹‰ –Š‡ —”˜ƒ–—”‡ ‘ˆ ƒ ‰‡‡”ƒŽ —”˜‡ ‘” ͳ ‘†‡Ž‹‰ ‘ˆ ƒ •›•–‡ǥǤǡ ƒŽŽ
•‹–—ƒ–‹‘• ‡‡† ƒ–Š‡ƒ–‹ •Ǥ
Š‡ ƒ—–Š‘” †‘‡• ‘– ‹–‡† –‘ „—”†‡ –Š‡ ›‘—‰ ”‡ƒ†‡” ™‹–Š ‘’Ž‡š ƒ–Š‡ƒ–‹ • ƒ† Šƒ•
ƒ†‘’–‡† ƒ Ž— ‹† ƒ’’”‘ƒ ŠǤ ŽŽ †‹• —••‹‘• ƒ”‡ Ž‹‹–‡† –‘ –Š‡ ˆ—†ƒ‡–ƒŽ ‡••‡–‹ƒŽ• ‘ˆ •–”‡•• ƒ†
˜‹„”ƒ–‹‘ ƒƒŽ›•‡•Ǥ

ͳǤʹ „Œ‡ –‹˜‡
Š‹• Šƒ’–‡” †‘‡• ‘– ‹–‡† –‘ ‹–”‘†— ‡ ƒ–Š‡ƒ–‹ • ƒ• ƒ ”‹‰‘”‘—• ‘—”•‡Ǥ Š‡ ‡› –ƒ‡ƒ™ƒ›•
ˆ”‘ –Š‹• Šƒ’–‡” ƒ”‡ ƒ• ˆ‘ŽŽ‘™•ǣ
ͳǤ ‘ ’”‘˜‹†‡ Žƒ”‹–› ‘ˆ ‹†‡ƒ• ‘ ƒ–Š‡ƒ–‹ • ”‡Ž‡˜ƒ– –‘ ‡ Šƒ‹ •ǡ –”‡••ǡ ‹„”ƒ–‹‘ ƒ†
Ǥ
ʹǤ  ‘—”ƒ‰‡ ͳ ‘†‡ŽŽ‹‰ ‘ˆ •›•–‡• ȋ ƒ•‹ †‹ˆˆ‡”‡–‹ƒŽ Ȁ ƒŽ‰‡„”ƒ‹ ‡“—ƒ–‹‘•Ȍ ™Š‹ Š ‹• –Š‡
—””‡– ’”ƒ –‹ ‡ ‹ ƒ› Ǥ
͵Ǥ ‡Ž’ ƒ’’”‡ ‹ƒ–‡ ‡‰‹‡‡”‹‰ Ž‹–‡”ƒ–—”‡ –Šƒ– ‹• ƒ–Š‡ƒ–‹ ƒŽ ‹ ƒ–—”‡

ͶǤ  ‘—”ƒ‰‡ Šƒ† - ƒŽ —Žƒ–‹‘ —Ž–—”‡Ǥ
ͷǤ ƒ› –Š‡ ƒ–Š‡ƒ–‹ ƒŽ ˆ‘—†ƒ–‹‘ ˆ‘” ‘†‹‰Ǥ
͸Ǥ ƒ› ˆ‘—†ƒ–‹‘ ˆ‘” Š‹‰Š‡” ƒ–Š‡ƒ–‹ •Ǥ

ͳǤ͵ ”ƒ –‹ ƒŽ ƒŽ—‡ ††‹–‹‘

Ø ‡ –‘” ƒŽ‰‡„”ƒ ƒ† ‡ –‘” †‹ˆˆ‡”‡–‹ƒ–‹‘ǣ

ŽŽ ‡••‡–‹ƒŽ ˜‡ –‘” ƒŽ‰‡„”ƒ‹ ‘’‡”ƒ–‹‘•ǡ ƒ‡Ž›ǡ ƒ††‹–‹‘ǡ •—„–”ƒ –‹‘ ƒ† —Ž–‹’Ž‹ ƒ–‹‘ǡ
ƒ”‡ †‹• —••‡† ™‹–Š ’”ƒ –‹ ƒŽ ‡šƒ’Ž‡•Ǥ ‡ –‘” †‹ˆˆ‡”‡–‹ƒ–‹‘ ‹• †‹• —••‡† ‹ –Š‡ ‘–‡š– ‘ˆ
‡ Šƒ‹ • ȋ–Š‹• ‹• —•‡† ‹ •‡˜‡”ƒŽ •‹–—ƒ–‹‘•ǡ ‡šƒ’Ž‡ǡ ‹” —Žƒ” ‘–‹‘ǡ ‰›”‘• ‘’‹ •›•–‡
ƒƒŽ›•‹•ǡ —”˜‹Ž‹‡ƒ” ‘–‹‘ǡ ‡– ǤǤȌǤ
‹‰‹ϐ‹ ƒ– ”ƒ –‹ ƒŽ ’’Ž‹ ƒ–‹‘ǣ –ƒ„‹Ž‹–› ‘ˆ ™‡‹‰Š– Ž‹ˆ–‹‰ ‡ Šƒ‹•
Ø ƒŽ —Ž—• ƒ† ƒ•‹ †‹ˆˆ‡”‡–‹ƒŽ ‡“—ƒ–‹‘ǣ

Š‹• Šƒ’–‡” †‡ƒŽ• ™‹–Š ƒŽ —Ž—• ‘ˆ ʹ ˜ƒ”‹ƒ„Ž‡•ǡ ‡ ‘’ƒ••‹‰ –Š‡ ˆ‘ŽŽ‘™‹‰ ‘ ‡’–•ǣ
ͳȌ ‹†‹‰ –Š‡ ”ƒ–‡ ‘ˆ Šƒ‰‡ ‘ˆ ˆ— –‹‘• ‘ˆ ǮšǯǤ
ʹȌ ‘†‡Ž‹‰ –‹‡ ˜ƒ”›‹‰ •‹–—ƒ–‹‘•ǡ ‡ƒ‹‰ǡ ˆ‘”‹‰ „ƒ•‹ †‹ˆˆ‡”‡–‹ƒŽ ‡“—ƒ–‹‘•Ǥ
͵Ȍ ‹†‹‰ –Š‡ ƒš‹— ƒ† ‹‹— ˆ— –‹‘• ‘ˆ ƒ •‹‰Ž‡ ˜ƒ”‹ƒ„Ž‡Ǥ
ͶȌ ‘’—–‡ ƒ”‡ƒ ƒ† ˜‘Ž—‡ ‘ˆ ‰‡‘‡–”‹ ‡–‹–‹‡• ‘ˆ ˜ƒ”‹‘—• •Šƒ’‡•Ǥ
ͷȌ ƒ†‹—• ‘ˆ —”˜ƒ–—”‡ ˆ‘” ƒ ‰‡‡”ƒŽ —”˜‡Ǥ
‹‰‹ϐ‹ ƒ– ”ƒ –‹ ƒŽ ’’Ž‹ ƒ–‹‘ǣ ‡‡”ƒŽ •‘Ž—–‹‘ ‘ˆ †ƒ’‡† ˜‹„”ƒ–‹‘

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