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SOLUTIONS
,Table of Contents
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1. Single-Degree-of-Freedom Systems g
2. Random Vibrationsg
3. Dynamic Response of SDOF Systems Using Numerical Methods
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4. Systems with Several Degrees of Freedom
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5. Equations of Motion of Continuous Systems
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6. Vibration of Strings and Bars
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7. Beam Vibrations
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8. Continuous Beams and Frames g g g
9. Vibrations of Plates g g
10. Vibration of Shells g g
11. Finite Elements and Time Integration Numerical Techniques
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12. Shock Spectra
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, Chapterg 1
1.1 Writegthegequationsgofgmotiongforgthegone-degree-of-freedomgsystemsgshowngingFigures1.72g(a)g…g(i).g Assume
thatgthegloadinggisgingthegformgofgagforcegP(t),gaggivengdisplacementga(t),gorgaggivengrotationg gtggasgindicatedgingt
hegfigure.
Figureg1.72g One-degree-of-freedomg systems
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, Solutions
(a) (b)
springgforceg=g 3EIg /gL3g u
springgforceg=g 48EIg/gL 3
g u 3EI
mug 3 uggP(t)
48EI L
mug g 3
ug gP(t)g
L
(c) (d)
springgforceg=g 3EIg/gL3g ugg 3EIg/gL2g (t)
springgforceg=g 3EIg /gL3g ugga mugg
3EIg
ugg
3EIg
(t)
L3 L2
3EI
mug g 3 uggaggg0
L
3EIg 3EIg
mugg ugg a(t)
3
L L3
(e) (f)
springgforceg=g EAg/gLu
gEAg
springgforceg=g2 3EIg/gL3g ugg 6EIg/gL3g u
mugg uggP(t) 6EI
L mug uggP(t)g
L3
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