Solutions Manual for Structural Dynamics Concepts and Applications 1st Edition

AllChaptersCovered
d d




SOLUTIONS

,TableofContents
d d




1. Single-Degree-of-Freedom Systems d




2. Random Vibrationsd




3. Dynamic Response of SDOF Systems Using Numerical Methods
d d d d d d d




4. Systems with Several Degrees of Freedom
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5. Equations of Motion of Continuous Systems
d d d d d




6. Vibration of Strings and Bars
d d d d




7. Beam Vibrations
d




8. Continuous Beams and Frames d d d




9. Vibrations of Plates d d




10. Vibration of Shells d d




11. Finite Elements and Time Integration Numerical Techniques
d d d d d d




12. Shock Spectra
d

, Chapter 1 d




1.1 Write the equations of motion for the one-degree-of-freedom systems shown in Figures1.72 (a) … (i). Assume
d d d d d d d d d d d d d d d




that the loading is in the form of a force P(t), a given displacement a(t), or a given rotation
d d d d d d d d d d d d d d d d d d d (t) as indicated in the
d d d d d d




d figure.




Figure 1.72 One-degree-of-freedom systems
d d d




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, Solutions


(a) (b)




spring force = (3EI / L )u 3

( )
d d d d d d




spring force = 48EI / L3 u
d d d d d d
3EI
mu + d
u = P(t)
d d




48EI L3
mu + 3 u = P(t)
d d d d


L d




(c) (d)




spring force = 3EI / L3 u − 3EI / L2 (t)
d d d ( d d d ) ( d d d d )
d




spring force = 3EI / L3
d d d ( d d )(u −a)
d d d mu +d
3EI
d
d


u=
d d
3EI
(t)
d




L3 L2
3EI
mu +
L3
d (u − a) = 0
d
d d d d d




3EI 3EI
mu + u= a(t)
d d


d d d d




L3
L3



(e) (f)




spring force = (EA/ L)u
( ) ( )
d d d d d




EA spring force = 2 3EI / L3 u = 6EI / L3 u
d d d d d d d d d d d



mu + u = P(t)
d d


d d d d
6EI
L mu +d
u = P(t)
d d d



L3




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