*****INSTANT DOWNLOAD****PDF****Solutions Manual for Structural Dynamics Concepts and Applications 1st Edition

AllChaptersCovered
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SOLUTIONS

,TableofContents
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1. Single-Degree-of-Freedom Systems v




2. Random Vibrations v




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 Barsv v v v




7. Beam Vibrations
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8. Continuous Beams and Frames v v v




9. Vibrations of Plates v v




10. Vibration of Shells v v




11. Finite Elements and Time Integration Numerical Techniques
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12. Shock Spectra v

, Chapter 1 v




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




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




v figure.




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




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, Solutions


(a) (b)




spring force = (3EI / L )u 3

( )
v v v v v v




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




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


L v




(c) (d)




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




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


u=
v v
3EI
(t)
v




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




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


v v v v




L3
L3



(e) (f)




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




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



mu + u = P(t)
v v


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



L3




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