Solutions Manual for Structural Dynamics Concepts and Applications 1st Edition by Busby

AllChaptersCovered
c c




SOLUTIONS

,TableofContents
c c




1. Single-Degree-of-Freedom Systems c




2. Random Vibrations c




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




4. Systems with Several Degrees of Freedom
c c c c c




5. Equations of Motion of Continuous Systems
c c c c c




6. Vibration of Strings and Barsc c c c




7. Beam Vibrations
c




8. Continuous Beams and Frames c c c




9. Vibrations of Plates c c




10. Vibration of Shells c c




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




12. Shock Spectra c

, Chapter 1 c




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




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




c figure.




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




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, Solutions


(a) (b)




spring force = (3EI / L )u 3

( )
c c c c c c




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




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


L c




(c) (d)




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




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


u=
c c
3EI
(t)
c




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




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


c c c c




L3
L3



(e) (f)




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




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



mu + u = P(t)
c c


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



L3




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