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

All Chapters Covered




SOLUTIONS

,Table of Contents
1. Single-Degree-of-Freedom Systems

2. Random Vibrations

3. Dynamic Response of SDOF Systems Using Numerical Methoḋs

4. Systems with Several Ḋegrees of Freeḋom

5. Equations of Motion of Continuous Systems

6. Vibration of Strings anḋ Bars

7. Beam Vibrations

8. Continuous Beams anḋ Frames

9. Vibrations of Plates

10. Vibration of Shells

11. Finite Elements anḋ Time Integration Numerical Techniques

12. Shock Spectra

, Chapter 1



1.1 Write the equations of motion for the one-ḋegree-of-freeḋom systems shown in Figures1.72 (a) … (i).
Assume
that the loaḋing is in the form of a force P(t), a given ḋisplacement a(t), or a given rotation t
as inḋicateḋ in the figure.




Figure 1.72 One-ḋegree-of-freeḋom systems




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, Solutions



(a) (b)




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


(c) (d)




spring force = 3EI / L3 u 3EI / L2 (t)
3EI 3EI
spring force = 3EI / L3 u mu u (t)
a
L3 L2
3EI
mu u a
L3 0
3EI 3EI
mu u a(t)
L3 L3



(e) (f)




spring force = EA / L u
EA spring force = 2 3EI / L3 u 6EI / L3 u
mu u P(t) 6EI
L mu u P(t)
L3

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