Busby Structural Dynamics 1st Edition Complete Solutions Manual

All Chapters Covered
q q




SOLUTIONS

,TableofContents q q




1. Single-Degree-of-Freedom Systems q




2. Random Vibrationsq




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




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




5. Equations of Motion of Continuous Systems
q q q q q




6. Vibration of Strings and Bars
q q q q




7. Beam Vibrations
q




8. Continuous Beams and Frames q q q




9. Vibrations of Plates q q




10. Vibration of Shells q q




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




12. Shock Spectra
q

, Chapter 1
q




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




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




ure.




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

, Solutions


(a) (b)




spring force = 3EI / L3 u  
 
q q q q q q

3
spring force = 48EI / L u
q q q q q q 3EI
mu  3 u  P(t)
q
q q


48EI L
mu  3 u  P(t)
q q q q

L q




(c) (d)




spring force = 3EI / L3 u  3EI / L2 (t)
q q q  q q  
q q q q q 
q




spring force = 3EI / L3
q q q  q q u  a
q q q mu 
q
3EI
q
q

u
q q
3EI
(t)
q




L3 L2
3EI
mu  3 u  a  0
q q q q q q

L q



3EI 3EI
mu  u
q q

q q a(t) q q

3
L L3



(e) (f)




spring force = EA / Lu
   
q q q q q



EA spring force = 2 3EI / L3 u  6EI / L3 u
q q q q q q q q q q q

mu  u  P(t)
q q

q q q q
6EI
L mu 
q u  P(t)
q q q

L3