Structural Dynamics Concepts and Applications Busby Solutions PDF

All Chapters Covered
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SOLUTIONS

,Table of Contents w w




1. Single-Degree-of-Freedom Systems w




2. Random Vibrationsw




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 Bars
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7. Beam Vibrations
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8. Continuous Beams and Frames w w w




9. Vibrations of Plates w w




10. Vibration of Shells w w




11. Finite Elements and Time Integration Numerical Techniques
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12. Shock Spectra
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, Chapter 1 w




1.1 Write the equations of motion for the one-degree-of-freedom systems shown in Figures1.72 (a) … (i). Assume
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that the loading is in the form of a force P(t), a given displacement a(t), or a given rotation
w w w w w w w w w w w w w w w w w w w  t  as indicated in the
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figure.
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Figure 1.72 One-degree-of-freedom systems
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, Solutions


(a) (b)




spring force = 3EI / L3 u  
 u
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3
spring force = 48EI / L
w w w w w w 3EI
mu  3 u  P(t)
w
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48EI L
mu  3 u  P(t)
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L w




(c) (d)




w 
spring force = 3EI / L3 u  3EI / L2 (t)
w w w w  
w w w w w 
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spring force = 3EI / L3
w w w  w w u  a
w w w mu w
3EI
w
w

u
w w
3EI
(t)
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L3 L2
3EI
mu  3 u  a   0
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L w



3EI 3EI
mu  u
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w w a(t) w w

3
L L3



(e) (f)




spring force = EA / Lu
   
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EA spring force = 2 3EI / L3 u  6EI / L3 u
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mu  u  P(t)
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w w w w
6EI
L mu 
w u  P(t)
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L3




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