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  Chapter 12 Structural Dynamics   1 Chapter 12 Structural Dynamics 12.1   Basics of Structural Dynamics12.2   Step-by-Step: Lifting Fork 12.3   Step-by-Step: Two-Story Building12.4   More Exercise: Ball and Rod12.5   More Exercise: Guitar String12.6   Review  Chapter 12 Structural Dynamics   Section 12.1 Basics of Structural Dynamics   2 Section 12.1 Basics of Structural Dynamics Key Concepts ã Lumped Mass Model ã Single Degree of Freedom Model ã Undamped Free Vibration ã Damped Free Vibration ã Damping Coef  fi cient ã Damping Mechanisms ã Viscous Damping ã Material Damping ã Coulomb Friction ã Modal Analysis ã Harmonic Response Analysis ã Transient Structural Analysis ã Explicit Dynamics ã Response Spectrum Analysis ã Random Vibration Analysis  Chapter 12 Structural Dynamics   Section 12.1 Basics of Structural Dynamics   3 Lumped Mass Model: The Two-Story Building   k 1   c  1   k 2   c  2   m 1   m 2 [1] A two-degrees-of-freedom model for fi nding the lateral displacements of the two-story building.[2] Total mass lumped at the fi rst fl oor.[3] Total mass lumped at the roof fl oor.[4] Total bending stiffness of the fi rst- fl oor's beams and columns.[5] Total bending stiffness of the second- fl oor's beams and columns.[6] Energy dissipating mechanism of the fi rst fl oor.[7] Energy dissipating mechanism of the second fl oor.  Chapter 12 Structural Dynamics   Section 12.1 Basics of Structural Dynamics   4 Single Degree of Freedom Model   F  ∑  = ma   p − kx  − c    x   = m   x    m   x  + c    x  + kx   = p  k  c   m  p   x    ã We will use this single-degree-of-freedom lumped mass model to explain some basic behavior of dynamic response. ã The results can be conceptually extended to general multiple-degrees-of-freedom cases.
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