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Modal analysis uncouples the equations of motion because the mode shapes

  • A.make the damping matrix vanish identically at every frequency
  • B.are all of the same amplitude at every degree of freedom
  • C.are independent of the mass distribution of the structure
  • D.diagonalise the mass and stiffness matrices

Answer: D

Transforming to modal coordinates leaves a set of independent single-degree equations, one per mode, each solved exactly as in the simple case. Damping must be of a form that diagonalises too, which is why classical damping is assumed.

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