For the three-story shear buildings shown in Fig. P9.8: (a) Determine the natural vibration…

For the three-story shear buildings shown in Fig. P9.8:

(a) Determine the natural vibration frequencies and modes; express the frequencies in terms of m, , and h. Sketch the modes and identify the associated natural frequencies.

(b) Verify that the modes satisfy the orthogonality properties.

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(c) Normalize each mode so that the modal mass Mn has unit value. Sketch these normalized modes. Compare these modes with those obtained in part (a) and comment on the differences.

 

 

 

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