Finding natural frequency and mode shape of damped 4 degree of freedom

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Assume that the m1= 40 kg, m2 = 1800 kg, I = 5000 kg-m2, l1 = 3.2 m, l2= 2.1 m, k1 = k2 = 90,000 N/m, and c = 800 Nm/s;
  1. Determine natural frequencies and the mode shapes.
  2. Considering the base displacement x1(t) = 0.1 sin (66t) applied on the right side only.

Answers (1)

J Chen
J Chen on 3 May 2022
Edited: J Chen on 3 May 2022
Use F=ma to develop the differntial equations for m1, m2. Use F=ma and M=Iw for m3. The natural frequencies and mode shapes are the eigenvalues and eigenvectors.


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