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February 24, 2021

Short Exercise 1:

Compute the natural frequencies and natural modes of the 3-degree of freedom system shown

below. Follow the following steps

1- Formulate the stiffness matrix. Use k as a prefactor.

2- Formulate the mass matrix. Use m as a prefactor.

3- Solve the eigenvalue problem assuming the natural frequencies can be written as

4- Compute the modal masses and modal stiffnesses. Would these values depend on the way

you normalize the eigenmodes.

5- Verify that the first Eigenmode is orthogonal to the second eigenmode.

Attachments:

Short-Exercis….pdf
Short-Exercis….docx
ShortExercise….pdf
ShortExercise….pdf

 

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