University of Florida/Eml4507/s13.team3.ADR6

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On my honor, I have neither given nor received unauthorized aid in doing this assignment.

Given

$m_{1} = 3$

$m_{2} = 2$

$k_{1} = 10$

$k_{2} = 20$

$k_{3} = 15$

Find

Solve by hand the gen. eigenvalue problem for the spring-mass-damper system on p.53-13, using the data for the masses in (2) p.53-13b, and the data for the stiffness coefficients in (4) p.53-13b.

Solution

First plug given values into the stiffness matrix:

$K = [\begin{matrix} a_{1} & 0 & 0 & - a_{1} & 0 & 0 \\ 0 & 12 a_{2} & 6 L a_{2} & 0 & - 12 a_{2} & 6 L a_{2} \\ 0 & 6 L a_{2} & 4 L_{2}^{2} & 0 & - 6 a_{2} & 2 L a_{2}^{2} \\ - a_{1} & 0 & 0 & a_{1} & 0 & 0 \\ 0 & - 12 a_{2} & - 6 L a_{2} & 0 & 12 a_{2} & - 6 a_{2} \\ 0 & 6 L a_{2} & 4 L_{2}^{2} & 0 & - 6 a_{2} & 4 L a_{2}^{2} \end{matrix}]$

$K = [\begin{matrix} (10 + 20) & - 20 \\ - 20 & (20 + 15) \end{matrix}]$

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University of Florida/Eml4507/s13.team3.ADR6

Given

Find

Solution

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