example_IV_1_08 - Example IV.1.8 3 3 2 L 2 1 L 1 L 0...

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Example IV.1.8 L L L θ 1 θ 2 θ 3 μ μ μ Κ Κ Κ Φ ξ ψ 3 2 1 0 Kinematics         EOM’s   Using the standard  linearization  process (about the equilibrium  state of    ), the EOM’s become:   or   Natural Frequencies and  Modes Although  we do NOT need  the natural frequencies and  modal vectors for finding  the particular   solution, we will use them  later on when  we interpret  the response.  The eigenvalue  problem  for this example is:   where    . Using Matlab, the natural frequencies and  mass normalized  modal vectors are found  to be: 1
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  Particular Solution  for the Response To simplify some of our algebra, we will first define a non-dimensional time,  τ,  such that:   Substituting  into the EOM’s:   where    . Particular solution:   where   Therefore,   where, by using the definition of the inverse of [H] in terms of its cofactor matrix:   where
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example_IV_1_08 - Example IV.1.8 3 3 2 L 2 1 L 1 L 0...

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