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Unformatted text preview: ME 563 Mechanical Vibrations Lecture #14 Eigenvalue Problem for Continuous Systems Discrete vs. Continuous 1 When we solved for the free response of a lumped parameter (discrete) mechanical system, we found that: But in a continuous system, there are an infinite number of possible spatial coordinates (and modal parameters). Therefore, we can expect to see a longer summation, but the form of the solution should still be of the form: Spatial pattern Temporal pattern Discrete vs. Continuous 1 When we solved for the free response of a lumped parameter (discrete) mechanical system, we found that: But in a continuous system, there are an infinite number of possible spatial coordinates (and modal parameters). Therefore, we can expect to see a longer summation, but the form of the solution should still be of the form: Spatial pattern Temporal pattern String Solution 2 Consider the string equation of motion: If we assume a solution of the form, , we obtain: String Solution 3 This last equation can only be satisfied for all...
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 Fall '09

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