lecture2110

lecture2110 - ME 563 Mechanical Vibrations Lecture #21...

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ME 563 Mechanical Vibrations Lecture #21 Multiple Degree of Freedom Modal Approach for Forced Response
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Modal Approach 1 We have considered one method for obtaining the forced response of a multiple degree of freedom system based on the use of frequency response functions. This approach produces the steady state response of the physical coordinates, but what if we are interested in the modal responses instead? The modal approach to forced response can be used to decouple the equations of motion and solve for the individual modal responses.
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Transforming Coordinates 2 Consider the system shown below. The equations of motion are given by: and we uncouple these equations using the substitution,
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Uncoupling EOMs 3 The equations of motion are uncoupled as follows, leading to the following forced modal equations: The modal forces are given by,
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What is the Meaning? 4 These equations indicate that: - The forced response of each mode is independent of the other modes. -
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lecture2110 - ME 563 Mechanical Vibrations Lecture #21...

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