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Dynamic Response of MDOF Structures

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Presentation on theme: "Dynamic Response of MDOF Structures"— Presentation transcript:

1 Dynamic Response of MDOF Structures

2 Equilibrium of forces condition gives the equations of motions:

3 Example: 2-DOF, identical mass & stiffness Free vibration
How do we solve this set of coupled equations?

4 By observation, the solution should be harmonic.
Substituting into the equations of motion: Need to find non-trivial solution  coefficient matrix has to be singular

5 Natural frequencies of the 2-DOF system.

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7 1 2

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11 Example: 5-DOF, identical mass & stiffness Free vibration

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14 Method for Uncoupling the Equations of Motion

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16 Orthogonality Properties of Modeshapes

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18 Scaling the Modeshapes
Arbitrary Set one modeshape coefficient equal to unity (ex: coeff. at roof level = 1.0) Mass normalized

19 Repeat the 2-DOF example

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22 Forced Vibration modal representation

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25 How to find the initial conditions in the modal space?
Premultiply by

26 Including damping

27 MDOF Examples

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29 find modes

30 rad/sec

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35 Mass-normalized modeshapes

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46 71 72

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48 Example

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