1. Structural damping - an energy dissipation mechanism
AAE 556 Aeroelasticity
Structural damping - an energy dissipation mechanism
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2. A few preliminaries Differences between viscous and structural damping
Viscous damping
Energy dissipation due to heat generation from viscous fluid drag in a fluid
Structural damping in metals
Sometimes called “hysteretic damping”
Due to slipping between micro surfaces
Heat is generated and energy dispersed
Different from viscous mechanism
Magnitude of energy loss depends upon material type and mode of vibration
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3. Viscous damping effect with harmonic forcing
Solution
Complex solution
Complex force
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4. Work done by viscous damping is the area inside a hysteresis loop
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5. Energy expended by the viscous forces (work done)
work done by viscous force is negative or dissipative
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6. Work is not frequency dependent
A different case - Dissipative structural damping - internal damping forces-not velocity dependent
The constant a is material and displacement dependent
Torsional motion damping is different than plunge damping.
Why?
Work is not frequency dependent
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7. Viscous and structural damping energy equivalence
What would an equivalent structural damping need to be to have the same energy extracted by a viscous damper?
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8. Purdue Aeroelasticity
Write the “viscous” equation of motion using equivalent structural damping
Use a complex solution approach
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9. Result after assumed solution substitution
No frequency dependence but there is an “i”
This is the harmonic response of a single DOF spring/mass system including structural damping. The constant a is a material parameter determined by experiment and it is always positive.
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10. Define a new engineering term - the structural damping coefficient, gx
This is a very poor choice of letters because damping looks like gravity!!
Single DOF spring/mass harmonic response with a “complex stiffness”
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11. Solution for response amplitude
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12. Measuring gx at resonance
Set the forcing frequency, w, equal to the system natural frequency
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13. Structural damping from harmonic shaker test
gx is not large - of the order of
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14. Purdue Aeroelasticity
Including structural damping in the equations of motion Modify existing stiffness elements
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15. Purdue Aeroelasticity
Summary
Structural damping depends on the type of strain (cantilever beam motion or twisting motion) but does not depend on strain rate (frequency).
Structural damping depends on the type of material (steel, aluminum, composite)
Structural damping constant is only meaningful (valid) for forced harmonic motion
Structural damping always dissipates (removes) energy from the system
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