Structural damping - an energy dissipation mechanism AAE 556 Aeroelasticity Structural damping - an energy dissipation mechanism Purdue Aeroelasticity

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 Purdue Aeroelasticity

Viscous damping effect with harmonic forcing Solution Complex solution Complex force Purdue Aeroelasticity

Work done by viscous damping is the area inside a hysteresis loop Purdue Aeroelasticity

Energy expended by the viscous forces (work done) work done by viscous force is negative or dissipative Purdue Aeroelasticity

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 Purdue Aeroelasticity

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? Purdue Aeroelasticity

Purdue Aeroelasticity Write the “viscous” equation of motion using equivalent structural damping Use a complex solution approach Purdue Aeroelasticity

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. Purdue Aeroelasticity

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” Purdue Aeroelasticity

Solution for response amplitude Purdue Aeroelasticity

Measuring gx at resonance Set the forcing frequency, w, equal to the system natural frequency Purdue Aeroelasticity

Structural damping from harmonic shaker test gx is not large - of the order of 0.01-0.05 Purdue Aeroelasticity

Purdue Aeroelasticity Including structural damping in the equations of motion Modify existing stiffness elements Purdue Aeroelasticity

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 Purdue Aeroelasticity