The dislocation string model proposed by Koehler, and further developed by Granato and Lucke has been used to study the contribution of dislocations towards the generation of acoustic higher harmonics in propagating ultrasonic waves. Granato and Lucke have considered the bowing and breakaway of a pinned dislocation loop to derive expressions for the dimensionless ‘decrement’ which measures the mechanical damping due to dislocations on a propagating ultrasonic wave. Barring the work by Chakrapani, which captures the effect of dislocation dynamics on the bulk nonlinear response of a resonant beam by considering the dislocation contribution to the acoustic nonlinearity parameter, there is no work that considers dislocation effects in nonlinear resonant condition.   
The present work focuses on the development of a model which incorporates the effects of both frequency and amplitude dependent dislocation damping on the resonant vibration of solid structures. A nonlinear beam model was derived following the classical plate theory assuming a linear viscoelastic Kelvin-Voigt material model with a von Karman type nonlinear strain-displacement relationship. The nonlinear equation of motion is derived assuming the linear vibration mode shape of a cantilever beam, subject to an external harmonic excitation. Expressions for the steady-state solution and energy loss per cycle were derived, first for the linear part of the equation of motion, and subsequently for the nonlinear equation of motion. The dimensionless decrement was computed from the expressions for the energy loss per cycle and the total energy stored in the oscillator, and considered together with a scaled decrement due to dislocations, resulting in a decrement accounting for both lattice and dislocation effects. The Kelvin-Voigt damping term was then rewritten using the final expression for the decrement and the geometry of the beam. The effect of frequency dependent and amplitude dependent decrement on the frequency response of the equation of motion was found considering the new expression of the Kelvin-Voigt damping term.  
The models developed here allow us to develop concepts of linear and nonlinear internal friction and its source contributions arising from the lattice as well as defects like dislocations. The eventual objective is to be able to expand this model to higher and lower order defects. 


Dislocation Damping Effects in Nonlinear Resonant Vibrations of Structures

No proceedings papers in 2020. Video only.

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