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17 April 2013 Nonlinear guided waves in solids under constrained thermal expansion
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Propagation of nonlinear guided waves is a field that has received an ever increasing interest in the last few decades. They are excellent candidates for nondestructively interrogating long waveguide like structures since they conveniently combine high sensitivity to structural conditions (typical of nonlinear parameters), with large inspection ranges (characteristic of wave propagation in bounded media). Nonlinear wave propagation in solids has been classically studied using finite strains theory. According to this framework a system of nonlinear PDEs is required to mathematically describe nonlinear phenomena such as acoustoelasticity (wave speed dependency on state of stress), wave interaction, wave distortion, higher harmonics generation, and so on. This work introduces a novel physical model aimed at predicting nonlinearity in constrained waveguides characterized by infinitesimal (ideally zero) strains subjected to thermal variations. Interatomic potentials are employed to explain the origin of nonlinear effects under constrained temperature changes. These potentials highlight at least a cubic dependence on strain of the residual strain energy that is stored in the material due to the prevented thermal expansion. The cubic relationship between strain energy and strain produces second-harmonic generation of propagating elastic waves. This principle is validated experimentally for longitudinal bulk waves propagating in a steel block under constrained thermal excursions.
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Claudio Nucera and Francesco Lanza di Scalea "Nonlinear guided waves in solids under constrained thermal expansion", Proc. SPIE 8695, Health Monitoring of Structural and Biological Systems 2013, 86950P (17 April 2013);

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