A Weakly Nonlinear Dynamic Problem for a Model of the Thermoelastic Medium Absorbing a Part of the Acoustic Spectrum

Mikhail Babenkov and Ekaterina Podolskaya ()
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Mikhail Babenkov: Higher School of Theoretical Mechanics, Peter the Great St. Petersburg Polytechnic University, 195251 St. Petersburg, Russia
Ekaterina Podolskaya: Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, 199178 St. Petersburg, Russia

Mathematics, 2022, vol. 10, issue 21, 1-11

Abstract: We consider a dynamic problem with a short laser impact on a semi-opaque insulated layer with free borders, accounting for the selective absorption of the acoustic spectrum regions by the media. The behavior of the material is modeled by the extended coupled thermoelasticity formulated in the previous work of the series. Following the experimental results, we introduce a weakly nonlinear correction to the thermal expansion coefficient. Thus, we aim to level out the inability of classical thermoelasticity (CTE) to correctly describe the deformation processes in a solid under a high-frequency impact, yet staying within the framework of linear models. The parameters of the system of novel equations can be tuned to fit the experimentally measured data, i.e., the frequency-dependent attenuation coefficient. The series solutions of the extended thermoelasticity problem are compared with those obtained within CTE. In contrast to CTE and in accordance with experiments, the model allows for the simultaneous existence of positive and negative extrema for stress over time.

Keywords: thermoelasticity; generalized Duhamel–Neumann law; dynamical problem; laser impulse heating; eigenfunction method; filter functions; integro-differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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