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Erschienen in: Continuum Mechanics and Thermodynamics 3/2021

10.01.2021 | Original Article

A model of the thermoelastic medium absorbing a part of the acoustic spectrum

Erschienen in: Continuum Mechanics and Thermodynamics | Ausgabe 3/2021

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Abstract

An analytical model extending classical thermal elasticity is presented. It allows to introduce a correction to the attenuation of the mechanical waves at the higher frequency range. A material data set taken from experimental studies can be used to identify the attenuation rate as a function of frequency. An example is provided. The particular solution of the developed equations system in the form of the traveling monochromatic wave is obtained.

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Fußnoten
1
\({\varvec{E}}{\varvec{E}}={\varvec{e}}_k {\varvec{e}}_k {\varvec{e}}_n {\varvec{e}}_n\), \({\varvec{I}}=\frac{1}{2}\left( {\varvec{e}}_k {\varvec{e}}_n {\varvec{e}}_n {\varvec{e}}_k+{\varvec{e}}_k {\varvec{e}}_n {\varvec{e}}_k {\varvec{e}}_n\right) \).
 
Literatur
1.
Zurück zum Zitat Nowacki, W.: Thermoelasticity. Elsevier, Amsterdam (2013)MATH Nowacki, W.: Thermoelasticity. Elsevier, Amsterdam (2013)MATH
2.
Zurück zum Zitat Müller, I., Müller, W.H.: Fundamentals of Thermodynamics and Applications: With Historical Annotations and Many Citations from Avogadro to Zermelo. Springer, New York (2009)MATH Müller, I., Müller, W.H.: Fundamentals of Thermodynamics and Applications: With Historical Annotations and Many Citations from Avogadro to Zermelo. Springer, New York (2009)MATH
3.
Zurück zum Zitat Ignaczak, J., Ostoja-Starzewski, M.: Thermoelasticity with Finite Wave Speeds. Oxford University Press, Oxford (2010)MATH Ignaczak, J., Ostoja-Starzewski, M.: Thermoelasticity with Finite Wave Speeds. Oxford University Press, Oxford (2010)MATH
4.
Zurück zum Zitat Jou, D., Lebon, G., Casas-Vázquez, J.: Extended Irreversible Thermodynamics. Springer, New York (2010)CrossRef Jou, D., Lebon, G., Casas-Vázquez, J.: Extended Irreversible Thermodynamics. Springer, New York (2010)CrossRef
5.
Zurück zum Zitat Papenfuss, C., Forest, S.: Walter de Gruyter. J. Non-Equilib. Thermodyn. 31(4), 319 (2006)ADSCrossRef Papenfuss, C., Forest, S.: Walter de Gruyter. J. Non-Equilib. Thermodyn. 31(4), 319 (2006)ADSCrossRef
6.
Zurück zum Zitat Ivanova, E.A. , Vilchevskaya, E.N.: Description of thermal and micro-structural processes in generalized continua: Zhilin’s method and its modifications. In: Generalized Continua as Models for Materials, pp. 179–197. Springer, New York (2013) Ivanova, E.A. , Vilchevskaya, E.N.: Description of thermal and micro-structural processes in generalized continua: Zhilin’s method and its modifications. In: Generalized Continua as Models for Materials, pp. 179–197. Springer, New York (2013)
7.
Zurück zum Zitat Ivanova, E.A., Vilchevskaya, E.N.: Zhilin’s Method and Its Modifications,"Encyclopedia of Continuum Mechanics", vol. Chap 7, pp. 1–9. Springer, Berlin (2018) Ivanova, E.A., Vilchevskaya, E.N.: Zhilin’s Method and Its Modifications,"Encyclopedia of Continuum Mechanics", vol. Chap 7, pp. 1–9. Springer, Berlin (2018)
8.
Zurück zum Zitat Zhilin, P.: Phase transitions and general theory of elasto-plastic bodies. In: Proceedings of XXIX Summer School-Conference. Advanced Problems in Mechanics, pp. 36–48 (2002) Zhilin, P.: Phase transitions and general theory of elasto-plastic bodies. In: Proceedings of XXIX Summer School-Conference. Advanced Problems in Mechanics, pp. 36–48 (2002)
9.
Zurück zum Zitat Zhilin, P.: Advanced Problems in Mechanics, vol. 2. Institute for Problems in Mechanical Engineering, St. Petersburg (2006) Zhilin, P.: Advanced Problems in Mechanics, vol. 2. Institute for Problems in Mechanical Engineering, St. Petersburg (2006)
10.
Zurück zum Zitat Indeitsev, D., Naumov, V., Semenov, B.: Dynamic effects in materials of complex structure. Mech. Solids 42(5), 672 (2007)ADSCrossRef Indeitsev, D., Naumov, V., Semenov, B.: Dynamic effects in materials of complex structure. Mech. Solids 42(5), 672 (2007)ADSCrossRef
11.
Zurück zum Zitat Indeitsev, D., Meshcheryakov, Y.I., Kuchmin, A.Y., Vavilov, D.: Multi-scale model of steady-wave shock in medium with relaxation. Acta Mechanica 226(3), 917 (2015)CrossRef Indeitsev, D., Meshcheryakov, Y.I., Kuchmin, A.Y., Vavilov, D.: Multi-scale model of steady-wave shock in medium with relaxation. Acta Mechanica 226(3), 917 (2015)CrossRef
12.
Zurück zum Zitat Ivanova, E.A.: Derivation of theory of thermoviscoelasticity by means of two-component medium. Acta Mechanica 215(1–4), 261 (2010)CrossRef Ivanova, E.A.: Derivation of theory of thermoviscoelasticity by means of two-component medium. Acta Mechanica 215(1–4), 261 (2010)CrossRef
13.
Zurück zum Zitat Ivanova, E.A.: Description of mechanism of thermal conduction and internal damping by means of two-component Cosserat continuum. Acta Mechanica 225(3), 757 (2014)MathSciNetCrossRef Ivanova, E.A.: Description of mechanism of thermal conduction and internal damping by means of two-component Cosserat continuum. Acta Mechanica 225(3), 757 (2014)MathSciNetCrossRef
14.
Zurück zum Zitat Krivtsov, A.: Heat transfer in infinite harmonic one-dimensional crystals. Doklady Phys. 60(9), 407 (2015)ADSCrossRef Krivtsov, A.: Heat transfer in infinite harmonic one-dimensional crystals. Doklady Phys. 60(9), 407 (2015)ADSCrossRef
16.
Zurück zum Zitat Sokolov, A.A., Krivtsov, A.M., Müller, W.H., Vilchevskaya, E.N.: Change of entropy for the one-dimensional ballistic heat equation: sinusoidal initial perturbation. Phys. Rev. E 99(4), 042107 (2019)ADSMathSciNetCrossRef Sokolov, A.A., Krivtsov, A.M., Müller, W.H., Vilchevskaya, E.N.: Change of entropy for the one-dimensional ballistic heat equation: sinusoidal initial perturbation. Phys. Rev. E 99(4), 042107 (2019)ADSMathSciNetCrossRef
17.
Zurück zum Zitat Babenkov, M.B., Krivtsov, A.M., Tsvetkov, D.V.: Unsteady heat conduction processes in a harmonic crystal with a substrate potential (2017). arXiv:1802.02037 Babenkov, M.B., Krivtsov, A.M., Tsvetkov, D.V.: Unsteady heat conduction processes in a harmonic crystal with a substrate potential (2017). arXiv:​1802.​02037
18.
Zurück zum Zitat Babenkov, M., Krivtsov, A., Tsvetkov, D.: Heat propagation in the one-dimensional harmonic crystal on an elastic foundation. Phys. Mesomech. (2019) Babenkov, M., Krivtsov, A., Tsvetkov, D.: Heat propagation in the one-dimensional harmonic crystal on an elastic foundation. Phys. Mesomech. (2019)
19.
Zurück zum Zitat Gavrilov, S.N., Krivtsov, A.M., Tsvetkov, D.V.: Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply. Contin. Mech. Thermodyn. 31(1), 255 (2019)ADSMathSciNetCrossRef Gavrilov, S.N., Krivtsov, A.M., Tsvetkov, D.V.: Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply. Contin. Mech. Thermodyn. 31(1), 255 (2019)ADSMathSciNetCrossRef
20.
Zurück zum Zitat Kuzkin, V.A.: Unsteady ballistic heat transport in harmonic crystals with polyatomic unit cell. Contin. Mech. Thermodyn. 31(6), 1573 (2019)ADSMathSciNetCrossRef Kuzkin, V.A.: Unsteady ballistic heat transport in harmonic crystals with polyatomic unit cell. Contin. Mech. Thermodyn. 31(6), 1573 (2019)ADSMathSciNetCrossRef
21.
Zurück zum Zitat Yu, Y.J., Hu, W., Tian, X.G.: A novel generalized thermoelasticity model based on memory-dependent derivative. Int. J. Eng. Sci. 81, 123 (2014)MathSciNetCrossRef Yu, Y.J., Hu, W., Tian, X.G.: A novel generalized thermoelasticity model based on memory-dependent derivative. Int. J. Eng. Sci. 81, 123 (2014)MathSciNetCrossRef
22.
Zurück zum Zitat El-Karamany, A.S., Ezzat, M.A.: Modified Fourier’s law with time-delay and kernel function: application in thermoelasticity. J. Therm. Stress. 38(7), 811 (2015)CrossRef El-Karamany, A.S., Ezzat, M.A.: Modified Fourier’s law with time-delay and kernel function: application in thermoelasticity. J. Therm. Stress. 38(7), 811 (2015)CrossRef
23.
Zurück zum Zitat Povstenko, Y.: Fractional Thermoelasticity, vol. 219. Springer, New York (2015)CrossRef Povstenko, Y.: Fractional Thermoelasticity, vol. 219. Springer, New York (2015)CrossRef
24.
Zurück zum Zitat Szabo, T.L.: Time domain wave equations for lossy media obeying a frequency power law. J. Acous. Soc. Am. 96(1), 491 (1994)ADSCrossRef Szabo, T.L.: Time domain wave equations for lossy media obeying a frequency power law. J. Acous. Soc. Am. 96(1), 491 (1994)ADSCrossRef
25.
Zurück zum Zitat Fellah, Z.E.A., Berger, S., Lauriks, W., Depollier, C.: Time domain wave equations for lossy media obeying a frequency power law: application to the porous materials. In: Acoustics, Mechanics, and the Related Topics of Mathematical Analysis, pp. 143–149. World Scientific, Singapore (2002) Fellah, Z.E.A.,  Berger, S.,  Lauriks, W.,  Depollier, C.: Time domain wave equations for lossy media obeying a frequency power law: application to the porous materials. In: Acoustics, Mechanics, and the Related Topics of Mathematical Analysis, pp. 143–149. World Scientific, Singapore (2002)
26.
Zurück zum Zitat Grigoriev, I.S., Meilikhov, E.Z.: Handbook of Physical Quantities. CRC Press, Boca Raton (1996) Grigoriev, I.S., Meilikhov, E.Z.: Handbook of Physical Quantities. CRC Press, Boca Raton (1996)
27.
Zurück zum Zitat Mathews, J., Walker, R.L.: Mathematical Methods of Physics, vol. 501. WA Benjamin, New York (1970)MATH Mathews, J., Walker, R.L.: Mathematical Methods of Physics, vol. 501. WA Benjamin, New York (1970)MATH
28.
Zurück zum Zitat Pervozvansky, A.A.: Theory Course of the Automatic Control. Moscow Izdatel Nauka, Moscow (1986) Pervozvansky, A.A.: Theory Course of the Automatic Control. Moscow Izdatel Nauka, Moscow (1986)
29.
Zurück zum Zitat Smith, C.A., Corripio, A.B.: Principles and Practice of Automatic Process Control, 2nd edn. Wiley, New York (1997) Smith, C.A., Corripio, A.B.: Principles and Practice of Automatic Process Control, 2nd edn. Wiley, New York (1997)
31.
Zurück zum Zitat Hütter, G.: An extended Coleman–Noll procedure for generalized continuum theories. Contin. Mech. Thermodyn. 28(6), 1935 (2016)ADSMathSciNetCrossRef Hütter, G.: An extended Coleman–Noll procedure for generalized continuum theories. Contin. Mech. Thermodyn. 28(6), 1935 (2016)ADSMathSciNetCrossRef
32.
33.
Zurück zum Zitat Nikol’skii, S.: A course of calculus. Nauka, Moscow (1991) Nikol’skii, S.: A course of calculus. Nauka, Moscow (1991)
34.
Zurück zum Zitat Sobolev, S.L., Browder, F.E.: Applications of Functional Analysis in Mathematical Physics. American Mathematical Society, New York (1963)CrossRef Sobolev, S.L., Browder, F.E.: Applications of Functional Analysis in Mathematical Physics. American Mathematical Society, New York (1963)CrossRef
35.
Zurück zum Zitat Vladimirov, V.S.: Equations of Mathematical Physics. Moscow Izdatel Nauka, Moscow (1976) Vladimirov, V.S.: Equations of Mathematical Physics. Moscow Izdatel Nauka, Moscow (1976)
36.
Zurück zum Zitat Polyanin, A.D., Manzhirov, A.V.: Handbook of Integral Equations. CRC Press, Boca Raton (1998)CrossRef Polyanin, A.D., Manzhirov, A.V.: Handbook of Integral Equations. CRC Press, Boca Raton (1998)CrossRef
37.
Zurück zum Zitat Altenbach, H., Forest, S., Krivtsov, A.: Generalized Continua as Models for Materials, with Multi-scale Effects or Under Multifield Actions. Springer, New York (2013)CrossRef Altenbach, H., Forest, S., Krivtsov, A.: Generalized Continua as Models for Materials, with Multi-scale Effects or Under Multifield Actions. Springer, New York (2013)CrossRef
38.
Zurück zum Zitat Kunin, I.A.: Elastic Media with Microstructure I: One-Dimensional Models, vol. 26. Springer, New York (2012) Kunin, I.A.: Elastic Media with Microstructure I: One-Dimensional Models, vol. 26. Springer, New York (2012)
39.
Zurück zum Zitat Ayzenberg-Stepanenko, M., Cohen, T., Osharovich, G., Timoshenko, O.: Waves in periodic structures (mathematical models and computer simulations). Manuscript (2005, Beer-Shev) Ayzenberg-Stepanenko, M., Cohen, T., Osharovich, G., Timoshenko, O.: Waves in periodic structures (mathematical models and computer simulations). Manuscript (2005, Beer-Shev)
40.
Zurück zum Zitat Mysik, S.V.: Analyzing the acoustic spectra of sound velocity and absorption in amphiphilic liquids. St. Petersburg Polytech. Univ. J.: Phys. Math. 1(3), 325 (2015) Mysik, S.V.: Analyzing the acoustic spectra of sound velocity and absorption in amphiphilic liquids. St. Petersburg Polytech. Univ. J.: Phys. Math. 1(3), 325 (2015)
41.
Zurück zum Zitat Landau, L., Lifshitz, E., Pitaevskij, L.: Course of Theoretical Physics. vol. 10: Physical Kinetics. Oxford (1981) Landau, L., Lifshitz, E., Pitaevskij, L.: Course of Theoretical Physics. vol. 10: Physical Kinetics. Oxford (1981)
42.
Zurück zum Zitat Mashinskii, E.: Amplitude-frequency dependencies of wave attenuation in single-crystal quartz: Experimental study. J. Geophys. Res.: Solid Earth 113(B11), (2008) Mashinskii, E.: Amplitude-frequency dependencies of wave attenuation in single-crystal quartz: Experimental study. J. Geophys. Res.: Solid Earth 113(B11), (2008)
Metadaten
Titel
A model of the thermoelastic medium absorbing a part of the acoustic spectrum
Publikationsdatum
10.01.2021
Erschienen in
Continuum Mechanics and Thermodynamics / Ausgabe 3/2021
Print ISSN: 0935-1175
Elektronische ISSN: 1432-0959
DOI
https://doi.org/10.1007/s00161-020-00957-2

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