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The Effect of Preheating on the Thermoelastic Structurally Inhomogeneous Medium Spectral Properties in the Presence of an Initial Strain

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Dynamics, Strength of Materials and Durability in Multiscale Mechanics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 137))

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Abstract

The boundary problem of a prestressed thermoelastic layered half-space oscillations subjected to the action of a mechanical or thermal load is considered. Initial stresses are induced in the body by stretching or compression and by the action of temperature. The two-dimensional Green’s function of the medium is constructed. We made the analysis of its real poles behavior, and their distribution is presented graphically. The effect of preheating, pinching, and initial deformation of the first mode phase velocity is studied.

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References

  • Achenbach, J. D. (2003). Laser excitation of surface wave motion. Journal of the Mechanics and Physics of Solids, 51, 1885–1902. https://doi.org/10.1016/j.jmps.2003.09.021

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Al-Qahtani, H., & Datta, S. K. (2004). Thermoelastic waves in an anisotropic infinite plate. Journal of Applied Physics, 96, 3645–3657. https://doi.org/10.1063/1.1776323

    Article  ADS  Google Scholar 

  • Alibert, J. J., Seppecher, P., & Dell’Isola, F. (2003). Truss modular beams with deformation energy depending on higher displacement gradients. Mathematics and Mechanics of Solids, 8(1), 51–73.

    Article  MathSciNet  Google Scholar 

  • Bao, H., Bielak, J., Ghattas, O., Kallivokas, L. F., O’Hallaron, D. R., Shewchuk, J. R., & Xu, J. (1998). Large-scale simulation of elastic wave propagation in heterogeneous media on parallel computers. Computer Methods in Applied Mechanics and Engineering, 152(1–2), 85–102.

    Article  ADS  Google Scholar 

  • Barchiesi, E., & Khakalo, S. (2019). Variational asymptotic homogenization of beam-like square lattice structures. Mathematics and Mechanics of Solids, 24(10), 3295–3318.

    Article  MathSciNet  Google Scholar 

  • Barchiesi, E., Laudato, M., & Di Cosmo, F. (2018). Wave dispersion in non-linear pantographic beams. Mechanics Research Communications, 94, 128–132.

    Article  Google Scholar 

  • Barchiesi, E., & Placidi, L. (2017). A review on models for the 3D statics and 2D dynamics of pantographic fabrics. Wave dynamics and composite mechanics for microstructured materials and metamaterials (pp. 239–258). Singapore: Springer.

    Chapter  Google Scholar 

  • Barchiesi, E., Spagnuolo, M., & Placidi, L. (2019). Mechanical metamaterials: A state of the art. Mathematics and Mechanics of Solids, 24(1), 212–234.

    Article  MathSciNet  Google Scholar 

  • Belyankova, T. I., Vorovich, E. I., Kalinchuk, V. V., & Puzanov, Yu. E. (1999). Dynamic contact problem for thermo-elastic layer. Scientific-Educational and Applied Journal University News. North-Caucasian Region. Natural Sciences Series, 4, 109–110. ((In Russian)).

    Google Scholar 

  • Belyankova, T. I., Kalinchuk, V. V., & Suvorova, G. Y. (2012). A dynamic contact problem for a thermoelastic prestressed layer. Journal of Applied Mathematics and Mechanics, 75, 537–546. https://doi.org/10.1016/j.jappmathmech.2012.11.013

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Belyankova, T. I., & Kalinchuk, V. V. (2016). Green’s function for a prestressed thermoelastic half-space with an inhomogeneous coating. Journal of Applied Mechanics and Technical Physics, 57, 828–840. https://doi.org/10.1134/S0021894416050096

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Boutin, C., Giorgio, I., & Placidi, L. (2017). Linear pantographic sheets: Asymptotic micro-macro models identification. Mathematics and Mechanics of Complex Systems, 5(2), 127–162.

    Article  MathSciNet  Google Scholar 

  • Dell’Isola, F., Andreaus, U., & Placidi, L. (2015). At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola. Mathematics and Mechanics of Solids, 20(8), 887–928.

    Article  MathSciNet  Google Scholar 

  • Dell’Isola, F., Corte, A. D., & Giorgio, I. (2017). Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives. Mathematics and Mechanics of Solids, 22(4), 852–872.

    Article  MathSciNet  Google Scholar 

  • dell’Isola, F., Giorgio, I., & Andreaus, U. (2015). Elastic pantographic 2D lattices: A numerical analysis on the static response and wave propagation. Proceedings of the Estonian Academy of Sciences, 64(3), 219.

    Article  Google Scholar 

  • Dell’Isola, F., Seppecher, P., Alibert, J. J., Lekszycki, T., Grygoruk, R., Pawlikowski, M., & Gołaszewski, M. (2019). Pantographic metamaterials: An example of mathematically driven design and of its technological challenges. Continuum Mechanics and Thermodynamics, 31(4), 851–884.

    Article  ADS  MathSciNet  Google Scholar 

  • Dell’Isola, F., Seppecher, P., & Madeo, A. (2012). How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: Approach “à la D’Alembert.” Zeitschrift für angewandte Mathematik und Physik, 63(6), 1119–1141.

    Article  ADS  MathSciNet  Google Scholar 

  • dell’Isola, F., Seppecher, P., Spagnuolo, M., Barchiesi, E., Hild, F., Lekszycki, T., & Eugster, S. R. (2019). Advances in pantographic structures: Design, manufacturing, models, experiments and image analyses. Continuum Mechanics and Thermodynamics, 31(4), 1231–1282.

    Article  ADS  Google Scholar 

  • Elhagary, M. (2013). A two-dimensional generalized thermoelastic diffusion problem for a half-space subjected to harmonically varying heating. Acta Mechanica, 224, 3057–3069. https://doi.org/10.1007/s00707-013-0902-6

    Article  MathSciNet  MATH  Google Scholar 

  • El-Maghraby, N. M. (2008). A two-dimensional generalized thermoelasticity problem for a half-space under the action of a body force. Journal of Thermal Stresses, 31, 557–568. https://doi.org/10.1080/01495730801978281

    Article  Google Scholar 

  • Eremeyev, V. A., Alzahrani, F. S., Cazzani, A., dell’Isola, F., Hayat, T., Turco, E., & Konopińska-Zmysłowska, V. (2019). On existence and uniqueness of weak solutions for linear pantographic beam lattices models. Continuum Mechanics and Thermodynamics, 31(6), 1843–1861.

    Article  ADS  MathSciNet  Google Scholar 

  • Eugster, S., & Steigmann, D. (2019). Continuum theory for mechanical metamaterials with a cubic lattice substructure. Mathematics and Mechanics of Complex Systems, 7(1), 75–98.

    Article  MathSciNet  Google Scholar 

  • Kumar, R., & Gupta, V. (2013). Reflection and transmission of plane waves at the interface of an elastic half-space and a fractional order thermoelastic half-space. Archive of Applied Mechanics, 83, 1109–1128. https://doi.org/10.1007/s00419-013-0737-6

    Article  ADS  Google Scholar 

  • Kumar, R., & Kansal, T. (2008). Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate. International Journal of Solids and Structures, 45, 5890–5913. https://doi.org/10.1016/S0020768308002710

    Article  MATH  Google Scholar 

  • Levi, G. Yu., & Belyankova, T. I. (2019). Some properties of the transversely isotropic thermoelastic layer under initial stress. Applied Mechanics and Systems Dynamics. Journal of Physics: Conference Series 1210. doi:10.1088/1742-6596/1210/1/012080.

    Google Scholar 

  • Levi, GYu., & Igumnov, L. A. (2015). Some properties of the thermoelastic prestressed medium Green function. Materials Physics and Mechanics, 23, 42–46.

    Google Scholar 

  • Levi, M. O., Levi, GYu., & Lyzhov, V. A. (2017). Some features of the dynamics of ferroelectric (ferromagnetic) heterostructures. Journal of Applied Mechanics and Technical Physics, 58, 47–53.

    Article  ADS  MathSciNet  Google Scholar 

  • Lurie, A. I. (1980). Nelinejnaja teorija uprugosti [Nonlinear Theory of Elasticity]. Moscow: Nauka Publishers, 512 p (In Russian).

    Google Scholar 

  • Madeo, A., Della Corte, A., Greco, L., & Neff, P. (2014). Wave Propagation in Pantographic 2D Lattices with Internal Discontinuities. arXiv preprint arXiv:1412.3926.

    Google Scholar 

  • Muratikov, K. L. (1998). On the theory of oscillations generation by laser radiation in solids with internal stresses by the thermoelastic method. Pisma v zhurnal tekhnicheskoi fiziki, 24, 82–88. ((In Russian)).

    Google Scholar 

  • Placidi, L., Dell’Isola, F., Ianiro, N., & Sciarra, G. (2008). Variational formulation of pre-stressed solid-fluid mixture theory, with an application to wave phenomena. European Journal of Mechanics-A/Solids, 27(4), 582–606.

    Article  ADS  MathSciNet  Google Scholar 

  • Sharma, J. N. (2001). Three-dimensional vibration analysis of a homogeneous transversely isotropic thermoelastic cylindrical panel. The Journal of the Acoustical Society of America, 110, 254–259. https://doi.org/10.1121/1.1378350

    Article  ADS  Google Scholar 

  • Sharma, J. N., Pal, M., & Chand, D. (2005). Propagation characteristics of Rayleigh waves in transversely isotropic piezothermoelastic materials. Journal of Sound and Vibration, 284, 227–248. https://doi.org/10.1016/j.jsv.2004.06.036

    Article  ADS  Google Scholar 

  • Sharma, J. N., & Sidhu, R. S. (1986). On the propagation of plane harmonic waves in anisotropic generalized thermoelasticity. International Journal of Engineering Science, 24, 1511–1516. https://doi.org/10.1016/0020-7225(86)90160-6

    Article  MATH  Google Scholar 

  • Sheydakov, D. N., Belyankova, T. I., Sheydakov, N. E., & Kalinchuk, V. V. (2008). Dynamics equations for prestressed thermo-elastic medium. Vestnik Yuzhnogo Nauchnogo Tsentra, 4, 3–8. ((In Russian)).

    Article  Google Scholar 

  • Singh, B. (2010). Wave propagation in an initially stressed transversely isotropic thermoelastic solid half-space. Applied Mathematics and Computation, 217, 705–715. https://doi.org/10.1016/j.amc.2010.06.008

    Article  MathSciNet  MATH  Google Scholar 

  • Singh, H., & Sharma, J. N. (1985). Generalised thermoelastic waves in transversely isotropic media. The Journal of the Acoustical Society of America, 77, 1046–1053. https://doi.org/10.1121/1.392391

    Article  ADS  MATH  Google Scholar 

  • Spagnuolo, M., & Andreaus, U. (2019). A targeted review on large deformations of planar elastic beams: Extensibility, distributed loads, buckling and post-buckling. Mathematics and Mechanics of Solids, 24(1), 258–280.

    Article  MathSciNet  Google Scholar 

  • Chirita, S. (2013). On the Rayleigh surface waves on an anisotropic homogeneous thermoelastic half space. Acta Mechanica, 224, 657–674. https://doi.org/10.1007/s00707-012-0776-z

    Article  MathSciNet  MATH  Google Scholar 

  • Verma, K. L. (2002). On the propagation of waves in layered anisotropic media in generalized thermoelasticity. International Journal of Engineering Science, 40, 2077–2096. https://doi.org/10.1016/S0020-7225(02)00030-7

    Article  MathSciNet  MATH  Google Scholar 

  • Xu, B. Q., Feng, J., & Xu, G. D. (2008). Laser-generated thermoelastic acoustic sources and Lamb waves in anisotropic plates. Applied Physics and-Materials Science & Processing, 91, 173–179. https://doi.org/10.1007/s11431-009-0065-9

    Article  ADS  Google Scholar 

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Acknowledgements

The reported study was performed as part of the implementation of the state assignment of the Southern Scientific Center of the Russian Academy of Sciences, project 01201354242 and with partial financial support from the Russian Foundation for Basic Research, grants № 19-01-00719, 19-08-01051.

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Authors and Affiliations

  1. Research Institute for Mechanics of Lobachevsky State University of Nizhny Novgorod, Gagarin ave., 23, 603950, Nizhny Novgorod, Russia

    Galina Yu. Levi & Leonid Igumnov

  2. Southern Scientific Center of Russian Academy of Sciences, st. Chehova, 41, 344006, Rostov-on-Don, Russia

    Galina Yu. Levi & Mikhail O. Levi

Authors
  1. Galina Yu. Levi
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  2. Leonid Igumnov
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  3. Mikhail O. Levi
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Correspondence to Leonid Igumnov .

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Editors and Affiliations

  1. Dipartimento di Ingegneria Strutturale, Università degli Studi dell’Aquila MEMOCS, L’Aquila, Italy

    Francesco dell'Isola

  2. Research Institute for Mechanics, National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Leonid Igumnov

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Levi, G.Y., Igumnov, L., Levi, M.O. (2021). The Effect of Preheating on the Thermoelastic Structurally Inhomogeneous Medium Spectral Properties in the Presence of an Initial Strain. In: dell'Isola, F., Igumnov, L. (eds) Dynamics, Strength of Materials and Durability in Multiscale Mechanics. Advanced Structured Materials, vol 137. Springer, Cham. https://doi.org/10.1007/978-3-030-53755-5_10

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