Elastic torsional wave and corresponding nonlinear wave equation





nonlinear elastic torsional wave, five-constant Murnaghan’s model, new nonlinear wave equation


The new nonlinear wave equation describing the propagation of a torsional wave as one type of the elastic
cylindrical waves is proposed. This equation is obtained using the tools of the nonlinear theory of elasticity
within the framework of the five-constant Murnaghan’s model. In additopn to the classical linear summands, it
contains the only cubically nonlinear ones. Some specifiсities of the derived equation are commented.


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Altayeb, Y. (2021). New scenario of decay rate for system of three nonlinear wave equations with viscoelasticities. AIMS Mathematics. 6, Iss. 7, pp. 7251-7265. https: //doi. org/10. 3934/math. 2021425

Arbab, I. A. (2011). A New Wave Equation of the Electron. J. Modern Physics. 2, No. 9, pp. 1012-1016. https: // doi. org/10. 4236/jmp. 2011. 29121

Du, X., Fletcher, R. P. & Fowler, P. J. (2008). A New Pseudo-acoustic Wave Equation for VTI Media. Conf. Proc. 70th EAGE Conf. and Exhibition incorporating SPE EUROPEC 2008, Jun. https: //doi. org/10. 3997/2214-4609. 20147774

Ueda, H. (2016). A new example of the dissipative wave equations with the total energy decay. Hiroshima Math. J. 46, No. 2, pp. 187-193. https: //doi. org/10. 32917/hmj/1471024948

Wu, Z. & Alkhalifah, T. (2017). A New Wave Equation Based Source Location Method with Full-waveform Inversion // Conf. Proc., 79th EAGE Conf. and Exhibition 2017, Jun. P. 1-5. https: //doi. org/10. 3997/2214- 4609. 201700753

Yang, J. & Zhu, H. (2018). A new time-domain wave equation for viscoacoustic modeling and imaging. Proc. of the 2018 SEG Int. Exp. and Annual Meeting, Anaheim, California, USA, October 2018. Paper Number: SEG-2018-2974332. https: //doi. org/10. 1190/segam2018-2974332. 1

Zakia, T., Boulaaras, S., Degaichia, H. & Allahem, A. (2020). Existence and blow-up of a new class of nonlinear damped wave equation. J. Intelligent & Fuzzy Systems. 38, No. 3. P. 2649-2660. https: //doi. org/10. 3233/JIFS-179551

Rushchitsky, J. J. (2014). Nonlinear Elastic Waves in Materials. Heidelberg: Springer. https: //doi. org/10. 1007/978-3-319-00464-8

Nowacki, W. (1970). Theory of Elasticity. Warszawa: PWN. 780 p.

Rushchitsky, J. J. (2012). Certain class of nonlinear hyperelastic waves: classical and novel models, wave equations, wave effects. Int. J. Appl. Math. Mech., 8, No. 6, pp. 400-443.

Rushchitsky, J. J. (2019). Plane Nonlinear Elastic Waves: Approximate Approaches to Analysis of Evolution, Chapter 3 in the book “Understanding Plane Waves”. London: Nova Science Publishers.



How to Cite

Rushchitsky Я. . (2022). Elastic torsional wave and corresponding nonlinear wave equation. Reports of the National Academy of Sciences of Ukraine, (2), 41–47. https://doi.org/10.15407/dopovidi2022.02.041