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Elastic Half Plane Under the Action of Nonstationary Surface Kinematic Perturbations

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A homogeneous isotropic elastic half plane with nonstationary normal displacements on the boundary is considered. With the use of the Laplace and Fourier integral transformations, we propose integral representations for displacements with kernels in the form of surface influence functions. The originals are computed by using an algorithm of joint inversion of these transformations based on the construction of analytic extensions of the transforms. The explicit form of the influence functions is obtained. Some examples of their evaluation are presented.

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References

  1. Ya. I. Burak, O. R. Hachkevych and R. F. Terletskyi, Thermal Mechanics of Multicomponent Bodies with Low Electroconductivity [in Ukrainian], Spolom, Lviv (2006), Vol. 1, in: Ya. I. Burak and R. M. Kushnir (Eds.), Modeling and Optimization in Thermomechanics of Electroconducting Inhomogeneous Bodies [in Ukrainian], Spolom, Lviv (2006–2011), Vol. 1–5.

  2. V. A. Vestyak, A. S. Sadkov, and D. V. Tarlakovskii, “Propagation of unsteady bulk perturbations in an elastic half plane,” Mech. Solids, 46, No. 2, 266–274 (2011).

    Article  Google Scholar 

  3. V. A. Vestyak and D. V. Tarlakovskii, “Nonstationary waves in electromagnetoelastic bodies,” in: V. D. Kubenko, R. M. Kushnir, and D. V. Tarlakovskii (Eds.), Nonstationary Processes of Deformation of Structural Elements Caused by the Action of Fields of Various Physical Nature [in Ukrainian], Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv (2012), pp. 22–25.

    Google Scholar 

  4. O. R. Hachkevych, R. S. Musii, and D. V. Tarlakovskii, Thermal Mechanics of Nonferromagnetic Electroconducting Bodies under the Action of Impulsive Electromagnetic Fields with Modulated Amplitude [in Ukrainian], Spolom, Lviv (2011).

    Google Scholar 

  5. A. G. Gorshkov, A. L. Medvedskii, L. N. Rabinskii, and D. V. Tarlakovskii, Waves in Continua [in Russian], Fizmatlit, Moscow (2004).

    Google Scholar 

  6. A. G. Gorshkov and D. V. Tarlakovskii, Dynamic Contact Problems with Moving Boundaries [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  7. E. L. Kuznetsova and D. V. Tarlakovskii, “Explicit form of the solution of the Lamb problem at any point of the half plane,” in: Proc. of the 12th Internat. Symp. “Dynamic and Technological Problems of the Mechanics of Structures and Continua” [in Russian], MAI, Moscow (2006), pp. 104–120.

    Google Scholar 

  8. L. I. Slepyan and Yu. S. Yakovlev, Integral Transformations in Nonstationary Problems of Mechanics [in Russian], Sudostroenie, Leningrad (1980).

    Google Scholar 

  9. He Tianhu, Tian Xiaogeng, and Shen Yapeng, “A generalized electromagneto-thermoelastic problem for an infinitely long solid cylinder,” Eur. J. Mech. A-Solid, 24, No 2, 349–359 (2005).

    Article  MATH  Google Scholar 

  10. J. S. Kim and W. Soedel, “On the response of three-dimensional elastic bodies to distributed dynamic pressures. Part I: Half space,” J. Sound Vibrat., 126, No. 2, 279–295 (1988).

    Article  Google Scholar 

  11. J. S. Kim and W. Soedel, “On the response of three-dimensional elastic bodies to distributed dynamic pressures. Part II: Thick plate,” J. Sound Vibrat., 126, No. 2, 297–308 (1988).

    Article  Google Scholar 

  12. H. Lamb, “On the propagation of tremors over the surface on an elastic solid,” Phil. Trans. Roy. Soc. London. Ser. A, 203, 1–42 (1904).

    Article  Google Scholar 

  13. R. K. N. D. Rajapakse, Y. Chen, and T. Senjuntichai, “Electroelastic field of a piezoelectric annular finite cylinder,” Int. J. Solids Struct., 42, No. 11-12, 3487–3508 (2005).

    Article  MATH  Google Scholar 

  14. M. Rakshit and B. Mukhopadhyay, “An electro-magneto-thermo-visco-elastic problem in an infinite medium with a cylindrical hole,” Int. J. Eng. Sci., 43, No. 11-12, 925–936 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  15. M. Ziv, “A half space response to a finite surface source of an impulsive disturbance,” J. Acoust. Soc. Amer., 89, No. 4, 1556–1571 (1991).

    Article  MathSciNet  Google Scholar 

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Published in Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 56, No. 2, pp. 164–172, April–June, 2013.

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Vestyak, V.A., Hachkevych, A.R., Tarlakovskii, D.V. et al. Elastic Half Plane Under the Action of Nonstationary Surface Kinematic Perturbations. J Math Sci 203, 202–214 (2014). https://doi.org/10.1007/s10958-014-2101-y

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  • DOI: https://doi.org/10.1007/s10958-014-2101-y

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