Equivalent dynamic stiffnesses and 3D wave propagations of a transversely isotropic elastic ground in rocking and torsional interactions with a harmonically loaded rigid foundation

References

• Y. Hayati, G. Havaei, A. Eslami, and M. Filippi, 3D soil-structure interaction analysis with a combined substructure-FEM under external forces and seismic waves, Mech. Adv. Mater. Struct., vol. 28, no. 4, pp. 1–34, 2021. DOI: 10.1080/15376494.2021.1909786.
   Google Scholar
• E. Carrera, M. Cinefra, M. Petrolo, and E. Zappino, Finite Element Analysis of Structures through Unified Formulation, John Wiley & Sons, United Kingdom, 2014.
   Google Scholar
• E. Carrera, and A. Pagani, Free vibration analysis of civil engineering structures by component-wise models, J. Sound Vib., vol. 333, no. 19, pp. 4597–4620, 2014. DOI: 10.1016/j.jsv.2014.04.063.
   Web of Science ®Google Scholar
• E. Carrera, A. Pagani, and M. Petrolo, Refined 1D finite elements for the analysis of secondary, primary, and complete civil engineering structures, J. Struct. Eng., vol. 141, no. 4, pp. 04014123, 2015. DOI: 10.1061/(ASCE)ST.1943-541X.0001076.
   Web of Science ®Google Scholar
• X. Xu, N. Fallahi, and H. Yang, Efficient CUF-based FEM analysis of thin-wall structures with Lagrange polynomial expansion, Mech. Adv. Mater. Struct., vol. 27, pp. 1–22, 2020. DOI: 10.1080/15376494.2020.1818331.
   Web of Science ®Google Scholar
• E. Carrera, R. Augello, A. Pagani, and X. Xu, Component-wise approach to reinforced concrete structures, Mech. Adv. Mater. Struct., vol. 28, pp. 1–19, 2021. DOI: 10.1080/15376494.2021.1912442.
   Web of Science ®Google Scholar
• E.E. Karataş, M. Filippi, and E. Carrera, Dynamic analyses of viscoelastic three-dimensional structures with advanced one-dimensional finite elements, Eur. J. Mech.-A/Solids., vol. 88, pp. 104241, 2021. DOI: 10.1016/j.euromechsol.2021.104241.
   Google Scholar
• A. Pagani, and E. Carrera, Unified one-dimensional finite element for the analysis of hyperelastic soft materials and structures, Mech. Adv. Mater. Struct., vol. 28, pp. 1–14, 2021. DOI: 10.1080/15376494.2021.2013585.
   Web of Science ®Google Scholar
• E. Carrera, and V. Zozulya, Carrera unified formulation (CUF) for the micropolar plates and shells. I. Higher order theory, Mech. Adv. Mater. Struct., vol. 29, no. 6, pp. 773–795, 2022. DOI: 10.1080/15376494.2020.1793241.
   Web of Science ®Google Scholar
• E. Daneshkhah, E. Carrera, X. Xu, and H. Yang, The effects of surroundings and stiffeners in the CUF-based postbuckling analysis of composite panels under in-plane shear, Mech. Adv. Mater. Struct., vol. 29, pp. 1–13, 2022. DOI: 10.1080/15376494.2022.2072983.
   Web of Science ®Google Scholar
• J. Shen, A. Pagani, M. Arruda, and E. Carrera, Exact component-wise solutions for 3D free vibration and stress analysis of hybrid steel–concrete composite beams, Thin-Walled Struct., vol. 174, pp. 109094, 2022. DOI: 10.1016/j.tws.2022.109094.
   Web of Science ®Google Scholar
• I.N. Sneddon, Mixed Boundary Value Problems in Potential Theory, North-Holland Publishing Company, Amesterdam, 1966.
   Google Scholar
• B. Mandal, and N. Mandal, Advances in Dual Integral Equations, Chapman & Hall/CRC Press, London, 1999.
   Google Scholar
• B. Noble, The solution of Bessel function dual integral equations by a multiplying-factor method, Math. Proc. Cambridge Philosophical Soc., vol. 59, no. 2, pp. 351–362, 1963. DOI: 10.1017/S0305004100036987.
   Google Scholar
• G. Gladwell, Forced tangential and rotatory vibration of a rigid circular disc on a semi-infinite solid, Int. J. Eng. Sci., vol. 6, no. 10, pp. 591–607, 1968. DOI: 10.1016/0020-7225(68)90061-X.
   Web of Science ®Google Scholar
• J.E. Luco, Vibrations of a rigid disc on a layered viscoelastic medium, Nucl. Eng. Des., vol. 36, no. 3, pp. 325–340, 1976.
   Web of Science ®Google Scholar
• A. Selvadurai, Rotary oscillations of a rigid disc inclusion embedded in an isotropic elastic infinite space, Int. J. Solids Struct., vol. 17, no. 5, pp. 493–498, 1981. DOI: 10.1016/0020-7683(81)90056-1.
   Web of Science ®Google Scholar
• J. Luco, and A. Mita, Response of a circular foundation on a uniform half‐space to elastic waves, Earthquake Eng. Struct. Dyn., vol. 15, no. 1, pp. 105–118, 1987. DOI: 10.1002/eqe.4290150108.
   Web of Science ®Google Scholar
• R. Pak, and J.-D. Saphores, Rocking rotation of a rigid disc in a half-space, Int. J. Solids Struct., vol. 28, no. 3, pp. 389–401, 1991. DOI: 10.1016/0020-7683(91)90201-P.
   Web of Science ®Google Scholar
• R. Pak, and F. Abedzadeh, Forced torsional oscillation from the interior of a half-space, J. Sound Vib., vol. 160, no. 3, pp. 401–415, 1993. DOI: 10.1006/jsvi.1993.1035.
   Web of Science ®Google Scholar
• Z.Y. Ai, and Z.X. Li, Time-harmonic response of transversely isotropic multilayered half-space in a cylindrical coordinate system, Soil Dyn. Earthquake Eng., vol. 66, pp. 69–77, 2014. DOI: 10.1016/j.soildyn.2014.06.023.
   Web of Science ®Google Scholar
• Z.Y. Ai, Z.X. Li, and N.R. Cang, Analytical layer-element solution to axisymmetric dynamic response of transversely isotropic multilayered half-space, Soil Dyn. Earthquake Eng., vol. 60, pp. 22–30, 2014. DOI: 10.1016/j.soildyn.2014.01.010.
   Web of Science ®Google Scholar
• A. Selvadurai, Asymmetric displacements of a rigid disc inclusion embedded in a transversely isotropic elastic medium of infinite extent, Int. J. Eng. Sci., vol. 18, no. 7, pp. 979–986, 1980. DOI: 10.1016/0020-7225(80)90070-1.
   Web of Science ®Google Scholar
• D.J. Kirkner, Vibration of a rigid disc on a transversely isotropic elastic half space, Int. J. Numer. Anal. Methods Geomech., vol. 6, no. 3, pp. 293–306, 1982. DOI: 10.1002/nag.1610060303.
   Web of Science ®Google Scholar
• S. Ahmadi, and M. Eskandari, Vibration analysis of a rigid circular disk embedded in a transversely isotropic solid, J. Eng. Mech., vol. 140, no. 7, pp. 04014048, 2014. DOI: 10.1061/(ASCE)EM.1943-7889.0000757.
   Web of Science ®Google Scholar
• Z.Y. Ai, C.L. Liu, and J.P. Jiang, Dynamic analysis of a vertically loaded rigid disc in a transversely isotropic multilayered half-space, Meccanica, vol. 51, no. 8, pp. 1887–1895, 2016. DOI: 10.1007/s11012-015-0340-8.
   Web of Science ®Google Scholar
• Z.Y. Ai, and Y.F. Zhang, Vertical vibration of a rigid strip footing on a transversely isotropic multilayered half-plane, Appl. Math. Modell., vol. 40, no. 23–24, pp. 10521–10532, 2016. DOI: 10.1016/j.apm.2016.07.005.
   Web of Science ®Google Scholar
• Z.Y. Ai, and Z.K. Ye, Analytical solution to vertical and rocking vibration of a rigid rectangular plate on a layered transversely isotropic half-space, Acta Geotech., vol. 17, no. 3, pp. 903–918, 2022. DOI: 10.1007/s11440-021-01253-2.
   Web of Science ®Google Scholar
• Z.Y. Ai, and Z.K. Ye, Dynamic analysis of eccentrically loaded rigid strip foundation on layered transversely isotropic poroelastic media, Appl. Math. Modell., vol. 109, pp. 473–491, 2022. DOI: 10.1016/j.apm.2022.05.001.
   Web of Science ®Google Scholar
• M. Rahimian, M. Eskandari-Ghadi, R.Y.S. Pak, and A. Khojasteh, Elastodynamic potential method for transversely isotropic solid, J. Eng. Mech., vol. 133, no. 10, pp. 1134–1145, 2007. DOI: 10.1061/(ASCE)0733-9399(2007)133:10(1134).
   Web of Science ®Google Scholar
• IN. Sneddon, The Use of Integral Transforms, McGraw-Hill, New York, 1972.
   Google Scholar
• Y. Hayati, G. Havaei, and A. Eslami, Complete general solution for Lord–Shulman generalized thermoelastodynamics by using potential functions for transversely isotropic solids, Acta Mech., vol. 230, no. 8, pp. 2751–2769, 2019. DOI: 10.1007/s00707-019-02423-w.
   Web of Science ®Google Scholar
• Y. Hayati, G. Havaei, and A. Eslami, 3D asymmetric dynamic Green’s functions of a thermoelastic transversely isotropic solid by a method of potentials, J. Therm. Stress., vol. 44, no. 11, pp. 1366–1388, 2021. DOI: 10.1080/01495739.2021.1982433.
   Web of Science ®Google Scholar
• J.E. Luco, Impedance functions for a rigid foundation on a layered medium, Nucl. Eng. Des., vol. 31, no. 2, pp. 204–217, 1974. DOI: 10.1016/0029-5493(75)90142-9.
   Web of Science ®Google Scholar
• Y. Hayati, M. Eskandari-Ghadi, M. Raoofian, M. Rahimian, and A.A. Ardalan, Dynamic Green's functions of an axisymmetric thermoelastic half-space by a method of potentials, J. Eng. Mech., vol. 139, no. 9, pp. 1166–1177, 2013. DOI: 10.1061/(ASCE)EM.1943-7889.0000540.
   Web of Science ®Google Scholar
• Y. Hayati, M. Eskandari-Ghadi, M. Raoofian, M. Rahimian, and A.A. Ardalan, Frequency domain analysis of an axisymmetric thermoelastic transversely isotropic half-space, J. Eng. Mech., vol. 139, no. 10, pp. 1407–1418, 2013. DOI: 10.1061/(ASCE)EM.1943-7889.0000577.
   Web of Science ®Google Scholar
• Y. Hayati, A. Eslami, and G. Havaei, Asymmetric 3D stress-and flux-induced wave propagation in transversely isotropic thermoelastic solids by using of analytical methods, Waves Random Complex Media., vol. 31, no. 10, pp. 1–18, 2021. DOI: 10.1080/17455030.2021.2000671.
   Google Scholar
• K. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, New York, 1997.
   Google Scholar
• M. Raoofian-Naeeni, M. Eskandari‐Ghadi, A.A. Ardalan, R.Y.S. Pak, M. Rahimian, and Y. Hayati, Coupled thermoviscoelastodynamic Green's functions for bi‐material half‐space, Z Angew. Math. Mech., vol. 95, no. 3, pp. 260–282, 2015. DOI: 10.1002/zamm.201200135.
   Web of Science ®Google Scholar
• M. Raoofian-Naeeni, M. Eskandari-Ghadi, A.A. Ardalan, M. Rahimian, and Y. Hayati, Analytical solution of coupled thermoelastic axisymmetric transient waves in a transversely isotropic half-space, J. Appl. Mech., vol. 80, no. 2, pp. 024502, 2013. DOI: 10.1115/1.4007786.
   Web of Science ®Google Scholar
• Y. Hayati, and M. Eskandari-Ghadi, Three-dimensional coupled thermoelastodynamic stress and flux induced wave propagation for isotropic half-space with scalar potential functions, Z Angew. Math. Phys., vol. 69, no. 1, pp. 18, 2018. DOI: 10.1007/s00033-018-0910-4.
   Web of Science ®Google Scholar
• R.Y.S. Pak, Asymmetric wave propagation in an elastic half-space by a method of potentials, J. Appl. Mech., vol. 54, no. 1, pp. 121–126, 1987. DOI: 10.1115/1.3172945.
   Web of Science ®Google Scholar