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Approximate Formulation of the Rigid Body Motions of an Elastic Rectangle Under Sliding Boundary Conditions


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1. Babenkova E., Kaplunov J. (2004), Low-frequency decay conditions for a semi-infinite elastic strip. Proc. R. Soc. A., 460(2048), 2153-2169. Search in Google Scholar

2. Babenkova Y.V., Kaplunov Y.D., Ustinov Y.A. (2005), Saint-venant’s principle in the case of the low-frequency oscillations of a half-strip, Appl. Math. Mech., 69(3), 405-416. Search in Google Scholar

3. Gregory R.D., Wan F.Y.M. (1985), On plate theories and Saint-Venant’s principle, International journal of solids and structures, 21(10), 1005-1024.10.1016/0020-7683(85)90052-6 Search in Google Scholar

4. Kaplunov J., Prikazchikov D.A., Prikazchikova L.A., Sergushova O. (2019), The lowest vibration spectra of multi-component structures with contrast material properties, J. Sound Vib., 445, 132-147. Search in Google Scholar

5. Kaplunov J., Prikazchikov D.A., Rogerson G.A. (2005), On three-dimensional edge waves in semi-infinite isotropic plates subject to mixed face boundary conditions, The Journal of the Acoustical Society of America, 118 (5), 2975-2983.10.1121/1.2062487 Search in Google Scholar

6. Kaplunov J., Prikazchikova L., Alkinidri M. (2021), Antiplane shear of an asymmetric sandwich plate, Continuum Mechanics and Thermodynamics, 1-16.10.1007/s00161-021-00969-6 Search in Google Scholar

7. Kaplunov J., Şahin O. (2020), Perturbed rigid body motions of an elastic rectangle, Z Angew Math Phys., 71(5), 1-15. Search in Google Scholar

8. Kaplunov J., Shestakova A., Aleynikov I., Hopkins B., Talonov A. (2015), Low-frequency perturbations of rigid body motions of a viscoelastic inhomogeneous bar, Mechanics of Time-Dependent Materials, 19(2), 135-151.10.1007/s11043-015-9256-x Search in Google Scholar

9. Kudaibergenov A., Nobili A., Prikazchikova L.A. (2016), On low-frequency vibrations of a composite string with contrast properties for energy scavenging fabric devices, Journal of Mechanics of Materials and Structures, 11 (3), 231-243.10.2140/jomms.2016.11.n3p3 Search in Google Scholar

10. Martin T.P., Layman C.N., Moore K.M., Orris G.J. (2012), Elastic shells with high-contrast material properties as acoustic metamaterial components, Physical Review B, 85 (16), 161103.10.1103/PhysRevB.85.161103 Search in Google Scholar

11. Milton G.W. and Willis J.R. (2007), On modifications of Newton’s second law and linear continuum elastodynamics, Proc. R. Soc. A., 463 (2079), 855-880.10.1098/rspa.2006.1795 Search in Google Scholar

12. Prikazchikova L., Aydın Y.E., Erbaş B., Kaplunov J. (2020), Asymptotic analysis of an anti-plane dynamic problem for a three-layered strongly inhomogeneous laminate, Math. Mech. Solids, 25 (1), 3-16. Search in Google Scholar

13. Qin Y., Wang X., Wang Z.L. (2008), Microfibre-nanowire hybrid structure for energy scavenging, Nature, 451 (7180), 809—813.10.1038/nature0660118273015 Search in Google Scholar

14. Şahin O. (2019), The effect of boundary conditions on the lowest vibration modes of strongly inhomogeneous beams, J. Mech. Mater. Struct., 14(4), 569-585.10.2140/jomms.2019.14.569 Search in Google Scholar

15. Şahin O., Erbaş B., Kaplunov J., Savsek T. (2020), The lowest vibration modes of an elastic beam composed of alternating stiff and soft components, Arch. Appl. Mech., 90 (2), 339-352. Search in Google Scholar

16. Srivastava A., Nemat-Nasser S. (2012), Overall dynamic properties of three-dimensional periodic elastic composites, Proc. R. Soc. A., 468 (2137), 269-287.10.1098/rspa.2011.0440 Search in Google Scholar

17. Vigak V.M., Tokovyi Y.V. (2002), Construction of elementary solutions to a plane elastic problem for a rectangular domain. International applied mechanics, 38(7), 829-836.10.1023/A:1020837409659 Search in Google Scholar

18. Viverge K., Boutin C., Sallet F. (2016), Model of highly contrasted plates versus experiments on laminated glass, International Journal of Solids and Structures, 102, 238-258.10.1016/j.ijsolstr.2016.09.035 Search in Google Scholar

19. Wang X. (2014), Dynamic behaviour of a metamaterial system with negative mass and modulus, Int. J. Solids Struct., 51(7-8), 1534-1541.10.1016/j.ijsolstr.2014.01.004 Search in Google Scholar

20. Willis J.R. (1981), Variational and related methods for the overall properties of composites, In Advances in applied mechanics, (21), pp. 1-78, Elsevier.10.1016/S0065-2156(08)70330-2 Search in Google Scholar

21. Willis J.R. (1981), Variational principles for dynamic problems for inhomogeneous elastic media, Wave Motion, 3(1) 1-11.10.1016/0165-2125(81)90008-1 Search in Google Scholar