Two classes of exact solutions in the linear elastodynamics of transversely isotropic solids

Heber, G., Leimanis, E.: The general problem of the motion of coupled rigid bodies about a fixed point. ZAMM J. Appl. Math. Mech. Zeitschrift für Angewandte Mathematik und Mechanik 46(5), 332–333 (1966). https://doi.org/10.1002/zamm.19660460539 Berker, R.: Intégration des équations du mouvement d’un fluide visqueux incompressible. Handbuch der Physik 3, 1–384 (1963). https://doi.org/10.1007/978-3-662-10109-4_1 Nemenyi, P.F.: Recent developments in inverse and semi-inverse methods in the mechanics of continua1. Adv. Appl. Mech. 2, 123–151 (1951) Truesdell, C., Toupin, R.: The Classical Field Theories. Handbuch der Physik 2, 226–858 (1960). https://doi.org/10.1007/978-3-642-45943-6_2 Truesdell, C., Noll, W.: The Non-Linear Field Theories of Mechanics, pp. 1–579. Springer, Berlin, Heidelberg (1992). https://doi.org/10.1007/978-3-662-13183-1_1 Coleman, B.D., Truesdell, C.A.: Homogeneous motions of incompressible materials. Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik 45, 547–551 (1965) Pucci, E., Saccomandi, G.: Elliptical flows perturbed by shear waves. Ricerche Mat. 67, 509–524 (2018) Holm, D.D.: Gyroscopic analog for collective motion of a stratified fluid. J. Math. Anal. Appl. 117(1), 57–80 (1986). https://doi.org/10.1016/0022-247X(86)90248-9 Craik, A.D.D.: Time-dependent solutions of the Navier–Stokes equations for spatially-uniform velocity gradients. Proc. R. Soc. Edinb. Sect. A Math. 124(1), 127–136 (1994). https://doi.org/10.1017/S0308210500029231 Rajagopal, K.R.: On a class of solutions in elastodynamics. In: Proc. R. Irish Acad. Sect. A Math. Phys. Sci. 90A(2), 205–214 (1990) Rajagopal, K.R., Wineman, A.S.: New exact solutions in non-linear elasticity. Int. J. Eng. Sci. 23(2), 217–234 (1985). https://doi.org/10.1016/0020-7225(85)90076-X Berker, R.: A new solution of the Navier–Stokes equation for the motion of a fluid contained between two parallel plates rotating about the same axis. Arch. Mech. 31(2), 265–280 (1979) Fu, D., Rajagopal, K.R., Szeri, A.Z.: Non-homogeneous deformations in a wedge of Mooney–Rivlin material. Int. J. Non-Linear Mech. 25(4), 375–387 (1990). https://doi.org/10.1016/0020-7462(90)90026-6 Taylor, G.I: LXXV. On the decay of vortices in a viscous fluid. Lond. Edinb. Dublin Philos. Mag. J. Sci. 46(274), 671–674 (1923). https://doi.org/10.1080/14786442308634295 Kelvin, W.T.: On a disturbing infinity in lord Rayleigh’s solution for waves in a plane vortex stratum. Nature 23, 45–46 (1880) Kaptsov, O.V.: New solutions for two-dimensional stationary Euler equations. Prikladnaia Matematika i Mekhanika 54, 409–415 (1990) Spencer, A.J.M.: In: Spencer, A.J.M. (ed.) Constitutive Theory for Strongly Anisotropic Solids, pp. 1–32. Springer, Vienna (1984). https://doi.org/10.1007/978-3-7091-4336-0_1 Coco, M., Saccomandi, G.: Superposing plane strain on anti-plane shear deformations in a special class of fiber-reinforced incompressible hyperelastic materials. Int. J. Solids Struct. 256, 111994 (2022). https://doi.org/10.1016/j.ijsolstr.2022.111994 Grine, F., Saccomandi, G., Arfaoui, M.: Elastic machines: a non standard use of the axial shear of linear transversely isotropic elastic cylinders. Int. J. Solids Struct. 185–186, 57–64 (2020). https://doi.org/10.1016/j.ijsolstr.2019.08.025 Horgan, C.O., Murphy, J.G., Saccomandi, G.: The complex mechanical response of anisotropic materials in simple experiments. Int. J. Non-Linear Mech. 106, 274–279 (2018). https://doi.org/10.1016/j.ijnonlinmec.2018.05.025 Destrade, M., Ogden, R.W., Saccomandi, G.: Small amplitude waves and stability for a pre-stressed viscoelastic solid. Z. Angew. Math. Phys. 60, 511–528 (2009). https://doi.org/10.1007/s00033-008-7147-6 Saccomandi, G., Speranzini, E., Zurlo, G.: Piezoelectric machines: achieving non-standard actuation and sensing properties in poled ceramics. Q. J. Mech. Appl. Math. 74(2), 159–172 (2021). https://doi.org/10.1093/qjmam/hbab002