38
A. M. Antonov et al.
along with Rayleigh waves, may be the existence of bending waves of the Rayleigh
type (Konenkov’s waves) (Konenkov 1960; Zakharov 2002; Wilde et al. 2010). For
structural elements, the materials of which obey the laws of the gradient theory of
elasticity, such waves are waiting for their researchers.
Acknowledgements This work was supported by a grant from the Government of the Russian
Federation (contract No. 14.Y26.31.0031).
References
Abali, B. E., Altenbach, H., dell’Isola, F., Eremeyev, V. A., & Ochsner, A. (Eds.). (2019).
New achievements in continuum mechanics and thermodynamics. A tribute to Wolfgang H.
Muller. Advanced Structured Materials (Vol. 108, 564 p.). Cham, Switzerland: Springer Nature
Switzerland AG. Part of Springer.
Abali, B. E., Muller, W., & dell’Isola, F. (2017). Theory and computation of higher gradient elasticity
theories based on action principles. Archive of Applied Mechanics, 87(9).
Aki, K., & Richards, P. (2009). Quantitative siesmology (2nd ed., p. 700). Mill Valley, CA: University
Science Books.
Alibert, J. J., Seppecher, P., & dell’Isola, F. (2003). Truss modular beams with deformation energy
de-pending on higher displacement gradients. Mathematics and Mechanics of Solids, 8(1).
Altenbach, H., Belyaev, A., Eremeyev, V. A.., Krivtsov, A., & Porubov, A. V. (Eds). (2019). Dynamical processes in generalized continua and structures. Advanced Structured Materials (Vol. 103,
526 p.). Cham, Switzerland: Springer Nature Switzerland AG. Part of Springer.
Altenbach, H., & Eremeyev V. A. (Eds.). (2013). Generalized continua—from the theory to
engineering applications (388 p.). Wien: Springer.
Altenbach, H., & Forest, S. (Eds.). (2016). Generalized continua as models for classical and
advanced materials. Advanced Structured Materials (Vol. 42, 458 p.). Switzerland: SpringerVerlag.
Altenbach, H., Forest, S., & Krivtsov, A. (Eds.). (2013). Generalized continua as models with
multi-scale effects or under multi-field actions. Advanced Structured Matherials (Vol. 22, 332
p.). Berlin-Heidelberg: Springer-Verlag.
Altenbach, H., Maugin, G. A., Erofeev, V. (Eds). (2011). Mechanics of generalized continua.
Advanced Structured Materials (Vol. 7, 350 p.). Berlin-Heidelberg: Springer-Verlag.
Altenbach, H., Pouget, J., Rousseau, M., Collet, B., & Michelitsch, T. (Eds.). (2018a). Generalized
models and non-classical approaches in complex materials 1. Advanced Structured Materials
(Vol. 90, 760 p). Springer International Publishing AG, part of Springer Nature.
Altenbach, H., Pouget, J., Rousseau, M., Collet, B., & Michelitsch T. (Eds.). (2018b). Generalized
models and non-classical approaches in complex materials 2. Advanced Structured Materials
(Vol. 90, 328 p.). Springer International Publishing AG, part of Springer Nature.
Auffray, N., dell’Isola, F., Eremeyev, V., Madeo, A., & Rossi, G. (2013). Analytical continuum
mechanics à la Hamilton-Piola: least action principle for second gradient continua and capillary
fluids. Mathematics and Mechanics of Solids.
Bagdoev, A. G., Erofeyev, V. I., & Shekoyan, A. V. (2016). Wave dynamics of generalized continua.
Advanced Structured Materials (Vol. 24, 274 p.). Berlin-Heidelberg: Springer-Verlag.
Barchiesi, E., Spagnuolo, M., & Placidi, L. (2018). Mechanical metamaterials: a state of the art.
Mathematics and Mechanics of Solids.
Cosserat, E., et al. (1909). Theorie des Corp Deformables (226 p.). Paris: Librairie Scientifique A.
Hermann et Fils.
A. M. Antonov et al.
along with Rayleigh waves, may be the existence of bending waves of the Rayleigh
type (Konenkov’s waves) (Konenkov 1960; Zakharov 2002; Wilde et al. 2010). For
structural elements, the materials of which obey the laws of the gradient theory of
elasticity, such waves are waiting for their researchers.
Acknowledgements This work was supported by a grant from the Government of the Russian
Federation (contract No. 14.Y26.31.0031).
References
Abali, B. E., Altenbach, H., dell’Isola, F., Eremeyev, V. A., & Ochsner, A. (Eds.). (2019).
New achievements in continuum mechanics and thermodynamics. A tribute to Wolfgang H.
Muller. Advanced Structured Materials (Vol. 108, 564 p.). Cham, Switzerland: Springer Nature
Switzerland AG. Part of Springer.
Abali, B. E., Muller, W., & dell’Isola, F. (2017). Theory and computation of higher gradient elasticity
theories based on action principles. Archive of Applied Mechanics, 87(9).
Aki, K., & Richards, P. (2009). Quantitative siesmology (2nd ed., p. 700). Mill Valley, CA: University
Science Books.
Alibert, J. J., Seppecher, P., & dell’Isola, F. (2003). Truss modular beams with deformation energy
de-pending on higher displacement gradients. Mathematics and Mechanics of Solids, 8(1).
Altenbach, H., Belyaev, A., Eremeyev, V. A.., Krivtsov, A., & Porubov, A. V. (Eds). (2019). Dynamical processes in generalized continua and structures. Advanced Structured Materials (Vol. 103,
526 p.). Cham, Switzerland: Springer Nature Switzerland AG. Part of Springer.
Altenbach, H., & Eremeyev V. A. (Eds.). (2013). Generalized continua—from the theory to
engineering applications (388 p.). Wien: Springer.
Altenbach, H., & Forest, S. (Eds.). (2016). Generalized continua as models for classical and
advanced materials. Advanced Structured Materials (Vol. 42, 458 p.). Switzerland: SpringerVerlag.
Altenbach, H., Forest, S., & Krivtsov, A. (Eds.). (2013). Generalized continua as models with
multi-scale effects or under multi-field actions. Advanced Structured Matherials (Vol. 22, 332
p.). Berlin-Heidelberg: Springer-Verlag.
Altenbach, H., Maugin, G. A., Erofeev, V. (Eds). (2011). Mechanics of generalized continua.
Advanced Structured Materials (Vol. 7, 350 p.). Berlin-Heidelberg: Springer-Verlag.
Altenbach, H., Pouget, J., Rousseau, M., Collet, B., & Michelitsch, T. (Eds.). (2018a). Generalized
models and non-classical approaches in complex materials 1. Advanced Structured Materials
(Vol. 90, 760 p). Springer International Publishing AG, part of Springer Nature.
Altenbach, H., Pouget, J., Rousseau, M., Collet, B., & Michelitsch T. (Eds.). (2018b). Generalized
models and non-classical approaches in complex materials 2. Advanced Structured Materials
(Vol. 90, 328 p.). Springer International Publishing AG, part of Springer Nature.
Auffray, N., dell’Isola, F., Eremeyev, V., Madeo, A., & Rossi, G. (2013). Analytical continuum
mechanics à la Hamilton-Piola: least action principle for second gradient continua and capillary
fluids. Mathematics and Mechanics of Solids.
Bagdoev, A. G., Erofeyev, V. I., & Shekoyan, A. V. (2016). Wave dynamics of generalized continua.
Advanced Structured Materials (Vol. 24, 274 p.). Berlin-Heidelberg: Springer-Verlag.
Barchiesi, E., Spagnuolo, M., & Placidi, L. (2018). Mechanical metamaterials: a state of the art.
Mathematics and Mechanics of Solids.
Cosserat, E., et al. (1909). Theorie des Corp Deformables (226 p.). Paris: Librairie Scientifique A.
Hermann et Fils.