Nonlinear surface elastic waves in materials

• Autorzy: Rushchitsky J.
• Konferencja: Symposium “Vibrations In Physical Systems” (26 ; 04-08.05.2014 ; Będlewo koło Poznania ; Polska)
• Języki publikacji: EN

Abstrakty

EN

This paper is devoted to analysis of the surface nonlinear elastic harmonic waves of four types (Rayleigh and Stoneley harmonic waves within the framework of plane strain state; Love and Mozhaev harmonic wave within the framework of anti-plane strain state). The nonlinear model is based on introducing the Murnaghan elastic potential, which includes both geometrical and physical nonlinearities. Each type of surface waves is discussed in four steps: statement of the problem, nonlinear wave equations, approximate solution (first two approximations), so-me conclusions. A nonlinear analysis of waves required many novelties: new variants of the Murnaghan potential, new nonlinear wave equations and new nonlinear boundary conditions. The nonlinear wave equations were solved by the method of successive approximations. A new approach to analyze the boundary conditions is offered. Some new nonlinear wave effects are observed theoretically: a wave picture is reached by the 2nd harmonic and becomes changing in time of propagation, the wave numbers become depending on the initial amplitude.

Słowa kluczowe

EN

surface nonlinear elastic harmonic waves; Rayleigh wave; Love wave; Stoneley wave; Mozhaev wave

PL

fale powierzchniowe; fale nieliniowe; fale harmoniczne; fale sprężyste; fala Rayleigha; fala Love'a; fala Stoneley'a; fala Mozhaeva

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2014
• Tom: Vol. 26
• Strony: 33--40
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Rushchitsky J.

• S .P. Timoshenko Institute of Mechanics, Nesterov str.3, Kiev, 03680, Ukraine

Bibliografia

• 1. A.E.H. Love, Some problems of geodynamics, Cambridge University Press, Cambridge 1911.
• 2. G.A. Maugin, Y. Chevalier, M. Louzar, Interfacial waves in the presence of areas of slip, Geophys. J. Int. 118 (1994) 305-316.
• 3. V.G. Mozhaev, A new type of surface waves in solids due to nonlinear elasticity, Physics Letters A, 139(7) (1989) 333-336.
• 4. J.W. Rayleigh, On waves propagated along the plane surface of an elastic body, Proc. Math. Soc. London, 17 (1885) 4-11.
• 5. J.J. Rushchitsky, Certain Class of Nonlinear Hyperelastic Waves: Classical and Novel Models, Wave Equations, Wave Effects, Int. J. Appl. Math. and Mech. 9(1) (2013) 400-443.
• 6. J.J. Rushchitsky, Theory of waves in materials, Ventus Publishing ApS, Copenhagen 2011 (free text-book in BookBooN.com)
• 7. J.J. Rushchitsky, Nonlinear Elastic Waves in Materials, Springer, Heidelberg 2014.
• 8. J.J. Rushchitsky, Quadratically nonlinear cylindrical hyperelastic waves: Derivation of wave equations for axisymmetric and other states, Int. Appl. Mech., 41(6) (2005) 646-656.
• 9. R. Stoneley, Elastic waves at the surface of separation of two solids, Proc. R. Soc. London A, 106 (1924) 416-428.