Khotenko O. Toward a theory of quadratically nonlinear Rayleigh waves

This dissertation is devoted to the study of the elastic Rayleigh waves propagation mechanisms in materials. The plane problem of quadratically nonlinear Rayleigh wave propagation is studied in the classical statement. The constitutive relations correspond to the nonlinear Murnaghan potential. The quadratically nonlinear wave equations for variants of general, geometrical and physical nonlinearities for cases of accounting and neglecting the nonlinear cross effect of displacements and potentials are obtained. A scheme is proposed to simplify the nonlinear system in potentials. The solutions of equations are obtained with the use of method of successive approximations within the framework of the first two approximations. A role of boundary conditions in the nonlinear analysis of Rayleigh wave is studied. The new nonlinear Rayleigh equation (equation in terms of the unknown wave number) is derived and its qualitative analysis is carried out. It follows from this equation that a change of the initial amplitude results in a change of the wave number. The numerical analysis of the effect, influence of initial amplitude, frequency and elastic material characteristics on evolution and attenuation of the nonlinear Rayleigh wave is carried out. It is shown that the numerical analysis allows detecting the effect of 2nd harmonics on the initially harmonic wave and the attenuation law as well as determining applicability limits of the second approximation, too. It is also noticed that the effect of nonlinearity on the attenuation law is localized only in the nearsurface layer of the one wavelength depth.