Yelagin A. Non-linear anharmonic effects at normal elastic waves propagation in a cylindrical waveguides

The problem of determination of small nonlinear effects in normal elastic waves is considered. It consists in a generation of the nonlinear second harmonics of normal axially symmetric elastic waves of torsion and longitudinal-shear type in an isotropic cylindrical body's circular section with free or rigid lateral surface. The model of geometrical and physical nonlinear deformation of isotropic elastic media is used. In the examined cases the boundary problems of the first (linear) and second (for deter-mination of normalized complex functions of intensity of nonlinear second harmonics normal torsion and longitudinal-shear waves) approximations are formulated and investigated with the use of theory of finite deformations and representation of Murnaghan elastic potential with square and cubic compo-nents on deformations. Solving is based on the method of small parameter. The analytical form of solu-tions of the researched heterogeneous boundary problems is build with application of specialized algo-rithm that is created in the environment of computer algebra. Series of principal amplitude-frequency dependences for normalized characteristics of intensity wave displacements in elastic waves of the se-cond harmonics is investigated. General effects of influence of type of boundary conditions on ampli-tudes of the second harmonics for monochromatic normal waves and on the indexes of nonlinear an-harmonic interaction of normal waves from one or different modes of corresponding dispersion spec-trums are generalized and described.