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Interaction of orthogonal-polarized waves in 1D metamaterial with kerr nonlinearity

Ampilogov D.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2017

Vol. 21, No 2

149--163

The investigation of the wave propagation in a 1D metamaterial is continued in this paper. A nonlinear evolution equation of the wave interaction of two polarizations by means of the projection operator method is obtained and a particular solution in the case of slow-varying envelopes is found.

Nonlinear Interactions between Gravity Waves in Water of Constant Depth

Szmidt K., Hedzielski B.

Archives of Hydro-Engineering and Environmental Mechanics

2015

Vol. 62, nr 1-2

3--25

The paper deals with interactions between water waves propagating in fluid of constant depth. In formulation of this problem, a nonlinear character of these interactions is taken into account. In particular, in order to simplify a solution to nonlinear boundary conditions at the free surface, a system of material coordinates is employed as independent variables in the description of the phenomenon. The main attention is focused on the transient solutions corresponding to fluid motion starting from rest. With respect to the initial value problem considered, we confine our attention to a finite fluid domain. For a finite elapse of time, measured from the starting point, the solution in a finite fluid area mimics a solution within an infinite domain, inherent for wave propagation problems. Because of the complicated structure of equations describing nonlinear waves, an approximate formulation is considered, which is based on a power series expansion of dependent variables with respect to a small parameter. Such a solution is assumed to be accurate in describing the main features of the phenomenon. Numerical experiments are conducted to illustrate the approximate formulation developed in this paper.

Numerical modeling of wave propagation and interaction in bars

Jankowiak T., Klepaczko J., Łodygowski T.

Foundations of Civil and Environmental Engineering

2006

No. 7

187-199

In the first part, the paper presents analytical solution of symmetric longitudinal impact of a semi-infinite circular bar. In the second part the Maple code is used in order to solve the differential equations, derived and solved by Skalak [1]. Based on this analytical solution, a verification is performed by Finite Element code. The calibration of parameters like the artificial viscosity and the mesh size is done. The initial FE calibration is used, together with cumulative fracture criterion, to verify the laboratory test results presented by Klepaczko [2,3,4,7]. The finite element solution is focused on the new experimental technique to test semi-brittle materials in dynamic tension via spalling. The technique which is based on Hopkinson pressure bar has been developed in LPMM-Metz [4].