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|Title: ||Fission of a longitudinal strain solitary wave in a delaminated bar|
|Authors: ||Khusnutdinova, Karima R.|
Samsonov, Alexander M.
|Issue Date: ||2008|
|Publisher: ||© American Physical Society|
|Citation: ||KHUSNUTDINOVA, K.R. and SAMSONOV, A.M., 2008. Fission of a longitudinal strain solitary wave in a delaminated bar. Physical Review E, 77, 066603, 11pp.|
|Abstract: ||The aim of the paper is to show that splitting of a waveguide leads to fission of bulk solitons in solids. We
study the dynamics of a longitudinal bulk solitary wave in a delaminated, symmetric layered elastic bar. First,
we consider a two-layered bar and assume that there is a perfect interface when x 0 and complete debonding
splitting when x 0, where the axis Ox is directed along the bar. We derive the so-called doubly dispersive
equation DDE for a long nonlinear longitudinal bulk wave propagating in an elastic bar of rectangular cross
section. We formulate the problem for a delaminated two-layered bar in terms of the DDE with piecewise
constant coefficients, subject to continuity of longitudinal displacement and normal stress across the “jump” at
x=0. We find the weakly nonlinear solution to the problem and consider the case of an incident solitary wave.
The solution describes both the reflected and transmitted waves in the far field, as well as the diffraction in the
near field in the vicinity of the jump . We generalize the solution to the case of a symmetric n-layered bar. We
show that delamination can lead to the fission of an incident solitary wave, and obtain explicit formulas for the
number, amplitudes, velocities, and positions of the secondary solitary waves propagating in each layer of the
split waveguide. We establish that generally there is a higher-order reflected wave even when the leading order
reflected wave is absent.|
|Sponsor: ||We thank W.A. Green and E.N. Pelinovsky for useful discussions.
The research is supported by EPSRC-GB Grant
|Publisher Link: ||http://dx.doi.org/10.1103/PhysRevE.77.066603|
|Appears in Collections:||Published Articles (Maths)|
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