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Two dimensional square lattice is considered when the forces between the lattice
particles are expressed both linearly and quadratically dependent on the spring elongations. The
shift operator approach, firstly developed by [1] and applied to the one-dimensional linear
problem, is extended on the two-dimensional nonlinear case. The discrete strain energy and the
discrete governing nonlinear equations of motion are obtained. Also, the continuum nonlinear
equation for the plane longitudinal waves propagation is obtained in a weakly nonlinear case.
Keywords: lattice; nonlinear modeling; strain wave. |
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