New Variant of the Method of Constraints for the Displacement Gradient that Arises When Analyzing the Evolution of a Torsional Wave

A new generalization of the method of constraints for displacement gradient occurring when studying a torsional displacement wave propagating in a nonlinear elastic material is proposed within the framework of the five-constant Murnaghan model. This method allows us to find an approximate solution of the recently proposed nonlinear wave equation and includes the constraints not only on the first partial derivatives of displacements, i.e., the smallness of the maximum amplitude of the wave relative to the wavelength, but also on the displacements, i.e., the real value of the maximum amplitude of the wave, and on the curvature of the wave profile.