Nonlinear stationary waves in a Timoshenko beam

The governing equations for the bending vibration of a Timoshenko beam accounting for geometric and physical nonlinearities are derived. For the case of small shear angles, this system can be reduced to one equation with respect to transversal displacement. Solutions for nonlinear Timoshenko beam in the form of stationary waves of deformation (periodic waves and solitons) are found and analyzed. Nonlinear dispersion equations for periodic stationary waves are derived. It is shown that dispersion properties of waves in metal rods are identical to that of linear waves. For the case of rods made of composite materials, an existence of essentially nonlinear waves is possible at the velocity band in which linear waves do not propagate.