The axial compression of the landing gear strut can directly lead to the change of system stiffness and rotational inertia，but the effect of strut axial displacement is mostly ignored in existing models of nose landing gear shimmy. A nonlinear dynamic model of six-degree-of-freedom dual-wheel nose landing gear shimmy with axial displacement and longitudinal bending of struts is established. The bifurcation theory is applied to study the effect of introducing axial displacement on the shimmy region，and the maximum compression stroke of the buffer is combined with sliding speed，vertical load，and wheel rotational inertia，respectively. The combined parameters are analyzed by two parameter bifurcation. The fourth order Runge-Kutta method and fast Fourier transform are used to calculate the time-frequency characteristics in the stable shimmy region，and the interaction between the degrees of freedom of torsion，lateral bending，and longitudinal bending of the strut is studied. The results show that under certain conditions，considering the influence of axial displacement of the strut，the areas of torsional and lateral shimmy of the strut have a tendency to shrink. In the bistable region of double wheel nose gear shimmy，when the initial excitation is close to zero equilibrium state，the longitudinal shimmy occurs near 2 times the natural frequency of torsional vibration. When the initial excitation is far from the zero equilibrium state，longitudinal shimmy occurs near 2 times the natural frequency of lateral vibration.