Dynamic Behaviour of an Elastic Orthotropic Shaft

The dynamic behaviour of an orthotropic shaft leads to a nonlinear differential equation, Mathieu type, whose solving is quite difficult. Certain problems in theoretical physics lead to Mathieu equation, particularly the problem of the propagation of electromagnetic waves in a medium with a periodic structure, the problem of the electrons' motion in a crystal lattice in the quantum theory of metals. The parametric equation was solved numerically for time history and was time integrated using Runge-Kutta method with initial boundary values. The results show a totally different dynamic behaviour of the shaft made of an orthotropic material compared with the one made of an isotropic material.