Three-Dimensional Vibrations of Orthotropic Cylinders

A method to analyze the three-dimensional vibrations of orthotropic cylinders is presented. The field equations are in the form of three coupled, second-order differential equations with nine elastic constants. The vibration problem is solved by means of the Frobenius method, using power series expansion in the radial coordinate, and assuming sinusoidal dependence on the longitudinal and circumferential coordinates and on time. Frequency equation for the free vibration of solid circular cylinders is derived and a numerical example is given. An extensive study of the dynamic behavior of orthotropic cylinders can be made by this analysis.