Wave propagation in a semi-infinite, cylindrical, orthotropic membrane

Abstract

A semi-infinite, cylindrical membrane of fiber-reinforced material with the fibers oriented helically along the membrane is considered. The equations of motion are written in terms of the orthotropic material properties and are solved for the condition of indeterminancy in the second derivatives of the displacements. This produces compatibility relations, valid along characteristics in the time-space plane, and wave speed equations. Due to the fiber orientation, an extensional disturbance generates a concomitant torsional disturbance, which propagates with a slower wave speed. The solution, thus, involves two sets of superimposed characteristics. The pertinent equations are written in finite-difference form and solved numerically. Some generalization is achieved due to nondimensionalization of the equations. Results are presented for various fiber orientations using representative material properties. The relationship of the results to the isotropic case is also discussed. Finally, documentation of the computer program, developed for the numerical solution, is appended.