Vibrational Analysis of Cables Using the Non Standard Finite Difference Method

Abstract

In continuous systems such as rods, cables, and shafts, the differential equation governing the behaviour of the structure can be obtained by applying Newton's second law. Only a limited group of these equations have an analytic solution; hence the provision of efficient and stable numerical methods is of particular importance. The method used in this study is a nonstandard finite difference (NSFD) scheme, which is an effective numerical method for solving the above-mentioned equations. One of the important features of this method is its relatively good high accuracy. Results obtained by nonstandard finite difference methods are more compatible with the exact behaviour of the problem than that of the standard finite difference method. In this research, the equations governing the vibrations of cables with three different boundary conditions are solved. Three solutions including the analytical solution, the standard finite difference method (SFD) and the NSFD method are compared. Results show that the error of the NSFD is significantly less than of the SFD.