Evolution of numerical model to identify the intersection of vibratory motion equations with discrete points in a mechanical system

Abstract Some mathematical functions which can’t be solved analytically and the solution for these functions can be determined by the intersection of their graphical plots. Computer programmes represent these functions with discrete points which are not continuous in nature. Since the resolution of the discretization is limited, the graphs may intersect in the interval between two points. It is difficult to find the intersection value of these functions from the computer plotted graphs as the intersection points do not exist. In such cases, intersection points can be approximately found by eye ball method, or by increasing the number of discrete points. This paper discusses about a logical method to find the intersection points of two discretely plotted graphs with much better accuracy. Novelty of this work is the improvement in the accuracy and resolution of determination of intersection points between two discretised graphs without increasing the resolution of discretisation. Existing methods requires increasing the number of discretised points to improve the accuracy and resolution in the determination of intersection points. A problem related to simulation of vibratory induced motions is taken as an example.