FINITE DIFFERENCE METHOD FOR STATIC AND DYNAMIC ANALYSIS: EULER-BERNOULLI BEAM ON WINKLER FOUNDATION AND VIBRATING MOTION OF SINGLE DEGREE OF FREEDOM SYSTEM

Abstract

The Finite Difference Method (FDM) is one of the most powerful numerical solution techniques and has the ability to handle most types of analysis in structural mechanics. In this study, examples of physical modeling of vibrational motion of a single-degree-of-freedom-system (SDOF) under the effect of a harmonic external load are examined by considering the effects of different system parameters. In its simplest form, the problem is represented by a second order differential equation with constant coefficient. The relevant equation is solved analytically and at the same time, the compatibility of the results is tested using the finitedifference method. In addition, the analysis of the beam resting on the elastic foundation is considered. The analytical solution of the fourth order differential equation is obtained and the finite-difference method is used in order to obtain its numerical solution. Different numerical example problems are considered for the above mentioned two problems and the results are tested with the existing literature.