General Scheme of Modeling of Longitudinal Oscillations in Horizontal Rods

Abstract

In this paper, we present the results of modeling nonstationary oscillatory processes in rods consisting of an arbitrary number of pieces. When modeling oscillatory processes that occur in many technical objects (automotive shafts, rods) an important role is played by finding the amplitude and frequency of oscillations. Solving oscillatory problems is associated with various difficulties. Such difficulties are a consequence of the application of methods of operation calculus and methods of approximate calculations. The method of modeling of oscillatory processes offered in work is executed without application of operational methods and methods of approximate calculations. The method of oscillation process modeling proposed in this paper is a universal method. The work is based on the concept of quasi-derivatives. Applying the concept of quasi-derivatives helps to avoid the problem of multiplication of generalized functions. Analytical formulas for describing oscillatory processes in rods consisting of an arbitrary number of pieces are obtained. It can be applied in cases where pieces of rods consist of different materials, and also when in places of joints the masses are concentrated. The proposed method allows the use of computational software. An example of constructing eigenvalues and eigenfunctions for a rod consisting of two pieces is given.