Copyright © 2018 Authors. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. International Journal of Engineering & Technology, 7 (4.3) (2018) 40-46 International Journal of Engineering & Technology Website: www.sciencepubco.com/index.php/IJET Research paper Mathematical Modelling of a Specialized Vehicle Caterpillar Mover Dynamic Processes Under Condition of the Distributing the Parameters of the Caterpillar Serhii Strutynskyi 1 *, Volodymyr Kravchuk 2 , Roman Semenchuk 1 . 1 National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute» 2 Leonid Pogorilly State Scientific Institution "Ukrainian Research Institute for forecasting and testing equipment and technologies for agricultural production” *Corresponding author E-mail: strutynskyi@gmail.com Abstract Features of a specialized vehicle caterpillar mover are considered. A dynamic model of caterpillar transverse oscillations as a system with distributed parameters is proposed. The differential equation in partial derivatives is obtained and its connection in the form of a decomposition by normal oscillation types is found. The analysis of frequencies and the type of caterpillar oscillations has been made. Inertial loads have been found. The mathematical model of forced oscillations of a caterpillar under the influence of random loads is developed and the mathematical modelling is executed. An analysis of the vibration movements and vibration velocities of the intersec- tions of the caterpillar is carried out. The mathematical modeling of the caterpillar oscillations caused by stochastic discrete loads was carried out. A model of random discrete loads has been developed, calculations of the realization of random loads are performed. It was established that the transverse discrete loads occur in points of mass concentration on the caterpillar surface. Keywords: caterpillar; frequencies; mathematical model; patterns; random oscillations; transient processes; vehicle 1. Introduction Specialized vehicles are used in terrestrial robotic workstations. They are equipped with manipulators or special devices. Modern terrestrial workstations have a low movement speed up to 20 ... 30 km\h. It reduces their effectiveness. Increasing the speed leads to intensive dynamic loads in a special vehicle chain (caterpillar) mover in particular. Reducing dynamic loads could be achieved by improving the caterpillar mover according to the results of special studies. Therefore, work in this direction is relevant. The problem in general is the development of highly efficient special vehicles with a chain (caterpillar) mover. The problem is related to important scientific and practical tasks of great im- portance for the state security of Ukraine. Recent studies and publications outline the results of the develop- ment and research of terrestrial robotic workstations for special purpose [1]. It is noted that robotic systems have small dimensions (1..2m) and include a chassis and a working module, for example, a manipulator [2]. Mechanisms with parallel kinematic structures are often used as a manipulator [3]. These mechanisms have low materials consumption and broad functionality [4]. Specialized vehicles use wheel or caterpilar chassis. The latter are more effective for use. There are results of researches of geomet- rical and power parameters of a special vehicle caterpillar mover in literary sources [5, 6]. Characteristics of the flotation ability, controllability and performance properties of the vehicles of this type are described [7, 8]. There are results of studying dynamic processes in caterpillar mover dynamic processes in literary sources [9]. The peculiarities of dynamics of drives, characteristics of transi- tional processes [10] in caterpillar movers are established. Dynam- ic properties of the caterpillar are investigated through numerical calculation by the finite element method [11]. The disadvantage of these studies is the specification of the calculations and, accord- ingly, the insignificant degree of the simulation results generaliza- tion. It could be achieved by applying combined methods that include analytical models of the system in distributed parameters and nu- merical methods. Similar approaches to the research of dynamic processes in caterpillar movers under condition of their parameters distribution have not been found in literary sources. Previously undecided parts of the general problem include the study of the peculiarities of dynamic processes in the chain (caterpillar) mov- ers in specialized vehicles using analytical models of caterpillars as systems with distributed parameters. The purpose of the research described in this article is to establish the peculiarities of the dynamic processes caused by the distribu- tion of parameters of a specialized vehicle chain (caterpillar) mov- er. The task of the research is the definition of the laws of the fundamental and forced oscillation processes in the caterpillar mover under condition of its parameters distribution along the length and random discrete caterpillar load. 2. Description of Main Research Materi- al.Calculation of Parameters of Fundamental Transverse Oscillations of a Caterpillar as a System with Distributed Parameters Specialized vehicles are designed to work with non-secure objects and are operated remotely. They have a caterpillar mover chassis and a manipulator working module (Fig. 1).