UDC 531 METHODS OF DIRECT LINEARIZATION FOR CALCULATION OF NONLINEAR OSCILLATIONS © A.A. Alifov, DSc, Blagonravov Mechanical Engineering Research Institute of RAS, Moscow, Russia Methods of calculation of nonlinear oscillatory systems by means of direct linearization of nonlinearities are described. <...> Despite such division, the general property of the dynamic systems is the condition of interaction mathematically described by nonlinear equations. <...> Methods of the analysis of nonlinear systems are developed in many books according to the theory of oscillations and nonlinear mechanics differ with various signs e.g. universality, simplicity, accuracy and each method possesses, in comparison with other, certain advantages and shortcomings. <...> In methods of research of nonlinear systems the form (law) of the decision with which use the further analysis of the initial equations is carried out is usually set. <...> With increase in an order or number (the second, third, etc.) approximations complexity and calculation time are sharply increased use the nonlinear characteristic of rather difficult view, removal of final settlement ratios turns into a big problem. <...> Complexity of calculations grows also with increase in degree of nonlinearity that leads to creation only of the first approach giving in most cases the same qualitative results, as the highest approximations. <...> Such properties are characteristic for direct linearization methods [1 – 11] which, being very simple 84 Engineering and automation problems, № 2 – 2015 ones, significantly (on some orders) reduce work and time expenses. <...> In them the knowledge (task) of a form of the solution of the initial nonlinear equation isn't required and there are no approximations of various orders. <...> METHOD OF DIRECT LINEARIZATION NONLINEARITY OF UNMIXED TYPE Nonlinear characteristics observed or received on experiences are, in most cases, approximated by usual polynomial functions f (y) containing even (even numbers in y degree) and odd (odd numbers in y degree) components. <...> Let a nonl inear force of the mixed type F(x, ẋ)=f(x) ẋ under the inf luence of which there is a system, be described by the equation . <...> Having entered replacement x = ẏ this equation it is possible to lead to a view , where G(ẏ)=∫ f(ẏ) dẏ. <...> We will enter a relation , which is similar <...>