6 research outputs found
Mathematical simulation of elastic systems with unilateral external interaction
No full textWe consider the behavior of elastic systems with external unilateral interaction (friction, recovering forces, forces of relay type), which are given as functions defined by inequalities relative to unknown variables. The investigation is based on application of the concept of motion separation (coupled application of methods of motion decomposition with respect to normal modes of oscillations, asymptotic methods of nonlinear mechanics and frequency separation of motions). This approach makes it possible to construct a discrete nonlinear model of the investigated system and the analytical-numerical method for its investigation. The transient modes of the system motion were studied. Peculiarities of manifestation of nonlinear properties of the system are discussed. We consider also the case of oscillations of elastic systems with variable stiffness coupled with unilateral interaction. The results of numerical simulation were presented. It was shown that the unilateral interaction generates conditions for prevention of the resonant development of oscillations and can be considered as a means for active suppression of oscillations
About a generalization of Bellman-Bihari-Type inequalities for discontinuous functions and their applications
No full textIn the present paper we introduce the conditions of solvability for Chaplygin’s problem with discontinuous functions in two independent variables, satisfying integro-sum inequalities. The new type of nonlinear integral and Wendroff’s inequality for discontinuous functions are investigated. As applications, the conditions of boundedness solutions of partial differential equations of hyperbolic type with impulse influence on some hypersurfaces {Γj} ⊂ R2 are obtained. Some historical aspects of the theory of integrosum inequalities are presented
Asymptotic solutions to the first order differential equation with deviated argument and slowly varying coefficients
No full textThe object of this paper is to study the problem of constructing an approximate solution of a first-order
weakly nonlinear ordinary differential equation with deviating argument and slowly varying coefficients.
On the basis of asymptotic techniques in nonlinear mechanics, we construct an algorithm for the asymptotic
integration of the differential equation under consideration
