Extension of the Method of Direct Separation of Motions for Problems of Oscillating Action on Dynamical Systems

AbstractA general approach to study oscillating action on nonlinear dynamical systems is developed. It implies a transition from initial governing equations of motion to much more simple equations describing only the main slow component of motions (the vibro-transformed dynamics equations). The approach is named as the Oscillatory Strobodynamics, since motions are perceived as under a stroboscopic light. The vibro-transformed dynamics equations comprise terms that represent the averaged effect of the oscillating action. The method of direct separation of motions (MDSM) appears to be an efficient and simple tool to derive these equations. A modification of the method applicable to study problems that do not imply restrictions on the spectrum of excitation frequencies is proposed. It allows also to abandon other restrictions usually introduced when employing the classical asymptotic methods, e.g. the requirement for the involved nonlinearities to be weak.Several relevant examples from Mechanics, Physics, Chemistry, and Biophysics are considered by means of the conventional MDSM and, in more details, by the modified MDSM, illustrating the efficiency the methods

Revisiting the models of vibration screening process

This talk presents two approaches for modeling of the vibration screening process. The first approach is analytical. It models the screening process as a diffusion of undersize fraction taking into account the special term for vibration separation (the Brazil nut effect). The talk provides a solution of the corresponding partial differential equation. The solution in turn allows estimation of the screening performance dependence on both deterministic and stochastic factors as well as evaluation of the factors dominance conditions. The talk presents simple evaluation formulae for the screening process performance. The second approach is based on a simulation model. The model deals with monolayer dynamics. Embodying traditional concepts of vibration transportation, the approach introduces some novel techniques of evaluation of the effect of the granular particles shape. Taking into account the particle shape factor may significantly improve the modeling precision for nonspherical particles

Vibrational mechanics: nonlinear dynamic effects, general approach, applications

This important book deals with vibrational mechanics - the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations. It offers a general approach to the study of the effect of vibration on nonlinear mechanical systems.The book presents the mathematical apparatus of vibrational mechanics which is used to describe such nonlinear effects as the disappearance and appearance under vibration of stable positions of equilibrium and motions (i.e. attractors), the change of the rheological properties of the media, self-synchronization, self-balancing, the vibra