ANALYTICAL STUDY OF FRICTIONAL AUTO-VIBRATIONS IN SYSTEMS WITH TWO DEGREES OF FREEDOM

Purpose of the study is to study the properties of frictional self-oscillations in systems with two degrees of freedom. As a research method, the asymptotic method of N.N. Bogolyubov and Y.A. Metropolitan. Research methods. The methodological basis of the work is the generalization and analysis of the known scientific results of the dynamics of systems in resonance modes and the use of a systematic approach. The analytical method and comparative analysis were used to form a scientific problem, goal and formulation of research objectives. When developing empirical models, the main provisions of the theory of stability of systems, methodology of system analysis and research of functions were used. The results of the study. A system with two degrees of freedom is considered, assuming that the friction function is approximated by a cubic polynomial in the sliding velocity, and friction is applied only to one of the masses. The exclusion of uniform rotation, corresponding to the third degree of freedom, leads to consideration not of the frictional moment, but the difference between the frictional moment and the moment of the moving forces. From the analysis of the results of the solutions of the equation, we can conclude that, with an accuracy up to the first approximation, inclusive, self-oscillations occur with constant frequencies equal to the natural frequencies of the system. This is consistent with the conclusions of other authors obtained using other methods. Stationary values of the amplitudes are found. The following four cases are possible: trivial solution corresponding to uniform rotation of the system without oscillations; single frequency oscillations with the first frequency; single frequency oscillations with a second frequency; two-frequency oscillatory mode. Conclusions. G. Boyadzhiev's method can be applied to study multi-mass self-oscillating systems and gives their general solution in the form of asymptotic expansions to any degree of accuracy. The obtained conditions for the stability of stationary regimes confirm the experimental results that in multi-mass systems, self-oscillations are possible only in the falling sections of the friction characteristics. The nature of the developing vibrations - their frequency and the ratio of the amplitudes of the constituent harmonics - is completely determined by the structure of the system, its elastic and inertial properties.

Non-Markovian modeling of protein folding

We extract the folding free energy landscape and the time-dependent friction function, the two ingredients of the generalized Langevin equation (GLE), from explicit-water molecular dynamics (MD) simulations of the α-helix forming polypeptide alanine9 for a one-dimensional reaction coordinate based on the sum of the native H-bond distances. Folding and unfolding times from numerical integration of the GLE agree accurately with MD results, which demonstrate the robustness of our GLE-based non-Markovian model. In contrast, Markovian models do not accurately describe the peptide kinetics and in particular, cannot reproduce the folding and unfolding kinetics simultaneously, even if a spatially dependent friction profile is used. Analysis of the GLE demonstrates that memory effects in the friction significantly speed up peptide folding and unfolding kinetics, as predicted by the Grote–Hynes theory, and are the cause of anomalous diffusion in configuration space. Our methods are applicable to any reaction coordinate and in principle, also to experimental trajectories from single-molecule experiments. Our results demonstrate that a consistent description of protein-folding dynamics must account for memory friction effects.

Bursting Oscillations and Sliding Motion in Permanent Magnet Synchronous Motor Systems with Friction Factor

The main purpose of this paper is to investigate the qualitative effects of external excitation and friction factor on the response of permanent magnet synchronous motor (PMSM) system. Three different modes of bursting oscillations are found. In particular, the introduction of friction function changes the governing equations from a smooth type to a nonsmooth (Filippov) type in which the special sliding motion is observed. The mechanism, attractor structure, vector field structure, and analytic bifurcation conditions of bursting oscillation and sliding motion are discussed in detail. The validity of theoretical results obtained is verified by numerical simulations and analysis.

Time-Dependent Fractional Diffusion and Friction Functions for Anomalous Diffusion

The precise determination of diffusive properties is presented for a system described by the generalized Langevin equation. The time-dependent fractional diffusion function and the Green-Kubo relation as well as the generalized Stokes-Einstein formula, in the spirit of ensemble averages, are reconfigured. The effective friction function is introduced as a measure of the influence of frequency-dependent friction on the evolution of the system. This is applied to the generalized Debye model, from which self-oscillation emerges as indicative of ergodicity that breaks due to high finite-frequency cutoff. Moreover, several inconsistent conclusions that have appeared in the literature are revised.

Impact Behavior of a Rotating Rigid Body with Impact and Viscous Friction

The impact between a rotating link and a solid flat surface is considered. For the impact, we consider three distinct periods: elastic period, elastoplastic period, and restitution period. A Hertzian contact force is considered for the elastic period. Nonlinear contact forces developed from finite element analysis are used for the remaining two phases. The tangential effect is taken into account considering a friction force that combines the Coulomb dry friction model and a viscous friction function of velocity. Simulations results are obtained for different friction parameters. An experimental setup was designed to measure the contact time during impact. The experimental and simulation results are compared for different lengths of the link.

Novel Method of Friction Identification with Application for Inverted Pendulum Control System

This text covers a novel method of friction identification for control systems. The friction function in the inverted pendulum model is described by means of a cubic polynomial. The method has been tested using the data recorded on a real inverted pendulum. It has been proven that the proposed cubic model offers the same level of accuracy as the Coulomb model. However, all the difficulties caused by Coulomb’s model discontinuity are omitted.

Research on Friction between Grade Flat Approach Slab and Sliding Material in Jointless Bridges

<p>The application of jointless bridges has been increasing year by year, because it could reduce the life‐cycle cost and improve the riding comfort. The approach slab in jointless bridges does not only have the function of road transition which is the same as the approach slab in bridges with expansion joints, but also transfer and absorb the deformation produced by the thermal expansion and contraction of the girder. The Grade Flat Approach Slab (GFAS) horizontally placed on the subgrade is one of the most common types of the approach slab in jointless bridges. The material placed between GFAS and subgrade should be able to properly slide to reduce the stress in GFAS. The friction coefficient between GFAS and sliding material is an important parameter affecting the mechanical behavior of GFAS in jointless bridges. In this paper, the tests of GFAS with different sliding materials subjected to horizontal displacement were conducted to obtain the corresponding friction coefficients (from 0.34 to 0.68). The mathematical model of bilinear spring could be adapted to simulate the friction function between GFAS and different sliding materials. One Deck‐Extension Bridge (DEB) that is one type of jointless bridges was chosen as a case study. The finite element model was implemented by using Midas‐Civil software. The influence of GFAS with different sliding materials on the mechanical properties of DEB under temperature variation was investigated. It can be concluded that the influence of the friction coefficient between GFAS and sliding material on the bending moment of DEB should be taken into account.</p>