D. M. Klimov

Theory of the shimmy phenomenon

The shimmy phenomenon is the appearance of angular self-excited vibrations of the carriage wheels. Such self-excited vibrations provide a serious safety hazard for motion, which explains the great interest of scientists in this phenomenon [1–6]. This problem is most serious for the aircraft fore wheels.It is commonly agreed that themain cause of the shimmyphenomenon is the tyre deformation [2]. We do not doubt this thesis, but still we note that this cause is not unique. The shimmy phenomenon can be observed in everyday life in the case of various hand trucks with rigid wheels, where the reference to the elastic tyre is out of place.In what follows, we show that the theory of polycomponent dry friction can completely explain the shimmy phenomenon for absolutely rigid wheels, and hence can be at least one of the causes of this phenomenon in the general case.Dry friction has been ignored by the scientists in their explanations of the shimmy phenomenon, because this friction has not been fully investigated until now, and it has been impossible to explain the shimmy phenomenon in the framework of the former representations.

Oscillatory-rotational processes in the Earth motion about the center of mass: Interpolation and forecast

The celestial-mechanics approach (the spatial version of the problem for the Earth-Moon system in the field of gravity of the Sun) is used to construct a mathematical model of the Earth’s rotational-oscillatory motions. The fundamental aspects of the processes of tidal inhomogeneity in the Earth rotation and the Earth’s pole oscillations are studied. It is shown that the presence of the perturbing component of gravitational-tidal forces, which is orthogonal to the Moon’s orbit plane, also allows one to distinguish short-period perturbations in the Moon’s motion. The obtained model of rotational-oscillatory motions of the nonrigid Earth takes into account both the basic perturbations of large amplitudes and the more complicated small-scale properties of the motion due to the Moon short-period perturbations with combination frequencies.The astrometric data of the International Earth Rotation and Reference Systems Service (IERS) are used to perform numerical simulation (interpolation and forecast) of the Earth rotation parameters (ERP) on various time intervals.

Fracture of Sedimentary Rocks under a Complex Triaxial Stress State

Most sedimentary rocks have layered structure, and their strength properties are therefore anisotropic; as a consequence, the rock strength depends on the direction of the applied stresses. In this case, various fracture mechanisms are possible. The following two possible fracture mechanisms are considered: actions along the bedding planes, which are weakening surfaces, and along the planes where stresses exceeding the total rock strength are attained. A triaxial independent loading test bench was used to study the fracture conditions for layered rocks composed of productive oil-and-gas strata in complex true triaxial loading tests. The study shows a good qualitative agreement between experimental results and theoretical estimates.

Mechanical-mathematical and experimental modeling of well stability in anisotropic media

Virtually allmodern gas and oil production technologies are based on directional drilling, and hence well stability issues are of primary importance. It was established that the stability of slanted wells significantly depends on the deformation and strength characteristics of rocks, on the presence and degree of rock anisotropy, and also on the well geometry and the pressure at the well bottom. We suggest a new approach to this problem by modeling the hole making process with the use of a triaxial independent loading test system (TAILTS) based on the mechanical-mathematical model developed here.

The main properties and peculiarities of the Earth’s motion relative to the center of mass

The methods of theoretical and celestial mechanics and mathematical statistics have been used to prove that the Earth’s motion relative to the center of mass, the polar wobble, in the principal approximation is a combination of two circumferences with a slow trend in the mean position corresponding to the annual and Chandler components. It has been established that the parameters (amplitude and phase shift) of the annual wobble are stable, while those of the Chandler component are less stable and undergo significant variations over the observed time intervals. It has been proven that the behavior of these polar motion parameters is attributable to the gravitational-tidal mechanisms of their excitation.

Experimental study of the influence of a triaxial stress state with unequal components on rock permeability

We present the experimental results of true triaxial independent loading test bench studies of the influence of a triaxial stress state with unequal components on the filtration properties of rock in oil and gas gathering mains. We show that the permeability of rock subjected to stresses can irreversibly decrease or increase. The discovered effects are of great importance when designing optimal oil and gas well drilling and operation regimes.

Numerical-Analytic Modeling of Perturbed Oscillatory Motions of the Earth Pole

An improved numerical-analytic model of multifrequency oscillatory motion of Earth’s pole with temporal variations in the geopotential coefficients taken into account is considered. The model is a natural improvement of the earlier developed basic model of the pole oscillations (the Chandler and annual components) by using the methods of celestial mechanics and the data of the terrestrial gravitational field observations. This model allows one to improve the accuracy of forecast of Earth’s pole motion trajectory in the periods of significant anomalies (irregular deviations). The fundamental aspects of Earth’s pole oscillation process are investigated, which allows qualitatively explaining the observed irregular effects in the oscillatory process. The results of numerical modeling of Earth’s pole coordinate oscillations are compared with the observation and measurement data of the International Earth Rotation and Reference Systems Service (IERS).

A new shimmy model

Shimmy is a phenomenon of intense angular self-excited vibrations of the wheels of a carriage. Such self-excited vibrations present a serious threat to traffic safety, which accounts for the great interest of researchers in this phenomenon. The problem is of highest importance for the front wheels of aircraft. Usually, the deformation of pneumatic tires is considered to be the main factor responsible for shimmy. Without challenging this thesis, we nevertheless note that this is not the only factor. The shimmy phenomenon can be observed in everyday life in the case of various carriages that often have nothing to do with pneumatics if the wheels are rigid. Below we will show that the theory of polycomponent dry friction fully explains the shimmy phenomenon for absolutely rigid wheels and, hence, is at least one of the factors responsible for shimmy in the general case. The reason why researchers have not taken dry friction into account when explaining shimmy is that the theory of this kind of friction has not been well developed; at the same time one has failed to explain shimmy in the framework of other existing theories.

A new model of shimmy

Shimmy is the phenomenon of intensive angular self-excited vibrations of a vehicle wheel. Such self-excited vibrations seriously threaten the safety ofmotion, which explains scientists’ profound interest in this phenomenon. This problem is most serious for the front wheels of aircraft. Tyre deformation is usually viewed to be the main cause of shimmy. Without casting doubt on this point, we still note that this is not the only cause. The shimmy phenomenon can also be observed in everyday life and for various hand carts, where any reference to tyre elasticity is most often irrelevant if the wheels are rigid.We show that the polycomponent dry friction theory can completely explain the shimmy phenomenon for absolutely rigidwheels and hence polycomponent dry friction is at least one of its causes in the general case.Dry friction has been neglected by scientists when explaining shimmy because dry friction theory has not been sufficiently well developed until recently; at the same time, shimmy cannot be explained in the framework of earlier conceptions.

Mechanical model of the perturbed motion of the earth with respect to the barycenter

A mechanical model of pole oscillations that fits the current views and the International Earth Rotation Service (IERS) data is constructed. The gravitational tidal torques due to the Sun and the Earth allowing for viscoelastic deformation of the Earth are considered to be the main perturbing factors. A bestfit, sixpara� metric mathematical model that takes into account the trend, annual oscillations, and Chandler oscilla� tions is constructed based on the IERS data using the spectral and dispersion analysis of a fairly complicated oscillation process. Major oscillation characteristics are determined using massive calculations. The inter� polation algorithm has been tested over long time scales, in particular, from 2000 through 2012. Algo� rithms for longscale prediction of oscillations at intervals of 60-900 days are proposed. 1. The dynamical theory of the rotation of the Earth with respect to the barycenter underlies many astrometric studies (1-5). It is known from astronom� ical observations (since the second half of the 19th century or, possibly, far back in the past) that the Earths rotation axis changes its orientation over time with respect to both the body coordinate system and the inertial coordinate system. This implies that the poles and latitudes evolve within noticeable ranges over a year. Measurements indicate that components with strongly different frequency and amplitude character� istics are involved in the very complicated oscillation process. Thus, small oscillations of the angular veloc� ity vector in a specific Earthfixed coordinate system (the reference system) contain the major component with an amplitude that reaches 0.20