Простийпошук |
Розширенийпошук |
Покажчики
|
Професійний пошук |
Рубрикатор НБУВ |
Розподілений пошук |
Бази даних
Наукова періодика України - результати пошуку
Книжкові видання та компакт-дискиЖурнали та продовжувані виданняАвтореферати дисертаційРеферативна база данихНаукова періодика УкраїниТематичний навігаторАвторитетний файл імен осіб
 |
Для швидкої роботи та реалізації всіх функціональних можливостей пошукової системи використовуйте браузер "Mozilla Firefox" |
|
|
Повнотекстовий пошук
| Знайдено в інших БД: | Реферативна база даних (3) |
Список видань за алфавітом назв: Авторський покажчик Покажчик назв публікацій  |
Пошуковий запит: (<.>A=Olshanskiy V$<.>) | |||
|
Загальна кількість знайдених документів : 3 Представлено документи з 1 до 3 |
|||
| 1. | 
Olshanskiy V. On Free Oscillations of a Quadratic Nonlinear Oscillator [Електронний ресурс] / V. Olshanskiy, S. Olshanskiy, M. Slipchenko // Ukrainian journal of mechanical engineering and materials science. - 2017. - Vol. 3, Num. 2. - С. 1-10. - Режим доступу: http://nbuv.gov.ua/UJRN/ujmems_2017_3_2_3 A free oscillations of a system with one degree of freedom, caused either by the initial deviation from the stable equilibrium position or by the initial velocity provided by the oscillator in this position was considered. Analytical solutions of the nonlinear Cauchy problem for a second-order differential equation were constructed. The solutions are expressed in terms of Jacobi's periodic elliptic functions relating to occultation of special functions. Compact equals are derived for calculating the displacements of the oscillator and the oscillation periods for various methods of motion perturbation and for various variants of the elastic characteristic. The restrictions on the initial excitations for an oscillator with a soft elastic characteristic are determined, when its free oscillations are possible. The existence of a solution of the nonlinear dynamics problem in elementary functions is established. The behavior of an oscillator with a soft characteristic of elasticity under conditions of its freezing are studied. It is shown that from the derived equals, as special cases, the results known in the theory of linear oscillators, as well as oscillators with a purely quadratic nonlinearity, without a linear component, follow when the solution of the problem can be expressed in terms of Ateb-functions. The aim of the work was to derive new calculation equals for determining the displacements of a mechanical system with one degree of freedom under conditions of free oscillations, in the absence of friction. To achieve this objective, the representation of the second integral of the differential equation of motion due to the incomplete elliptic integral of the first kind were used. Using the known tables of the indicated integral, examples of calculations are given in which the probability of the derived equals is confirmed. According to the results of the study, it is also established that in the case of a quadratic elasticity characteristic of the linear component, the motion of the oscillator is described by the periodic elliptic Jacobi function, both in providing it with an initial deviation from the stable equilibrium position, and giving it the initial velocity in this position. In the case of a soft elasticity characteristic, free oscillations are possible only with certain restrictions on the initial perturbations of the system. | ||
| 2. |
Olshanskiy V. Free Oscillations of an Oscillator with Nonlinear Positional Friction [Електронний ресурс] / V. Olshanskiy, V. Burlaka, M. Slipchenko // Ukrainian journal of mechanical engineering and materials science. - 2018. - Vol. 4, Num. 2. - С. 50-57. - Режим доступу: http://nbuv.gov.ua/UJRN/ujmems_2018_4_2_7 The variations of a system with one degree of freedom in the presence of nonlinear positional friction were considered. The restoring force of the oscillator's elasticity is described by the power function. A nonlinear solution of the Cauchy problem for the case of a power nonlinearity of positional friction were constructed. It is expressed through known periodic Ateb functions, which in recent years have become widespread in the theory of oscillations thanks to the efforts of the Lviv School of Mathematics and Mechanics. Formulas for calculating the displacements of the oscillator in time, as well as the amplitudes and periods of oscillations caused by the initial deviation of the system from the equilibrium position or the initial velocity given to the oscillator in this position were derived. The analytical dependence of the oscillation periods on the amplitude for cases of soft and rigid characteristics of the elastic system was established. It was found that due to the non-linearity of the damping of the system of the amplitudes, it leads to a change in the period of the oscillations of the system during its motion. The period may decrease or increase with oscillation, depending on the value of the indicator of non-linearity in the expression of the restoring force. It is shown, that from the obtained analytical solutions, as separate cases, there were known formulas related to free nonlinear oscillation oscillators without friction or with linear position friction. In order to simplify the using of the obtained solutions, we recommend well-known approximations of the Ateb-functions with the help of elementary functions. Examples of calculations are presented, where comparison of the results obtained with the use of constructed analytical solutions and numerical integration of the equation of oscillation on a computer is carried out. The good consistency of numerical results obtained in different ways is noted. | ||
| 3. |
Olshanskiy V. Solution of the equation of force of impact of solids expressed by the Ateb-sine [Електронний ресурс] / V. Olshanskiy, V. Burlaka, M. Slipchenko // Ukrainian journal of mechanical engineering and materials science. - 2019. - Vol. 5, Num. 2. - С. 53-60. - Режим доступу: http://nbuv.gov.ua/UJRN/ujmems_2019_5_2_8 A nonlinear differential equation of the force of direct central quasistatic impact of elastic bodies bounded in the area of their contact by rotation surfaces is compiled. To determine the coefficients of the equation and the order of its degree nonlinear force, we used the well-known solution of the axisymmetric contact problem of elasticity theory, constructed in due time by I. Ya. Shtaerman, for the case of dense static contact of bodies, when the order of their boundary surfaces is not lower than the second. In the case of the second order, it goes into the well-known static solution of G. Hertz, whose assumption in the theory of shock is also taken here in the formulation of the dynamics problem. A closed analytic solution of the composite differential equation with respect to the force of impact as a function of time is constructed. It is expressed through Ateb-sine. This function also describes the process of motion of the centers of mass of bodies in the stages of their compression and expansion. Compact formulas are derived for calculating the maximum values of the impact force, the approach of the centers of mass of the bodies and the duration of the impact. Thanks to the use of the Ateb-sine and its approximation by elementary functions, it was possible to obtain a fairly simple scan of the fleeting process of mechanical shock in time. It is shown that well-known dependencies that describe the impact of elastic balls follow from the derived formulas. Examples of calculations are given in which the influence of various factors on the main characteristics of the impact is investigated. It is noted that the theory set forth concerns only the impact of bodies with low velocities, when plastic deformation does not occur during their dynamic compression. To extend the theory beyond the limits of elasticity, it is necessary to determine a constant for the stage of compression in the impact force equation not by calculation, but by experimental method. Then, during compression and decompression of bodies, the impact force will be described by different analytical expressions, and the speed recovery coefficient will become less than one, which is consistent with practice. | ||
Попередній перегляд: 
Реферативна БД
 |
| Відділ наукової організації електронних інформаційних ресурсів |
 Пам`ятка користувача |