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PL
W artykule przedstawiono dodatkowe kryteria wytrzymałościowe, decydują- ce o bezpieczeństwie zestawów kołowych pojazdów trakcyjnych oraz tocznych. Kryteria te obowiązują dla przeprowadzonego prawidłowego montażu zestawu kołowego. Przedstawiono aktualny stan wiedzy na temat drgań skrętnych oraz giętnych zestawu kołowego. Omówiono również kryteria, decydujące o wytrzymałości statycznej i zmęczeniowej złącza wtłaczanego.
EN
In paper we investigated the influence of geometry imperfections on coupled flexural-torsional vibrations in the transient states, at start-up, in rotating systems. Consideration was given to two types of errors: the permanent deflection of a shaft in place of rotors installation (shaft bow) and inclination of a rotor plane with respect to the designed axis of rotation of the machine (angular misalignment). Used was the specialist Simulink library developed by the authors.
EN
The flexural vibration stability of a coupled double-walled viscoelastic carbon nanotube conveying a fluid based on the Timoshenko beam (TB) model is investigated. The coupled system is surrounded by an elastic medium which is simulated as Pasternak foundation. Van der Waals (vdW) forces between the inner and outer CNTs are taken into account based on the Lenard-Jones model. Using small scale theories, Hamilton’s principle and applying two dimensional (2D) magnetic field higher order governing equations are derived. The differential quadrature method (DQM) is applied to solve partial differential equations and investigate natural frequency of the system. The effects of viscoelastic constant, magnetic field with variable magnitudes and surface stresses on natural frequency of the structure are demonstrated in this study.
EN
In this paper the free in–plane flexural vibration of a thin ring with elastic foundation of a Winkler type is analysed on the basis of the analytical and numerical methods. Mathematical model of the three–parameter elastic foundation is proposed. The separation of variables method is used to obtain the general solution of the considered system free vibration. Then the eigenvalue problem is solved by using the finite element method. Natural frequencies and normal modes of the system vibration are determined. The achieved results of calculation are discussed and verified by experimental data. FE model is formulated by using ANSYS software. It is important to note that the problems discussed in the paper bring practical advice for engineers dealing with dynamics of circular ring systems like aviation gears and railway wheels, respectively.
PL
W pracy analizowane są drgania giętne w płaszczyźnie cienkiego pierścienia współpracującego z podłożem sprężystym typu Winklera, w oparciu o metody analityczne i numeryczne. Zaproponowano trzyparametryczny model matematyczny podłoża sprężystego. Zagadnienie drgań własnych układu rozwiązano metodą rozdzielenia zmiennych. Następnie wykorzystując metodę elementów skończonych, rozwiązano zagadnienie własne omawianego układu. Otrzymane rozwiązania zweryfikowano badaniami doświadczalnymi. Wymagane modele MES opracowano w środowisku obliczeniowym ANSYS. Warto podkreślić, że omawiane w pracy zagadnienia mogą być pomocne inżynierom, zajmującym się obliczeniami dynamiki układów kołowych (kół zębatych, kół kolejowych).
5
Content available remote Natural vibrations of thick circular plate based on the modified Mindlin theory
EN
Outline of the modified Mindlin theory is presented in which the Mindlin mathematical model with three differential equations of motion for total deflection and rotations is decomposed into a single equation for pure bending vibrations with transverse shear and rotary inertia effects and two differential equations for in-plane shear vibrations. The governing equations are transformed from orthogonal to polar coordinate system for the purpose of circular plate vibration analysis. The fourth order differential equation of flexural vibrations is split further into two second order equations of Bessel type. Also, the in-plane shear differential equations are transformed to Bessel equation by introducing displacement potential functions. The exact values of natural frequencies are listed and compared with FEM results.
EN
Purpose: The vibration characteristics of flexural vibration disk in ultrasonic honing system were studied systematically through experiments. Design/methodology/approach: The vibration of flexural vibration disk was tested using the acoustic system of ultrasonic honing. Findings: The results showed that the amplitude of vibration disk increases with the reducing of its thickness, when the disk was thin disk (the ratio between the thickness and radius was less than or equal to one fifths) the vibration of disk was flexural vibration, the good vibration effect could be obtained. The maximal amplitudę could reach 20.5μm,at the same time, the number of the wave crests and size could be obtained. There exist amplifying characteristics in the vibration of the disk. When the diameter of disk was not changed, the resonant frequency would decrease with the reducing of the thickness of disk. The resonance could be excited at different frequencies. The corresponding maximal amplitude value provides certain reference value for the dimensional design and application of flexural vibration disk. Research limitations/implications: From analysis, the ratio between diameter and thickness of flexural vibration disk has direct effect on amplitude. The rational diameter and thickness of flexural vibration disk should be selected according to specific machining conditions and the size requirements of the whole honing equipment during the course of design of ultrasonic honing acoustic system. Originality/value: The studied on relationship between geometric dimensions of flexural vibration disk and its vibration characteristics were made.
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