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EN
In this article, the problem of the free vibration behavior of a cantilever Euler-Bernoulli beam with various non-classical boundary conditions, such as rotational, translational spring, and attached mass is investigated. For describing the differential equation of the system. An analytical procedure is proposed firstly, and a numerical method based on the differential transform method DTM is developed in order to validate the obtained results. A parametric study for various degenerate cases is presented with the aim to analyze the influence of rotational stiffness, vertical stiffness, and mass ratio on the free vibration response of the beam, particularly on its modal characteristics. The results show that the non-classical boundary conditions significantly affect the natural frequency and mode shapes of the studied beam system in comparison to the case of a classical boundary conditions such as Simply supported, clamped-clamped, etc. The comparison between the obtained results based on the proposed analytical solution and numerical scheme, and those available in the literature shows an excellent agreement.
EN
In this paper, the dynamic behaviour of the tensegrity domes is explored. The consideration includes all cable structures called Geiger domes, i.e., two cases of configurations (with a closed and open upper section) and two variants of the nature of a dome (regular and modified) are taken into account. Particularly, the impact of the number of girders on the natural frequencies is analysed. A geometrically quasi-linear model is used, implemented in an original program written in the Mathematica environment. The results confirm that the number of girders affects the number of infinitesimal mechanisms. However, the dynamic behaviour does not depend on the number of mechanisms. The most important is the nature of a dome and the type of load-bearing girder. Especially, the behaviour of Geiger domes with a closed upper section is specific. In this case, not only the frequencies corresponding to the infinitesimal mechanisms depend on the prestress. There are additional frequencies that depend on prestress. The number of them, and the sensitivity on the initial prestress changes, depends on the number of girders. Generally, for the same number of girders, the natural frequencies of regular domes are higher than for the modified ones.
PL
W artykule zbadano zachowanie dynamiczne kopuł Geigera. W sposób szczególny przeanalizowano wpływ liczby dźwigarów nośnych na częstotliwość drgań własnych. Analizie poddano dwa typy dźwigarów nośnych tj. z zamkniętą (typ A) oraz otwartą (typ B) górną częścią dźwigara. Dodatkowo wzięto pod uwagę dwa typy geometrii kopuły (zwykłą i zmodyfikowaną). Przedstawione rozważania odpowiadają na następne pytania tj. czy jest możliwa kontrola liczby mechanizmów poprzez zmianę liczby dźwigarów nośnych? Jaki typ kopuły (zwykła czy zmodyfikowana) jest łatwiejszy do kontroli? Czy zachowanie kopuł z taką samą liczbą mechanizmów infinitezymalnych jest podobne? Czy liczba częstotliwości drgań własnych, zależnych od wstępnego sprężenia, jest równa liczbie nieskończenie małych mechanizmów? Analiza potwierdziła, że liczba dźwigarów nośnych ma wpływ na liczbę nieskończenie małych mechanizmów. Jednak zachowanie dynamiczne kopuł zależy głównie od geometrii kopuły oraz od typu dźwigara nośnego, a nie od liczby mechanizmów.
EN
The functionally graded plates (FGP) with two new porosity distributions are examined in this paper. In this work the plate is modeled using the higher-order shear deformation plate principle. The shear correction variables are neglected. To evaluate the equations of motion, the Hamilton method will be used herein. Therefore, the free vibration analysis of FG plate is developed in this work. For porous smart plates with simply-supported sides, natural frequencies are obtained and verified with the established findings in the literature. The impact of the porosity coefficient on the normal frequencies of the plate for various thickness ratios, geometric ratios, and material properties was investigated in a thorough numerical analysis.
EN
In this paper, the effects of plane pre-stresses on the free vibration and static analyses of circular and annular sandwich panels are examined based on an accurate formulation, as first time. It is assumed that initially pre-stresses consist of in-plane normal (tensile/compressive) and pure bending stresses. New first-order shear deformation theory together with a layerwise approach for sandwich panel is utilized. The sandwich panels are made up of either orthotropic or heterogeneous polar orthotropic materials. Furthermore, piecewise-defined linear local in-plane displacements are adopted based on zigzag theory. The governing partial differential equations are extracted by implementing principle of minimum total potential energy. A unified analytical solution procedure is developed based on power series method for the analysis of heterogeneous initially stressed annular and circular sandwich panels with arbitrary boundary conditions. The transverse shear stress is precisely calculated by considering three-dimensional theory of elasticity. To validate the proposed formulation, the obtained results are compared with those of finite element method. After numerically demonstrating the accuracy of the method, the effects of different geometrical and material parameters, boundary conditions and in-plane pre-stresses on the free vibration and static behavior of circular and annular sandwich panels are investigated.
EN
The concrete structures under impact loading duress may be destroyed within an extremely short period of time. The importance and complexity of exploration on the impact resistance of concrete members make this area still open for discussion. In the present study, a 3-D mesoscale numerical model was established to investigate the effect of the combination of impact mass and velocity on the mechanical behavior of reinforced concrete (RC) beams subjected to impact loadings. Heterogeneity of concrete and strain rate effects of concrete and steel bars were taken into account. Furthermore, nonlinear interaction between the concrete and steel bars was considered herein. Results from macroscale and mesoscale simulation were compared with the available physical tests, indicating that the mesoscale numerical model can better represent the influence of heterogeneity of concrete on the mechanical behavior of RC beams. Five different impact energy levels were involved to study the effect of the combination of impact mass and velocity on the impact resistance of RC beams. At last, the residual bearing capacity and natural frequency of impacted RC beams were numerically calculated and their relationship was discussed. It is indicated that the deformation of RC beams is influenced strongly by the impulse, which increases with the increasing impact mass at identical impact energy. Besides, the failure mode of RC beams turns from shear-dominant failure mode to bending shear failure mode with the increase of impact mass, accompanied by the increase of energy dissipation of steel bars and the whole member. Despite this, in the present work, the combination of the impact mass and velocity had little influence on the damage extent (based on the performance) of the RC beams. Moreover, an empirical relationship between the residual bearing capacity and the natural frequency of the impacted RC beams was established as a rough reference for damage evaluation in engineering practice.
EN
An N1 vehicle model is created, which allows for changing suspension parameters and conditions of experimental performance. A methodology of computer testing performance for vehicle ride comfort and stability service properties’ characterization in a virtual environment is proposed. Vehicle suspension system modelling and simulation are performed. The results of the N1 vehicle suspension system from full-scale laboratory and road tests are given.
8
Content available Spring-loaded batcher
EN
On the base of the analysis of the application of vibration mechanisms in the motor transport vehicles, considering the possibilities of fuel injection systems, the study presents survey of possibilities the usage of the devices micro-dosing and spraying apparatus, the construction and the principle of the operation of vibration-assisted spring-loaded batcher, the necessary for its functioning vibration operation forms and the dependences of measured fuel amount on the leakage chamber width and how it is related to vibration frequency and amplitude. The results of mathematical modeling and experimental analysis based on laser holographic interferometry are presented.
PL
W pracy przedstawiono analizę dynamiczną kompozytowej konstrukcji cienkościennej o przekroju zamkniętym prostokątnym, o różnych schematach statycznych. Do analizy wykorzystano modele powłokowe i odpowiadające im uproszczone modele prętowe. W modelach powłokowych uwzględniona została ortotropia materiału kompozytowego i różne warianty ułożenia włókien nośnych w poszczególnych warstwach. W modelach belkowych dokonano homogenizacji materiału uzyskując materiał izotropowy o średniej sztywności zastępczej. W analizie uwzględniono dodatkowe usztywnienia w postaci przepon wewnętrznych. Analizowano częstotliwości własne i odpowiadające im postacie drgań. Zbadano jaki wpływ na wyniki ma kąt orientacji włókien w warstwach, smukłość belki i schemat statyczny oraz porównano wyniki otrzymane dla modeli powłokowych z wynikami otrzymanymi dla uproszczonych modeli prętowych.
EN
The paper presents a dynamic analysis of closed thin-walled (CTW) section composite structures with different boundary conditions. Analysis is carried out with a use of shell models and corresponding simplified beam models. The shell models include orthotrophy of the composite material and different fiber orientation angles in laminas. In the beam models the material is homogenized and treated as isotropic with mean material properties. The numerical analysis is also performed for the same beam with added internal diaphragms. The results are presented in the form of natural frequencies and corresponding mode shapes. The effects of the boundary conditions, fiber angle and slenderness are studied. The results obtained for the shell models are compared with those for the simplified beam models.
EN
Due to the advanced lightweight characteristic of sandwich structures, ambient air can significantly affect their natural frequency. In order to clarify the importance and magnitude of this effect, the natural frequency of a sandwich panel surrounded by air layers using experiment and numerical simulation was investigated in this study. The experiment setup based on modal testing was proposed with the feature of simulating air layers around the sandwich panel. The numerical simulation was formulated on the basis of fluid–structure interaction analysis. The experimental and numerical simulation results correspondingly demonstrated that the fundamental natural frequency of sandwich panel tends to decrease to be less than 25% of the frequency neglecting the air effect when the air layer thickness becomes thinner than 3 mm.
EN
The article describes application of selected methods of technical diagnostics for assessing the operating status of precision gearboxes. Within the confines of experimental measurements in the field of physical metallurgy materials of diagnosed system were being examined while taking into account the process of degradation of material properties during operation of monitored gearboxes. Measurements and collecting of dynamic data were realized on 4 selected gearboxes where a high-frequency vibrations and acoustic emission (noise) measurements were carried out. Retrieved values were subsequently used for mutual correlation and verification of applied methods. Results of both selected methods underlined unsatisfactory operation status with 3 inspected gearboxes. Measured values were identified as being above suggested caution limit of Alarm 2, representing a level of danger.
12
Content available remote Parametric Study on Thick Plate Vibration Using FSDT
EN
The prime objective of the research is to investigate the influence of various structural parameters like aspect ratio, boundary condition, size of cut-out etc. on the free vibration frequencies of a thick rectangular plate. Plates being one the most common structural elements has always enticed the interest of many researchers towards this problem. In here a general first order shear deformation theory (FSDT) is used to analyse the free vibration behaviour of rectangular isotropic plates. A finite element program has been developed using 9 node isoparametric element. A number of numerical examples are presented here. Two different sets of mass lumping scheme are considered to carry the analysis using and without using rotary inertia. The definite advantage of this work over other similar works done by using FEM pakages is its exceptional accuracy. At most the error calculated for convergence study with published literature is 1%.
PL
Poziom emitowanych przez maszynę drgań staje się podstawą do wykorzystania ich w diagnostyce maszyn. Jej skuteczność polega na systematyce, dzięki której można zaobserwować zmieniający się w czasie trend wynikający z pogarszającego się stanu urządzeń. Stosując diagnostykę drganiową umożliwiamy zatem prowadzenie gospodarki remontowej uwarunkowanej wyłącznie stanem maszyny.
RU
На примере модели тягового привода локомотива в режиме боксования показано, каким образом могут быть учтены электромагнитные переходные процессы в тяговом двигателе при использовании метода энергетического баланса для оценки устойчивости системы по отношению к фрикционным автоколебаниям. Построены области существования фрикционных автоколебанийв пространстве параметров привода. Предлагаемый метод может быть использован для анализа устойчивости широкого класса динамических систем с малой диссипацией, содержащих как колебательные, так иинерционные звенья.
EN
On the model of a locomotive traction drive in a slipping mode, it is demonstrated how the electromagnetic transient processes in the traction motor may be accounted for using the energy balance method for assessing the stability of the system with respect to frictional self-oscillations. The regions of existence of frictional self-oscillations in the parameter space of the drive are built. The proposed method differs from the prior art in that it can be used to analyze the stability of a wide class of dynamical systems with small damping, containing both oscillatory and inertial units.
EN
The paper analyses the influence of the stiffness of the elastic support of the stepped column on the natural vibration frequency and the critical load values. The exact stability analysis and dynamic analysis using a continuous mass distribution were carried out. The safe areas and the natural frequency for different column support conditions were determined.
EN
The present paper deals with the experimental studies carried out on free vibration of isotropic and laminated composite skew plates. The natural frequencies were also determined using QUAD8 finite element of MSC/NASTRAN and a comparison was made between the experimental values and the finite element solution. The effects of the skew angle and aspect ratio on the natural frequencies of isotropic skew plates were studied. The effects of the skew angle, aspect ratio, fiber orientation angle and laminate sequence (keeping the number of layers constant) on the natural frequencies of antisymmetric composite laminates were also studied. The experimental values of natural frequencies are in good agreement with the FE solutions. The natural frequencies are found to increase with an increase in the skew angle. The variation of natural frequencies with the aspect ratio is small and negligible both for isotropic and laminated composite skew plates.
EN
The stiffness and the natural frequencies of a rectangular and a V-shaped micro-cantilever beams used in Atomic Force Microscope (AFM) were analysed using the Finite Element (FE) method. A determinate analysis in the material and dimensional parameters was first carried out to compare with published analytical and experimental results. Uncertainties in the beams’ parameters such as the material properties and dimensions due to the fabrication process were then modelled using a statistic FE analysis. It is found that for the rectangular micro-beam, a ±5% change in the value of the parameters could result in 3 to 8-folds (up to more than 45%) errors in the stiffness or the 1st natural frequency of the cantilever. Such big uncertainties need to be considered in the design and calibration of AFM to ensure the measurement accuracy at the micron and nano scales. In addition, a sensitivity analysis was carried out for the influence of the studied parameters. The finding provides useful guidelines on the design of micro-cantilevers used in the AFM technology.
EN
The vibration characteristics of stiffened plates with cutouts subjected to in-plane partial edge loadings at one end at the plate boundaries are studied using the finite element method. Buckling loads and vibration frequencies are determined for different cutout ratios and extent of partial edge loading at one end. In the structural modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The main elegance of the formulation lies in the treatment of the stiffeners. The stiffeners can be placed anywhere within the plate element, and need not be placed on the nodal lines. The vibration characteristics are discussed and the results are compared with those available in the literature. Numerical results are presented for a range of cutout to plate size from 0 to 0.8.
19
Content available remote Tests of local vibration in the node of a truss bridge
EN
The paper describes results of dynamic tests of a truss railway bridge. Placement of the sensors (accelerometers and tensometers) allowed detection of local vibration patterns in a node being subject to the tests. In addition that placement of deflection sensors made possible recording of main natural frequency in the tested bridge. Prevailing part of the identified vibration frequency was near the theoretically obtained natural frequencies of the structure which proves that the properly planned and conducted dynamic tests can be a good basis for verification and qualitative analysis of theoretical models.
PL
W referacie opisano wyniki badań dynamicznych dźwigara kratowego mostu kolejowego. Zastosowany w czasie badań sposób rozmieszczenia akcelerometrów i tensometrów elektrooporowych zapewnił ujawnienie lokalnych postaci drgań w badanym węźle kratownicy. Natomiast zastosowany w czasie badań sposób rozmieszczenia indukcyjnych czujników przemieszczeń umożliwił zarejestrowanie podstawowych częstotliwości drgań własnych w badanym przęśle. Zdecydowana większość ze zidentyfikowanych częstości drgań odpowiada wyznaczonym teoretycznie częstotliwościom drgań własnych konstrukcji. Tak przeprowadzone badania dynamiczne dają więc dobrą podstawę do weryfikacji i analizy jakościowej teoretycznych modeli obliczeniowych.
EN
The paper gives general procedures for development characteristics frequencies in a simple and elaborate gearbox systems. The gearboxes systems may consists of compound and complex gear- boxes. The gearbox classification for compound and complex gearboxes is presented. The complex systems consists of planetary gearboxes. Three different planetary gearboxes are considered. These three types of planetary gearboxes are used in driving systems for mining machinery like bucket wheel excavators, shearers. The introduction to frequency characteristic development is presented. The characteristic frequencies are: sequence of recurrent excitations for short recurrent frequencies, meshing frequencies, shaft frequencies, local fault frequencies.
PL
W pracy przedstawiono procedurę znajdowania charakterystycznych częstotliwości w prostych i złożonych układach przekładni zębatych. Przekładnie mogą tworzyć złożone i zespolone przekładnie. Przedstawiono sposób klasyfikacji przekładni złożonych i zespolonych. Zespolone przekładnie tworzą przekładnie planetarne. Trzy różne przekładnie planetarne są rozpatrywane. Te trzy rodzaje przekładni planetarnych są stosowane w koparkach kołowych i w kombajnach węglowych. Przedstawiono wprowadzenie do wyznaczania częstotliwości charakterystycznych. Przedstawiono charakterystyczne częstotliwości, takie jak: częstotliwość powtarzania się sekwencji spotykania się tych samych zębów, częstotliwości zazębienia, częstotliwości obrotów wałów, częstotliwości uszkodzeń lokalnych.
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