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EN
With the continuous development of railway systems in China, the speed grades of trains have been consistently elevated, and the electrification of railways has become increasingly widespread. Consequently, higher requirements have been placed on the safety of electrified railway operations. However, during actual operation, pantograph-catenary failures occur frequently, disrupting current collection and affecting normal train operation. Particularly in the case of newly constructed tunnels employing rigid catenary systems, it is essential to consider the impact of pantograph-catenary dynamic interactions on cantilever type supporting devices. Through finite element analysis of the cantilever assembly, the regions of maximum stress and strain, as well as areas susceptible to fatigue, were identified. Vibration characteristics and modal analysis were also conducted. The results indicate that fatigue-prone failure points in the rigid catenary system are primarily concentrated at the elastic clamps and rotating base. By reinforcing the material of these components to achieve sufficient strength and increasing the vibration frequency, the torsional vibration mode of the cantilever assembly was significantly improved. Furthermore, the addition of a leaf spring structure to the clamp assembly demonstrated excellent shock absorption and energy dissipation effects, thereby further enhancing the stability of the reinforced components.
EN
Corrosion, particularly in marine and offshore environments, often leads to material loss and surface irregularities that compromise structural integrity. Traditional non-destructive testing methods, such as ultrasonic thickness measurements, are limited in regard to detecting widespread or irregular corrosion damage. This study explores the use of vibration-based analysis to assess the effects of corrosion by examining changes in the dynamic behaviour—specifically, the natural frequencies—of steel plates. Numerical simulations are conducted using Abaqus that include random surface irregularities, modelled with Gaussian random fields, to represent generalised corrosion. Experimental validation involves steel plates subjected to accelerated electrochemical corrosion, with degradation assessed based on mass loss and ultrasonic thickness measurements. Changes in modal parameters due to progressive corrosion are recorded using impact hammer excitation and accelerometers. The results show a clear relationship between corrosioninduced thickness reduction and shifts in modal characteristics. The findings demonstrate that modal analysis offers a viable, non-invasive method for detecting and evaluating global corrosion damage in large-scale steel structures.
PL
Konstrukcje stalowe są poddawane dużym obciążeniom dynamicznym, co znajduje wyraźne odzwierciedlenie w generowanych procesach drganiowych. Drgania te mogą wpływać na stan użytkowalności konstrukcji poprzez obniżenie komfortu osób w niej pracujących, jak również mogą osiągać poziom zagrażający bezpieczeństwu konstrukcji. Wpływ drgań na konstrukcję objawia się głównie dodatkowymi naprężeniami w danym przekroju, które sumują się z naprężeniami wynikającymi z obciążeń statycznych. Obciążenia dynamiczne mogą powodować szkodliwe skutki w budynkach o różnych typach konstrukcji, a nawet prowadzić do ich zniszczenia. Uznając konieczność doskonalenia metod oceny jakości konstrukcji budowlanych na potrzeby szacowania ich stanu oraz współczynników bezpieczeństwa dla konstrukcji stalowych, autorzy niniejszej pracy podjęli próbę zbadania procesu niszczenia wybranego obiektu metodą eksperymentalnej analizy modalnej.
EN
Steel structures are subject to large dynamic loads clearly reflected by generated vibration processes. The vibrations may affect state of serviceability of structures by lowering comfort of persons working there as well as possible reaching the level hazardous to safety of the structures. The effect of vibrations to structure is mainly manifested by additional stresses in a given cross-section, which are summed up with those resulting from static loads. The dynamic loads may cause damaging effects in buildings of various structural types or even lead to their destruction. Judging the necessity of improving the quality assessment methods of building structures for purposes of estimation of their state as well as safety factors for steel structures, the authors of this work undertook an attempt to investigate destruction process of selected object by using the method of experimental modal analysis.
EN
In the paper, the formulated Weibull vibration reliability methodology is based on the cumulative vibration damage analysis. It lets us determine the reliability index of each damage element, each damage block, and the reliability of the analyzed element. Vibration damage is cumulated until 𝐷 = 1 , by using the addressed vibration stress and a nonlinear cumulative damage model. Based on static and modal analysis, the vibration stress is determined by incorporating to it, the geometry, weight and resonance effects. In the reliability analysis the Weibull shape (𝛽) parameter is determined directly from the number of damage blocks, for which 𝐷 = 1 . The damage element, damage block, and element reliability are all determined based on the beta (𝛽) value and 𝐷𝑖 elements. Finally, based on the cumulated applied cycles 𝑛𝑖 the Weibull scale (𝜂𝑖 ) parameter is determined by each 𝐷𝑖 elements, damage block, and analyzed element.
EN
Throughout the operational lifecycle of centrifugal pumps, cavitation is an omnipresent phenomenon that frequently leads to cavitation erosion and a decline in hydraulic heads, leading to mechanical failures and substantial damage to the pump assembly. Although the cavitation phenomenon has been widely studied in existing literature, it is still a challenging task for reliable flow dynamics analysis of centrifugal pumps using the modal order reduction technique. In this study, the modal decomposition and reconstruction of the flow field of a centrifugal pump considering the cavitation are conducted. The dynamic modal decomposition (DMD) based on the singular value decomposition (SVD) is employed to explore the dynamic behaviour of the cavitation flow field by reducing the modal order of the flow field. Then, the modal characteristics of the pump flow field are systematically analyzed. The results demonstrate that the DMD method can improve the accuracy of the order reduction model and reduce the modal reconstruction error, the reconstruction error loss is less than 5%, and the calculation efficiency is significantly enhanced to analyze the pump cavitation flow field. In addition, a comparison of the calculation data between the finite element simulation and the DMD reconstructed flow field indicates the potential application of the DMD method in investigating the degradation of the flow field due to cavitation, which provides new perspective and solid technique support for centrifugal pump cavitation analysis.
PL
W pracy przedstawiono wyniki badań eksperymentalnych mających na celu wyznaczenie wpływu częstotliwości wymuszenia drgań podstawy na zachowanie się stworzonych modeli wspornikowych oraz prostych przestrzennych modeli prętowych w celu oszacowania obszaru rezonansu. W testach wykorzystano samodzielnie zaprojektowany i stworzony stolik wibracyjny. Uzyskane wyniki zestawiono z wartościami częstotliwości drgań własnych modeli, określonych w sposób teoretyczny, z zastosowaniem wzorów analitycznych, oraz numeryczny przy wykorzystaniu analizy modalnej. Dla stworzonych modeli określono wartości częstotliwości wymuszenia, dla których w trakcie drgań konstrukcja przybierała odpowiednie formy deformacji i obserwowano negatywne efekty związane z wystąpieniem zjawiska rezonansu. Całość pracy opatrzono stosownymi wnioskami dotyczącymi wpływu zastosowanych rozwiązań konstrukcyjnych na częstotliwości drgań własnych.
EN
The paper presents the results of experimental research aimed at determining the impact of excitation frequency of base and its effect on behaviour of created cantilever models and simple spatial bar models for the purpose of estimating the area of resonance. The tests used self-designed and made vibration table. The obtained results were compared with the natural vibration frequencies determined theoretically, using the analytical equations and numerical using modal analysis. For the created models, the values of excitation frequencies were determined in which during vibrations the structure assumed the relevant forms of deformations, and the negative effects caused by the resonance was observed. The entire work was accompanied by relevant conclusions concerning the impact of the applied design solutions on the natural vibration frequencies.
EN
The resistance spot welding is one of the main methods used to join thin-walled metal parts, while a number of factors adversely affect the process and thus the quality of the connections made. This article presents the study results of the possibility of applying modal analysis in the quality examination of welded parts by detecting the missing weld. It was aimed to determine this kind welding process imperfections influence on modal shapes and frequencies by the study of the dynamic properties of welded elements in the frequency domain. The research included real and numerical tests. The proposed testing method for spot welded constructions is a scientific novelty in the world, but the investigation results indicated, that the modal analysis may find application in detecting welding defects such as the lack of the welds. To assess the quality of the numerical models, the results obtained in the simulation and experimental test results were compared. The analysis involved the first five modes. The mode shapes in relation to the first five modal frequencies identified using the FEM analyses and the experimental tests was consistent with respect to element distortion. The differences indicate the satisfactory conformity of the numerical simulation results with the experimental test results. The article fundamentally demonstrates the applicability of the above-mentioned method to analyse the performance of all welds at once.
PL
Punktowe zgrzewanie oporowe jest jedną z głównych metod stosowanych do łączenia cienkościennych elementów metalowych, przy czym szereg czynników wpływa niekorzystnie na proces, a tym samym na jakość wykonanych połączeń. W artykule przedstawiono wyniki badań możliwości zastosowania analizy modalnej w analizy jakości zgrzewanych elementów w aspekcie wykrywania brakującej zgrzeiny. Celem było określenie wpływu tego typu niedoskonałości procesu zgrzewania na postać i częstotliwości drgań własnych poprzez badanie w dziedzinie częstotliwości właściwości dynamicznych elementów zgrzewanych. Badania obejmowały testy rzeczywiste i analizy numeryczne. Zaproponowana metoda badania konstrukcji zgrzewanych jest nowością naukową na świecie, a wyniki badań wskazały, że analiza modalna może znaleźć zastosowanie w wykrywaniu wad zgrzewalniczych takich jak brak zgrzein. Skuteczna weryfikacja wykonania danej zgrzeiny w zgrzewanym elemencie zależy od wielu czynników, w tym m.in. materiału i kształtu konstrukcji, lokalizacji zgrzein, miejsca wzbudzenia i pomiaru podczas jej badania. W związku z tym każda badana geometria będzie wymagać opracowania indywidualnych założeń wymuszeń i pomiaru, natomiast ogólne założenia stosowania analizy modalnej pozostają niezmienne. W celu oceny wyników modeli numerycznych, porównano wyniki uzyskane w symulacji i wyniki badań eksperymentalnych. Analiza wykazała, iż postaci drgań własnych w odniesieniu do pierwszych pięciu częstotliwości zidentyfikowanych za pomocą analiz MES i testów eksperymentalnych były zgodne pod względem odkształceń elementów. Różnice wskazują na zadowalającą zgodność wyników symulacji numerycznej z wynikami testów eksperymentalnych, a tym samym zasadne jest stosowanie MES w opracowaniu założeń do opracowania stanowiska pomiarowego konstrukcji zgrzewanych. Artykuł zasadniczo demonstruje możliwość zastosowania wyżej wymienionej metody do analizy jakości wszystkich spoin jednocześnie.
EN
Fluid-structure interaction (FSI) significantly influences the dynamic behaviour of submerged or fluid-containing structures. The “added mass” effect lowers natural frequencies and alters mode shapes. Understanding and accurately predicting this phenomenon is crucial for the design and safety assessment of various engineering systems, from offshore structures and storage tanks to hydraulic machinery. This paper presents a detailed numerical procedure, to investigate and quantify the added mass effect on the modal characteristics of a simple cylindrical container. The methodology for setting up the coupled fluid-structure problem, inherently capturing the inertial effects of the contained water, is described. The study validates the numerical approach against experimental results, showing frequency reductions of 24-33% due to added mass, with prediction errors for primary modes below 4%. This work establishes a reliable and validated FEM-based procedure for analysing vibroacoustic phenomena due to added mass, serving as an essential foundation for future analyses of such effects in more complex geometries, such as Francis turbine runners, where precise modal characterization is critical for operational dynamics and resonance avoidance.
EN
This paper aims to perform modal and harmonic response analyses to show how the piston skirt length reacts. The studied aluminium piston was generated in CATIA CAD Software and consequentially this was simulated in ANSYS software using modal and harmonic response tools. The piston finite element model was built to predict the basic modal parameters such as: natural frequencies, vibration modes and deformations. Different grid sensitivity tests have been done to improve the accuracy of the piston model. The piston with larger skirt has shown 77% higher vibration deformations than piston with smaller skirt. The proposed methodology can be easily used by a design engineer to perform dynamic behaviour studies of moving components and assemblies in Internal Combustion engines and not only.
PL
Przedstawiono sparametryzowany, cyfrowy model pantografu pojazdu szynowego konstrukcji połówkowej. Zaprezentowano wyniki badań symulacyjnych jego dynamiki. Badania zostały przeprowadzone stosując obliczeniową analizę modalną. Obliczenia przeprowadzono modyfikując współczynniki sprężystości wybranych elementów konstrukcyjnych. Określono wartości częstotliwości drgań własnych analizowanej konstrukcji. Rezultaty symulacji porównano z prezentowanymi w literaturze wynikami badań eksperymentalnych raportami eksploatacyjnymi.
EN
The parameterised digital model of a rail vehicle pantograph. The results of simulation studies of its dynamics are presented. The tests were carried out using computational modal analysis. Calculations were carried out by modifying the elasticity coefficients of selected structural components. The values of the natural frequencies of the analysed structure were determined. The simulation results were compared with the results of experimental research presented in the literature and with operating reports.
PL
W artykule przedstawiono przykłady analiz dynamicznych i ich efektów dotyczące kilku obiektów mostowych z praktyki zawodowej autora.
EN
The design of bridge structures is mainly based on static calculations. However, in some cases – this applies in particular to railway bridges on high-speed lines or light footbridges – the scope of design calculations should be supplemented with dynamic analyses. They include theoretical modal analysis (eigenvalue problem) and time-step analysis (dynamic response of a structure). Performing a modal analysis of footbridges or railway structures is not a problem today. However, in the case of time-step analysis, software with more sophisticated numerical procedures is required to approximate the solution of the differential equation of motion. The article presents examples of dynamic analyses and their effects concerning several bridge structures from the author’s professional practice.
EN
In this contribution, the author will attempt to demonstrate the potential applicability of frequency-domain estimators in the field of modal analysis. The basics of vibration and modal analysis will be briefly summarised. In modal analysis, it is important to identify a mechanical system with a few inputs and hundreds of outputs. This requires the adaptation of frequency-domain estimators designed to handle large amounts of data in a reasonable amount of time. A practical example will be shown of truss bridge element research.
PL
Metamateriały to nowoczesne materiały o nieklasycznych właściwościach mechanicznych, optycznych, termicznych i elektromagnetycznych, które zyskują na popularności w wielu dziedzinach inżynierii. W przeprowadzonych badaniach numerycznych analizowano trzy struktury metamateriałowe o różnych kątach wewnętrznych. Wyniki pokazały, że geometria struktury ma istotny wpływ na wartość zastępczych parametrów mechanicznych. Porównawcza analiza modalna belki z segmentem metamateriałowym oraz belki pełnej wykazała znaczny spadek częstotliwości drgań własnych wywołany redukcją sztywności w obrębie segmentu. Wyniki ujawniły także lokalne drgania w strukturze metamateriałowej, które mają istotny wpływ na zachowanie się konstrukcji, co podkreśla znaczenie dalszych badań w tej dziedzinie. Metamateriały mogą przyczynić się do postępu technologicznego w różnych gałęziach inżynierii.
EN
Metamaterials are modern materials with non-classical mechanical, optical, thermal, and electromagnetic properties, gaining popularity in various fields of engineering. The conducted numerical studies analyzed metamaterial structures with different internal angles. The results showed that the geometry of structure significantly affect the values of mechanical parameters. A comparative modal analysis of a beam with a metamaterial segment and a solid beam showed a significant decrease in the natural frequencies of vibration resulting from the reduction of stiffness in the area of the segment. The results also revealed local vibrations within the metamaterial segment, which have a significant impact on the behavior of the structure, highlighting the importance of further research in this area. Metamaterials could contribute to technological advancements in various branches of engineering.
EN
This study presents an examination of the transmission properties of multilayered partitions made up of multiple micro-perforated plates (MPPs) coupled to acoustic enclosures with general impedance boundaries. Multi-layered MPPs can lower the transmission while minimizing reflection in the source and receiving enclosure. Previous research has mainly focused on the double MPPs or triple MPPs partition itself. However, it is vital to analyze the in-situ sound transmission loss of the multi-layered MPP and their efficiency in a complex vibro-acoustic environment. The case when the multilayered MPPs are coupled to a receiving enclosure or coupled to both a source and receiving enclosure is investigated. The objective is to provide an analytical method to evaluate the transmission properties of multilayered MPPs coupled to acoustic enclosures while being computationally more efficient than the finite element method (FEM). Using the modified Fourier series for the acoustic pressure, a variational form for the acoustic and structure medium yields a completely coupled vibroacoustic system. A comparison between the sound transmission loss of the double MPPs, when mounted on an impedance tube and coupled to acoustics enclosures, shows the modal effect of the enclosures. The effect of enclosure shape, impedance boundary, perforation ratio, air gap thickness on the sound transmission properties of the double MPPs structure is examined for both cases. Finally, in both situations, the performance of triple MPP structure insulation is evaluated.
EN
The purpose of this study was to investigate dynamic responses of Lenke1B+ spines of adolescent scoliosis patients to different frequencies. Methods: Modal analysis, harmonic response analysis and transient dynamics of a full spine model inverted by the finite element method using Abaqus. Results: The first-order axial resonance frequency of 4.51 Hz produced a maximum axial displacement of 30.15 mm. Comparison of the five frequencies indicated that the 10 Hz frequency response curve was smoothest, while the amplitudefrequency curve at 4 Hz showed the greatest fluctuations accompanied by resonance phenomena. At the resonance frequency, the maximum axial displacement of the thoracic spine was at T1, being 31.17 mm, while that of the lumbar spine was at L1, with 0.56 mm. The maximum stress of the intervertebral discs was located between T4 and T5, representing 3.496 MPa, the maximum stress in the small joints was located in the concavity between T7 and T8, with 19.97 MPa and the maximum axial displacement was 54.31 mm, located in the convexity between T6 and T7. Conclusions: The first-order axial resonance frequency was the most harmful to the patient. The uneven stress distribution in the spine was closely related to the degree of spinal deformity, with the thoracic spine being more sensitive to low frequencies than the lumbar spine. The concave side of the spinal deformity was more prone to stress concentrations while the convex side was more prone to deformity, indicating that disc degeneration and small-joint disease are more likely to occur at the most deformed part of the spine.
EN
The studying the dynamic response of steel-concrete railway bridges of Langer type is huge importance of ensuring the safety of such structures under high-speed train loads. Numerical simulations at the design stage require knowledge of the modal characteristics: natural frequencies, shapes and damping. In addition, in the dynamics of railway bridges subjected to high-speed trains, it is important to check the impact of dynamic effects on the ultimate and serviceability limit states. As part of the investigations displacements and accelerations of selected measurement points arising from driving the test rolling stock are analyzed. In the first stage, calculations of the eigenvalues and the corresponding eigenvectors were carried out in the Robot program for two variants of mass description (distributed and discrete). In the second stage, dynamic train passages for various vehicle speeds were examined in terms of displacements and accelerations of measurement points by using the authors’ program MES3D.
PL
Badanie odpowiedzi dynamicznej stalowo-betonowych mostów kolejowych typu Langera ma ogromne znaczenie dla zapewnienia bezpieczeństwa takich obiektów pod obciążeniem pociągów dużych prędkości. Symulacje numeryczne na etapie projektowania wymagają znajomości charakterystyk modalnych: częstotliwości drgań własnych, form i tłumienia. Dodatkowo w dynamice mostów kolejowych poddanych działaniu pociągów szybkobieżnych istotne jest sprawdzenie wpływu efektów dynamicznych na stany graniczne nośności i użytkowalności. W ramach badań analizowano przemieszczenia i przyspieszenia wybranych punktów pomiarowych powstałych od jazdy taborem próbnym. W pierwszym etapie przeprowadzono obliczenia wartości własnych i odpowiadających im wektorów własnych w programie Robot dla dwóch wariantów opisu masy (rozłożonej i dyskretnej). W drugim etapie zbadano przebiegi dynamiczne dla różnych prędkości pociągów pod kątem przemieszczeń i przyspieszeń punktów pomiarowych za pomocą autorskiego programu MES3D.
EN
The suspension hole of a gearbox case was cracked after the mining test vehicle has covered 7000 km. In order to analyze and solve this problem, in this paper, based on the modal analysis of the suspension system and failure analysis of the faulty parts, the finite ele- ment model of the powertrain system was established using Ansys, and strength analysis of the gearbox case was carried out. According to the analysis results, improvement and optimization measures were proposed. The analysis results show that the maximum stress of the optimized gearbox case was reduced by 6.9%, and the test vehicle could operate for 50 000 km without failure after the improvement, which verified the effectiveness of those measures. Accumulating experience in the gearbox case design and simulation, modal anal- ysis and finite element analysis were combined to quickly identify the failure causes of the suspension support hole, and targeted improvement measures were taken, which effectively shortened the research and development cycle and saved production costs.
EN
Based on the inverse approach and the finite element method, the quality of a reconstructed signal is discussed in this work. The responses caused by a distributed impact on a portion of a composite structure can be recovered using dynamic analysis. The structure is thought to be complex and made up of two different-sized plates made of two different materials. The robustness of the inversion method was studied, as well as the sensitivity of the numerical method compared to modal truncation and sampling of the frequency response function (FRF). Once the FRF had been identified, regularized deconvolution as per generalized singular value decomposition was used to reconstruct the impact signal characteristics. It was revealed that only one mode is required to reconstruct the impact signal.
EN
Mechanical vibrations are a common problem encountered in many machines, especially for vertical turbine pumps. These pumps are generally difficult to stiffen or damp, but the effective diagnosis must begin with an understanding of the underlying vibratory sources. In the present work, a deep well vertical turbine pump experienced extremely high vibrations for a long time although it still being new. It hasn't been in operation for over 6 months. The pump system suffers from extremely high vibration levels relative to the rotational speed (1X motor dominant frequency). An efficient strategy was implemented by using well-conceived techniques. The experimental modal analysis confirmed a presence of a natural frequency. Modifications were carried out to overcome resonance. Finite element analysis was done to determine the reed critical frequencies as a powerful tool to identify and mitigate vibration issues. On-site motor balancing was done to remove vibrations due to the residual imbalance. Results revealed decreasing vibration level by about 66% after solving all problems.
EN
The paper presents arch structures modeled by finite elements in which the nodes can be flexibly connected. Two-node curved elements with three degrees of freedom at each node were used. Exact shape functions were adopted to obtain stiffness and consistent mass matrices but they were modified by introducing rotational flexibility in the boundary nodes. Calculations of statics and dynamics of arches with different positions of flexible joints and different values of rotational stiffness of the joints were carried out.
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