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EN
A numerical computation-based analysis of the free vibration analysis of uniform beams with rectangular cross-sections is presented in this work using finite element analysis. The approach involves dividing the beam into segments at the crack section, which is then modelled for simulation for eigenfrequencies on the ABAQUS platform. The numerical simulation results are in excellent agreement with the findings of previous research, confirming the efficacy and applicability of the developed beam model. A sequential comprehensive approach towards analysis of the effects of the position and depth of the cracks on the natural frequencies are addressed in numerical results. The research findings confirm that the simulation model is suitable for the vibration analysis of beams or beam-like elements with different cross-sections.
PL
W artykule przedstawiono wyniki eksperymentów niszczących, które rzucają nowe światło na projektowanie mostów zespolonych w Polsce. Różnica między tradycyjnymi normami a nowoczesnym podejściem opartym na Eurokodzie 4 jest widoczna. Wyniki badań opisane przez autorów stanowią solidny argument za zmianą tradycyjnych praktyk.
EN
The article presents the results of destructive experiments, which shed new light on the design of composite bridges in Poland. The difference between traditional norms and a modern approach based on Eurocode 4 is evident. The test findings described by the authors provide a strong argument for changing traditional practices.
PL
W artykule omówiono sposób wyznaczania wytrzymałości resztkowych z wykorzystaniem zdolności pochłaniania energii przez fibrokompozyt. Badania przeprowadzono przez zginanie płyt o przekroju kwadratowym podpartych przegubowo na obwodzie. Określone w ten sposób wytrzymałości resztkowe cechują się znacznie mniejszym współczynnikiem zmienności niż wyznaczone wg PN-EN 14651:2007. Opisane badanie jest alternatywą dla 3-punktowego zginania belek i pozwala na wyznaczenie tej cechy z większą wiarygodnością.
EN
The article discusses the method of determining residual strength using the energy absorption capacity of fibrecomposite. The research was carried out by bending square cross-section plates simply supported at the perimeter. The residual strengths determined in this way are characterized by a much lower coefficient of variation than those determined using the normative method according to PN-EN 14651:2007. The described test is an alternative to 3-point bending of beams and allows to determine this feature with greater reliability.
EN
In this work, we present a posteriori error estimates for the Euler-Bernoulli beam theory with inexact flexural stiffness representation. This is an important subject in practice because beams with non-uniform flexural stiffness are frequently modeled using a mesh of elements with constant stiffness. The error estimates obtained in this work are validated by means of two numerical examples. The estimates presented here can be employed for adaptive mesh refinement.
EN
The study analyzed the influence of materials and different types of damping on the dynamic stability of the Bernoulli-Euler beam. Using the mode summation method and applying an orthogonal condition of eigenfunctions and describing the analyzed system with the Mathieu equation, the problem of dynamic stability was solved. By examining the influence of internal and external damping and damping in the beam supports, their influence on the regions of stability and instability of the solution to the Mathieu equation was determined.
6
Content available remote Numerical failure analysis of laminated beams using a refined finite element model
EN
In the present investigation, laminated composite beams subjected to a bending static loading are studied in order to determine their failure mechanisms and the first ply failure (FPF) load. The FPF analysis is performed using a refined rectangular plate element. The present element is formulated based on the classical lamination theory (CLT) to calculate the in-plane stresses. To achieve this goal, several failure criterions, including Tsai-Wu, Tsai-Hill, Hashin, and Maximum Stress criteria, are used to predict failure mechanisms. These criterions are implemented within the finite element code to predict the different failure damages and responses of laminated beams from the initial loading to the final failure. The numerical results obtained using the present element compare favorably with those given by the analytic approaches. It is observed that the numerical results are very close to the analytical results, which demonstrates the accuracy of the present element. Finally, several parameters, such as fiber orientations, stacking sequences, and boundary conditions, are considered to determine and understand their effects on the strength of these laminated beams.
EN
The paper deals with the active reduction of beam vibrations using piezoelectric transducers (PZT). The LQR parameters of the control of an asymmetric actuator (a-PZT) depending on the length of its arms were analysed. The results were compared to those of the symmetrical PZT (s-PZT), so far used as standard. The actuator is modeled with two bending moments or two pairs of forces. The design of the LQR controller also took into account the location of the PZT on the beam. The reduction efficiency can also be increased by using asymmetrical PZT. To obtain the vibration asymmetry of the beam, simply supported at both ends, an asymmetrically point mass was added. The LQR control was applied to an asymmetric actuator on the beam. Two-parameter optimization was used to find the optimal proportions of the a-PZT arms. For such a problem, the LQR control parameters were found, which ensure the highest efficiency of vibration reduction.
EN
This paper analyses the transverse deflection in a homogeneous, isotropic, visco-thermoelastic beam when subjected to harmonic load. The ends of the beam are considered at different boundary conditions (both axial ends clamped, both axial ends simply supported and left end clamped and right end free). The deflection has been studied by using the Laplace transform. Numerical computation of analytical expression of deflection obtained after Inverse Laplace transform has been done using MATLAB software. The graphical observations have been discussed under various boundary conditions for different values of time and length. The above work has applications in design of resonators.
9
Content available A method for comparison of large deflection in beams
EN
The deflection analysis of beams has been recently an active area of research. The large deflection of beams refers to deflections occurring due to large displacements and small strains. This type of deflection has been one of the areas of interest in the development of beam deformation methods. The wide diversity of beam deformation methods highlights the importance of their comparison to further elucidate the properties and features of each method and determine their benefits and limitations. In this study, a new comparison model is introduced which involves three steps, instead of only comparing final results for verification in common studies. In the first step, a complete comparison is made based on the assumptions and approximations of each method of the kinematics of deformation, displacement, and strain fields. After selecting the most accurate method in the first step, the displacement functions are determined by polynomial approximation under different loading and support conditions based on the selected method. In the third step, the displacement functions are used to calculate the strains in each method. The conclusion is based on comparing the strains. This comparative model can be used as a benchmark to compare different theories of deformation analysis.
EN
The article extended the idea of active vibration reduction of beams with symmetric modes to beams with asymmetric modes. In the case of symmetric modes, the symmetric PZT (s-PZT) was used, and the optimization of the problem led to the location of the s-PZT centre at the point with the greatest beam curvature. In the latter case, the asymmetric modes that occur due to the addition of the point mass cause an asymmetric distribution of the bending moment and transversal displacement of a beam. In this case, the optimal approach to the active vibration reduction requires both new asymmetric PZT (a-PZT) and its new particular distribution on the beam. It has been mathematically determined that the a-PZT asymmetry point (a-point), ought to be placed at the point of maximum beam bending moment. The a-PZT asymmetry was found mathematically by minimizing the amplitude of the vibrations. As a result, it was possible to formulate the criterion of the maximum bending moment of the beam. The numerical calculations confirmed theoretical considerations. So, it was shown that in the case of asymmetric vibrations, the a-PZTs reduced vibrations more efficiently than the s-PZT.
PL
W artykule przedstawiono projekt układu doświadczalnego do badania materiałów w silnych, impulsowych polach magnetycznych. Do wytwarzania pola wykorzystano ogniskowanie wiązek mikrofal w układzie złożonym z magnetronów albo wirkatorów oraz falowodów, soczewek i zwierciadeł parabolicznych. Wykonane obliczenia pokazały możliwość otrzymania pól magnetycznych o indukcji 9,64 T w obszarze o rozmiarach 10 mm oraz 967 T w obszarze o rozmiarach 0,1 mm. Przedyskutowano zalety i wady proponowanego układu i oceniono jego wykonalność.
EN
The experimental setup to research of materials in the pulsed high magnetic fields is presented. Focusing of the microwave beams in the system composed of magnetrons or vircators, and waveguides, parabolic lenses and mirror is exploited in the setup. Executed computation shows possibilities obtaining of the magnetic.
EN
Many educational institutions do not have sufficient resources to acquire expensive devices to make the dialoged and practical classes more attractive, both for students and for teachers. In view of these concerns, it is proposed a procedure that integrates PBL (Problem based Learning) and HIL (Hardware in The Loop) methods to test different dynamic systems, verify stability of the implemented control equations, or even validate useful algorithms in many areas, from basic disciplines of Exact Sciences to Technical and Engineering courses. The conception approach is presented here to justify the best possible cost-effectiveness benefits to simulate real-time systems, with financial and time reductions. The project consists of developing three prototypes (heat exchanger, electronic converter and “Beam and Ball” experiment) by means of a mathematical modeling using the Matlab / Simulink software, to embedded this model in a HIL hardware in order to simulate / diagnose the performance of such systems. These examples can be used in both practical and theoretical classes, in order to encourage students to deal with real problems in search of their solutions.
PL
Wiele instytucji edukacyjnych nie ma wystarczających srodków na zakup drogich urządzeń które uczynią prowadzone z dialogiem i zajęcia praktyczne bardziej atrakcyjnymi zarówno dla uczniów, jak i nauczycieli. W związku z powyzszym proponuje się procedurę integrującą metody PBL (Problem based Learning) i HIL (Hardware in The Loop) w celu testowania róznych układów dynamicznych, weryfikacji stabilności zaimplementowanych równan sterowania, a nawet walidacji użytecznych algorytmów w wielu obszarach, od z podstawowych dyscyplin nauk ścisłych po kursy techniczne i inżynierskie. Przedstawione jest tutaj podejście koncepcyjne w celu uzasadnienia możliwie najlepszych korzyści w zakresie efektywnosci kosztowej symulacji systemów w czasie rzeczywistym, przy jednoczesnym ograniczeniu finansowym i czasowym. Projekt polega na opracowaniu trzech prototypów (wymiennik ciepła, przetwornik elektroniczny i eksperyment „Belka i kula”) za pomocą modelowania matematycznego z wykorzystaniem oprogramowania Matlab / Simulink, w celu osadzenia tego modelu w sprzęcie HIL w celu symulacji / zdiagnozowania działania takiego systemy. Przykłady te mozna wykorzystać zarówno na zajęciach praktycznych, jak i teoretycznych, aby zachęcic uczniów do rozwiązywania rzeczywistych problemów w poszukiwaniu ich rozwiązania.
EN
Introduction: The aim of this study is to analyze the gradient of percentage depth dose for photon and electron beams of LINACs and to simplify the data set. Materials and Methods: Dosimetry measurements were performed in accordance with Technical Reports Series No. 398 IAEA. Results and discussion: The gradient of percentage depth dose was calculated and compared with the available published data. Conclusion: Instead of percentage depth dose for increasing and decreasing parts, the findings suggest using only two numbers for specific gradient of dose, separately. In this way, they can replace the whole set of the percentage depth dose (PDD).
PL
Oszacowanie wyważenia zespołu pomp żerdziowych bez żurawia na podstawie wartości zużywanego prądu
PL
Porównano sprężyste momenty krytyczne belek ze zbieżnym środnikiem, obliczone metodami analitycznymi i numerycznymi przedstawionymi w ostatnich latach przez badaczy zajmujących się tym zagadnieniem z obliczeniami własnymi, przeprowadzonymi dostępnymi narzędziami. Głównym celem było zweryfikowanie dokładności i zbieżności wyników otrzymanych różnymi metodami i różnymi prętowymi elementami skończonymi 1D o 7 stopniach swobody w węźle (7DOF).
EN
In this article, the elastic critical bending moments of the web-tapered I-beams calculated by the analytical and numerical solutions developed last years by researchers involved in the topic were compared with own calculations carried out with available common tools. The main goal was to verify the accuracy and convergence of the results provided by different modern methods and different finite bar elements 1D with 7 degrees od freedom at the node (7DOF).
PL
W niniejszej pracy zbadano zachowanie się beleczek betonowych z włóknami i bez nich. W części doświadczalnej wykonano łącznie 16 próbek beleczek o różnych wymiarach przekroju. 12 próbek zostało wzmocnionych włóknami syntetycznymi, które nadają betonowi twardość, udarność i wytrzymałość zmęczeniową. Stosunek masowy włókien w próbkach wynosi od 0% do 0.20%. Próbki poddawane są próbie czteropunktowego zginania w celu uzyskania maksymalnych wartości obciążenia i przemieszczenia, aż do osiągnięcia stanu zniszczenia. Następnie próbki belek są modelowane w programie do analizy elementów skończonych Abacus. Ze względu na porównanie wartości doświadczalnych i numerycznych oraz rozkładów naprężeń w próbkach widać, że analiza numeryczna może być rozwiązaniem przy badaniu zachowania się beleczek o różnych wymiarach w zginaniu czteropunktowym.
EN
In this study, the behavior of concrete beams with and without fiber was investigated. In the experimental part, a total of 16 beam specimens were manufactured having different section sizes. 12 specimens were reinforced with synthetic fibers, that provide toughness, impact, and fatigue strength to concrete. The fiber ratios of the samples varied between 0% and 0.20% by mass. The samples were subjected to a four-point bending test to obtain the maximum load and displacement values, until they reached the failure modes. Subsequently, the beam samples were modelled in the Abacus finite element analysis software. Due to the comparison of experimental and numerical values and stress distributions of the specimens, it is seen that numerical analysis could be an option when investigating the behavior of beams with different dimensions in four-point bending.
EN
The paper presents the results of tests on dynamic stability of Bernoulli-Euler beam with damages. Damages (cracks) were modeled using three rotational springs. An analysis of the influence of crack depth and their position relative to the beam ends on dynamic stability of the beam was carried out. The problem of dynamic stability was solved by applying the mode summation method. Applying an orthogonal condition of eigenfunctions, the dynamic of the system was described with the use of the Mathieu equation. The obtained equation allowed the dynamic stability of the tested system to be analyzed. Stable and unstable solutions were analyzed using the Strutt card.
EN
The structural damages can lead to structural failure if they are not identified at early stages. Different methods for detecting and locating the damages in structures have been always appealing to designers in the field. Due to direct relation between the stiffness, natural frequency, and mode shapes in the structure, the modal parameters could be used for the purpose of detecting and locating the damages in structures. In the current study, a new damage indicator named “DLI” is proposed, using the mode shapes and their derivatives. A finite element model of a beam is used, and the numerical model is validated against experimental data. The proposed index is investigated for two beams with different support conditions and the results are compared with those of two well-known indices – MSEBI and CDF. To show the capability and accuracy of the proposed index, the damages with low severity at various locations of the structures containing the elements near the supports were investigated. The results under noisy conditions are investigated by considering 3% and 5% noise on modal data. The results show a high level of accuracy of the proposed index for identifying the location of the damaged elements in beams.
EN
Two models of vibrations of the Euler–Bernoulli beam under a moving force, based on two different versions of the nonlocal gradient theory of elasticity, namely, the Eringen model, in which the strain is a function of stress gradient, and the nonlocal model, in which the stress is a function of strains gradient, were studied and compared. A dynamic response of a finite, simply supported beam under a moving force was evaluated. The force is moving along the beam with a constant velocity. Particular solutions in the form of an infinite series and some solutions in a closed form as well as the numerical results were presented.
PL
Badania związane z wykrywaniem uszkodzeń i osłabień elementów konstrukcyjnych stanową bardzo ważny element kompleksowej analizy budowli inżynierskich. W analizie identyfikacji uszkodzeń wiodącą rolę odgrywają tzw. metody nieniszczące, które pozwalają dostatecznie precyzyjnie zlokalizować powstałe uszkodzenia. Prezentowana praca poświęcona jest zastosowaniu dyskretnej transformacji falkowej w procesie lokalizacji uszkodzeń konstrukcji. Dowolne uszkodzenie, np. w postaci lokalnego osłabienia sztywności konstrukcji (pęknięcia), jest przyczyną zaburzenia w rejestrowanym sygnale odpowiedzi - ugięciu, deformacji przekroju lub np. przyspieszeniu wybranego punktu konstrukcji. Zaburzenie sygnału jest na tyle małe, że dopiero jego przetworzenie za pomocą analizy falkowej pozwala zlokalizować miejsce uszkodzenia. Zaletą przedstawionej procedury jest wykorzystanie wyłącznie sygnału odpowiedzi rzeczywistej konstrukcji uszkodzonej. Przedstawiono krótki przegląd dotychczasowych analiz konstrukcji płytowych (płyt cienkich).
EN
Research related to the detection of damage and weakening of structural elements is a very important element of a comprehensive analysis of engineering structures. In the analysis of damage identification, the leading role is played by the so-called non-destructive methods that allow for sufficiently precise localization of the damage. The presented work is devoted to the application of the discrete wavelet transformation (DWT) to the process of identification and localization damages in structures. Any damage, e.g. in the form of a local weakening of the structure stiffness (cracks), causes disturbances in the recorded response signal - deflection, deformation of the cross-section or e.g. acceleration of a selected point of the structure. However, the signal disturbance is so small that only its processing by means of wavelet analysis allows to locate the damage site. The advantage of the presented procedure is the use of the response signal only of the real - damaged structure. The presented work is an overview of the results obtained so far. The slabs were analyzed as the basic surface structural systems that form the building structure.
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