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EN
This study investigates natural frequencies of simply supported thin-walled rectangular plates made of laminates with arbitrary stacking sequences. A detailed analysis is made of laminates whose stacking sequences meet the non-zero condition for coupling stiffness submatrix B components. Twelve laminate stacking sequences exhibiting different types of in-plane and out-plane coupling effects are selected, assuming that the plies are of the same thickness. A comparison is made between the effects of selected components of the coupling stiffness submatrix B and inertial force components on the natural frequencies of the rectangular laminate plates under consideration. Classical laminate plate theory (CLPT) is used in the considerations. Obtained solutions of the eigenproblems for the cases of unloaded rectangular plates made of a general laminate show that the correct determination of eigenvalues requires a detailed analysis of all B stiffness matrix components and beam model reduction factors.
EN
Over time, the technical condition of buildings deteriorates due to material fatigue, environmental effects, and structural damage. These processes lead to a decrease in stiffness, which directly affects the dynamic characteristics of the structure. This study investigates the influence of stiffness degradation on the natural frequencies and mode shapes of a single-storey masonry building located on the campus of the Cracow University of Technology. Two numerical models were developed using the Finite Element Method (FEM): an intact model and a weakened model with locally reduced stiffness simulating wall cracks and material losses. The modal analysis revealed that a 20% reduction in the Young’s modulus of masonry resulted in a 3–8% decrease in the natural frequencies. Moreover, the weakened model exhibited a visible modification of vibration mode shapes, with higher local displacement amplitudes in the cracked zones. These results confirm that the dynamic response of a building is highly sensitive to local stiffness changes. From a practical perspective, the observed decrease in natural frequencies can be used as a quantitative diagnostic indicator of the structural condition. Tracking changes in modal parameters over time allows early detection of stiffness degradation and supports preventive maintenance strategies. The study confirms that modal analysis, combined with numerical modelling, provides an effective, non-destructive method for assessing the technical state and dynamic stability of existing and renovated masonry buildings.
EN
The study considers an elastic rod within the framework of Bernoulli’s hypotheses, subjected to a time-independent longitudinal load. The problem formulation accounts for the squares of the section rotation angles, leading to the well-known stability equations for straight rods. Boundary conditions for both follower and dead loads at the ends are examined. Dimensionless state equations are presented, along with an analytical expression for the fundamental solution of the free transverse vibration problem. The dependencies of the first four natural frequencies on the compressive load are provided. Additionally, static and dynamic bending problems of rods under a time-independent longitudinal force are analyzed. The eigenstates are determined using the initial parameter method.
EN
This paper presents changes in modal parameters, i.e. natural frequencies and the curvature of the mode shape, as a result of damage in the steel I-beam of a composite member. A steel-concrete composite beam was analyzed, for which numerical simulations (rigid finite element model) and experimental tests were carried out. The damage analyzed was intended to simulate actual propagation of cracking in the steel I-beam. Two levels of damage occurring at two different locations in the beam were studied. The value of frequency changes of experimental and numerical evaluations have shown high consistency (margin of a few percent). Natural frequencies turned out to be sensitive to the introduced damage – their values decreased as the degree of damage in the beam increased. The Curvature Damage Factor was used to analyze the curvature of the mode of vibration. The results obtained in the numerical evaluations were satisfactory. In relation to experimental tests, lower effectiveness was achieved, which was most likely caused by a different density of the measurement grid compared to numerical analyses.
PL
W pracy przedstawiono zmiany parametrów modalnych tj. częstotliwości drgań własnych oraz krzywizny postaci drgań w wyniku uszkodzeń powstałych w dwuteowniku stalowym belki zespolonej. Analizie poddano belkę zespoloną stalowo-betonową, dla której przeprowadzono symulacje numeryczne (w modelu RFE) oraz badania doświadczalne. Analizowane uszkodzenie miało symulować rzeczywiste postępujące pęknięcie dwuteownika stalowego. Badano dwa poziomy uszkodzeń pojawiające się w dwóch różnych miejscach belki. Uzyskano bardzo wysoką zgodność zmian częstotliwości (na poziomie kilku procent) określonych na podstawie numerycznej i eksperymentalnej symulacji uszkodzeń. Częstotliwości drgań okazały się być wrażliwe na wprowadzone uszkodzenia - ich wartości obniżały się wraz ze wzrostem stopnia uszkodzeń w belce. Do analizy krzywizny postaci drgań wykorzystano parametr CDF. W tym zakresie otrzymano zadowalające wyniki na podstawie przeprowadzonych analiz numerycznych. W odniesieniu do badań eksperymentalnych uzyskano mniejszą skuteczność, co najprawdopodobniej spowodowane było zróżnicowaną gęstością siatki pomiarowej w porównaniu do analiz numerycznych.
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.
EN
In this work, we study the bending vibrations of a thin wing for a profile with two axes of symmetry, taking into account the influence of torsional vibrations on them. The primary focus of the current study is on finding an analytic solution for the wing-bending equation through the Laplace transform, determining the frequency of free-bending vibrations, and constructing the amplitude-frequency response and phase-frequency response of the wing.
EN
The natural frequencies and mode shapes of fibre metal laminates (FMLs) were numerically investigated and validated using commercially available finite element analysis software (ANSYS). Various grades of GLARE and FML were considered for free vibration analysis, and the effect of the central metal layer and aspect ratios on the frequencies were analysed for simply supported, clamped edge conditions. The obtained fundamental frequencies, natural frequencies and mode shapes comply with the available literature. The effect of the outermost metal layer on the natural frequencies was also investigated for various combinations of edge conditions. The obtained results indicate that there is a significant effect of the central and outermost metal layer on the natural frequencies, irrespective of the edge conditions and aspect (width/length) ratios.
EN
The basic dynamic characteristics of façade scaffolding are natural frequencies of vibrations and corresponding mode shapes. These properties affect the scaffolding safety, as well as comfort and safety of its users. Many of the dynamic actions present at scaffolding are in the low frequency range, i.e. below 10-15 Hz. The first natural frequency of a structure is usually in the range of 0.7 to 4 Hz which corresponds to resonant frequencies of human body and it means that vibrations induced at scaffolding may strongly affect the human comfort. The easiest way of increasing the rigidity of the structure is by ensuring correct boundary conditions (support, anchorage) and bracing of the structure. The numerical analysis was performed for the real scaffolding structure of medium size. The analysis consisted of natural frequencies calculation for the original structure and for models with modified bracing and anchoring systems. The bracing modifications were introduced by reducing or increasing the number of vertical bracing shafts. The anchor system was modified by reduction of the 6 anchors in the top right corner of the scaffolding in three stages or by evenly removing nearly 1/3 of the total number of anchors. The modifications of bracing and anchor systems resulted in changing the natural frequencies. The increase of natural frequencies due to higher number of anchors and more bracing is not even for all mode shapes. Bracing is more effective in acting against longitudinal vibrations, while anchoring against vibrations perpendicular to the façade.
PL
Rusztowania fasadowe to tymczasowe konstrukcje użytkowe wspomagające prace budowlane. Istotne jest zapewnienie bezpieczeństwa konstrukcji i pracowników, a także komfortowych warunków pracy ich użytkownikom poprzez zmniejszenie poziomów drgań docierających do nich. Podstawowe charakterystyki dynamiczne rusztowań fasadowych to częstotliwości drgań własnych oraz odpowiadające im postacie drgań. Pierwsza częstość drgań własnych w przypadku konstrukcji tego typu zazwyczaj mieści się w zakresie od 0,7 do 4 Hz, a więc są to wielkości zgodne z częstościami generowanymi przez wiele urządzeń działających na rusztowaniu, a także są one zbliżone do częstości rezonansowych części ciała ludzkiego. Częstotliwość drgań własnych uzależniona jest od rozmiarów rusztowania, jego masy oraz masy dodatkowej zgromadzonej na rusztowaniu (materiały budowlane, siatki ochronne i plandeki, użytkownicy rusztowania), a także od sztywności konstrukcji. Projektant pojedynczego rusztowania nie ma wpływu na elementy katalogowe systemu rusztowaniowego. Możliwe jest jednak zwiększenie sztywności rusztowania poprzez odpowiednio zaprojektowany system kotwienia konstrukcji rusztowania i przez prawidłowe stosowanie stężeń. Wymagany układ stężeń oraz rozstawy zakotwień w typowych rusztowaniach fasadowych można znaleźć w przepisach normowych lub katalogach producentów systemów rusztowań. Przeprowadzono obliczenia komputerowe przykładowego rusztowania fasadowego o średniej wielkości. Model metody elementów skończonych został stworzony w programie Autodesk Simulation Multiphysics 2013. Oryginalny model zawierał stężenia i zakotwienia zaproponowane przez projektanta konstrukcji rusztowania na podstawie wymagań producenta systemu. W kolejnych wariantach modyfikacji ulegała liczba pionów ze stężeniami, tj. z oryginalnej liczby pionów stężeń (3) pozostawiono 2 (rusztowanie słabo stężone), a następnie liczbę pionów stężeń zwiększono do 5 (rusztowanie przesztywnione). Podobnie, analizie poddano wpływ liczby zakotwień. Założono, że fragment konstrukcji pozostaje niezakotwiony, co wprowadzono do modelu przez eliminację 6 kotew w trzech etapach. Ostatni wariant modyfikacji oryginalnego sytemu zakotwień to równomierne usunięcie 10 spośród 36 ogółem punktów zakotwień. Wyniki obliczeń zostały zebrane w postaci pierwszych dziesięciu częstości drgań własnych. Analizowano także postacie drgań własnych, odpowiadające zbliżonym częstościom drgań. Zwiększenie liczby stężonych pól i większa liczba zakotwień powoduje zwiększenie częstotliwości drgań własnych. Nie jest to jednakowa zmiana dla wszystkich częstości i postaci. Stężenia mają większy wpływ na postaci związane z drganiami poziomymi wzdłuż fasady, podczas gdy liczba zakotwień wpływa istotnie na wartości związane z postaciami z przemieszczeniami prostopadle do fasady. Pozostawienie dużego obszaru pozbawionego zakotwień powoduje znaczne zmniejszenie przede wszystkim pierwszej częstości drgań własnych. Taka sytuacja jest niedopuszczalna, a mimo to spotykana w przypadku rusztowań zlokalizowanych przy istniejących budynkach, gdzie z powodów technologicznych kotwienie części konstrukcji jest utrudnione i czasem przez projektantów zaniedbywane. Należy również mieć na uwadze, że niedostateczne kotwienie i stężenie rusztowań fasadowych ma wpływ nie tylko na ich charakterystyki dynamiczne, ale także na wytężenie elementów konstrukcji. Może to prowadzić do stanów awaryjnych, mimo nieprzekroczenia dopuszczalnych wielkości obciążeń.
EN
The widespread use of perforated vibrating surfaces in various industries requires maximum productivity and construction reliability. The research task is to determine the significant factors and their degree of influence on the natural oscillations of vibrating surfaces with multiple holes of complex geometry. For this purpose, studies were carried out for three samples of plates: non-perforated, with basic round holes and holes of complex geometry in the form of a five-petal epicycloid. Studies of the natural oscillations of perforated vibrating surfaces have been conducted using the finite element method in Abaqus, which has proved sufficient accuracy of calculations. The dependencies of the natural oscillation frequency of perforated surface samples on their thickness, partition width between the holes, material type, and fixing method have been obtained. In addition, the analysis involved the study of eight modes of oscillation common in practice. The dependencies of the natural oscillation frequency of perforated surface on the relative parameters of ligament efficiency and stiffness coefficient have also been obtained. These parameters take into account the ratios of the partition width between the holes to the plate thickness and the dimensions of the holes. The research results allow to obtain levels of influence of the perforated vibrating surface parameters on their natural oscillations frequency. The obtained research results make it possible to further determine the absence of damage between the holes and predict the durability of perforated vibration surfaces in the presence of holes of complex geometry.
EN
Rods with a relatively short length in relation to their transverse dimensions with a variable cross-section along the axis, subjected to longitudinal vibrations, have the character of stocky rods, for which the classic geometric principles used for rods are not fully met. For small engineering elements, the postulated design frequencies of natural vibrations in the very high cycle fatigue analyses reach the values of a dozen or so, small, several dozen kHz. In the article, the sensitivity of the value of the basic natural frequency to the change in the shape of the element is analysed and discussed. The analysis is conducted using finite element method.
PL
Współczesne konstrukcje kratownicowe są projektowane, aby sprostały wymogom wytrzymałościowym niezagrażającym bezpieczeństwu ich użytkowania. Może to spowodować fakt, że wpływ drgań na konstrukcję kratownicową narażoną na działanie sił poziomych, jak też sił poprzecznych spowodowanych działaniem wiatru może być niebezpieczny dla bezpiecznego użytkowania (np.: konstrukcje mostowe). Uznając potrzebę doskonalenia oceny ich stanu, jak również współczynników bezpieczeństwa, wykonano badania destrukcji zamodelowanego elementu przęsła mostowego za pomocą metody teoretycznej analizy modalnej.
EN
Contemporary truss structures must maintain appropriate strength requirements for safe use. This may result in the fact that the influence of vibrations on a truss structure exposed to horizontal forces as well as transverse forces caused by wind may be dangerous for safe use (e.g. bridge structures). Recognizing the need to improve methods of testing truss elements for the purpose of assessing their condition as well as assessing the safety factors in this work, an attempt was made to examine the destruction of the modelled bridge span element using the theoretical modal analysis method.
EN
This paper presents an analysis of the natural frequency and mode shapes of the arm and the working tip of the da Vinci robot, which is used in various types of surgical procedures. The survey was conducted using Autodesk Fusion 360. Using the da Vinci robot's construction data, a model was designed taking into account the characteristic dimensions and materials used. The obtained shapes of vibrations for natural frequencies allowed us to predict the influence of resonance phenomenon on the manipulator's arm. The movement of the tool along the wrong track, caused by an increase in vibration amplitude, may adversely affect the operation of the device. The results of the conducted research, therefore, provide information for which natural frequencies the values of these amplitudes increase.
EN
In this paper, natural frequencies of a three-layered foot prosthesis are investigated. The model of foot prosthesis consisted of a three-layered base, which substitutes a human foot and an element in the shape of an arc that represents a shank of human. The base consists of three layers made of carbon fiber. In the lower part of the prosthesis, the auxetic layer is used as the inner layer. Numerical analysis is made for different parameters of the central layer: the thickness and the value of Poisson’s ratio. The simulations are used to investigate the influence of an auxetic layer on prosthesis vibrations and compare the impact of different parameters on results. Calculations are made using the finite element method implemented in Autodesk Fusion 360. The results show that the auxetic layer has a great impact on tolerance to vibrations and mobility.
EN
The methodology of modeling and determining the natural frequencies of oscillations of a robotic structure made of composite material including motors, bearings, gears, and ratio changers is considered. The vibration forms of a multi-stage bench for semi-natural modeling from composite material determined using the finite element method are presented. The developed methods allow the study of complex robotic systems of homogeneous and composite materials.
PL
Rozważana jest metodologia modelowania i określania naturalnych częstotliwości drgań konstrukcji robotycznej wykonanej z materiału kompozytowego, w tym silników, łożysk, kół zębatych i zmieniaczy przełożeń. Opracowane metody pozwalają na badanie złożonych systemów robotycznych z materiałów jednorodnych i kompozytowych.
EN
A structural beam is a common element in many mechanical structures such as ship propeller shaft, crane boom, and aircraft wings. In the present paper experimental and numerical modal analysis are carried out for estimating the damage, geometric location of the damage, severity of damage and residual life of structural beam to prevent unexpected failures of mechanical structures. Experimental and numerical modal analysis results for healthy and cracked beam are compared for validation of numerical methodology used in the present paper. Experimental modal analysis is performed on both healthy and cracked beam with the help of impact hammer, acceleration sensor and FFT (Fast Fourier Transformer) analyzer associated with EDM (Engineering Data Management) software. Modal tests are conducted using impact method on selected locations of the entire healthy and cracked beam to find the first three natural frequencies, which are used to detect the presence of damage and geometric location of the damage. Three parametric studies are carried out to know the effect of crack depth, crack location and crack orientation on the natural frequencies of the cracked beam. Finally, the residual life of a healthy and cracked beam was estimated using Basiquin’s equation and finite element analysis software called ANSYS 18.1.
EN
Nowadays, noise generated by devices is a serious issue in industry and in everyday life, because it may cause health damage to humans. In this research, a cubic rigid device casing built of double-panel thin steel walls is employed to reduce noise emitted from an enclosed noise source. Double-panel structure is used because of good sound insulation it provides. There exist three main groups of noise reduction methods, i.e. passive, semi-active and active. In this paper, a semi-active modification of double-panel structure is applied and examined. The bistable actuator (solenoid) mounted between incident and radiating plates changes its state due to applied constant voltage, causing the coupling of plates. Experimentally measured natural frequencies and modeshapes of the structure are compared to the simulation results. The influence of proposed modification on dynamical properties of the structure is analyzed and discussed.
EN
The article presents an FEM model of the spindle system, in which angular contact ball bearings with active preload control are used. This model allowed determining the frequency and form of natural vibrations of the system. The model was prepared using the Abaqus programming environment. Various bearing preload states were adopted during the tests. It was shown that the spindle system is sensitive to the changes in the stiffness of bearing supports. The tests conducted using models were then verified on a real stand. First of all, using the external excitation from an electromagnetic exciter, the frequency range of resonance vibrations of the spindle system was determined. Then, the amplitude - frequency characteristics of the tested spindle were determined at various bearing preload values. A general operation scheme of the control system for the active change of the preload value of the angular contact ball bearings during the work of the spindle system was proposed.
EN
A new formula that allows the first natural frequency of transverse vibrations of axially loaded steel helical springs to be determined has been presented in the paper. The relationship is easy to use and allows finding the first natural frequency of spring vibrations without the necessity of solving analytical or numerical models. According to the authors’ knowledge, this is the first such a formula and, consequently, when this frequency becomes zero, it enables determination of the critical axial force or deflection causing the buckling of the spring. The way of obtaining the described formula is presented in the paper. The results of this formula are compared with those obtained using FEM and experiments. The advantages, drawbacks and limitations of the proposed relationship are also discussed.
19
Content available remote Dynamic behavior of sandwich FGM beams
EN
This work is consisted to investigate the vibration behavior of FGM beams under different boundary conditions with diverse volume fraction. The main objective in this paper is to study the thickness in influence of the sandwich beams skin on the frequencies of the structures. The classical Euler-Bernoulli theory (CLBT) with assuming that the material properties of the FGM layer will evaluated continuously in the thickness direction according to the power law (P-FGM) is used to derived the equation of motion. The frequencies obtained are compared with the natural frequencies of a two-material and those of the base materials.
EN
Damage detection in structural elements like beams is one of important research areas for health monitoring. Initiation of a fault in the form of a crack or any damage puts a limitation on the service life of a structural member. So, in this paper, a method is proposed which uses the advantages of soft computing techniques like Fuzzy Inference Systems (Mamdani and Sugeno) and Adaptive Genetic Algorithm for three stage refinement of the data base generated using dynamic responses from a cracked fixed-free aluminum alloy beam element. For the crack element reference, a finite element model of a single transverse crack has been considered. The proposed method describes both Mamdani and Sugeno Fuzzy Inference Systems for training of damage parameters. In the Adaptive Genetic Algorithm, a statistics based method has been incorporated to limit the randomness of the search process. Finally, the results from the Mamdani-Adaptive Genetic-Sugeno model (MAS) are validated with the results from the experimental analysis.
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