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1
Content available Vibration of a mistuned three-bladed rotor under regular and chaotic excitations
Warminski J., Latalski J., Szmit Z.
Journal of Theoretical and Applied Mechanics
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2018
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Vol. 56 nr 2
549--566
EN
This study considers forced vibrations of a rotating structure consisting of a rigid hub and three flexible beams. The blades are nominally made of a multilayered laminate with a specific stacking sequence resulting in full isotropic macroscopic material behaviour. However, in the performed analysis it is assumed that the rotor has been mistuned because of manufacturing tolerances of the composite material. These inaccuracies are represented by deviations of reinforcing fibres orientations from their nominal values. The considered tolerances break the intended macroscopic material isotropy and make the laminate to exhibit the fully orthotropic behaviour. Based on previous authors research, the system of four mutually coupled dimensionless ordinary differential governing equations is adopted. Forced responses of the system under regular and chaotic excitations are investigated.
2
Content available remote Suppressing Vibrations of a Rotating Active Composite Beam by a Cubic Velocity Feedback Control Method
Mitura A., Latalski J.., Warmiński J.
Machine Dynamics Research
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2016
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Vol. 40, No. 2
19--32
EN
This study presents an analysis of a dynamic system consisting of a rigid hub and a cantilever flexible composite beam with an embedded active piezoelectric element. The system is excited by periodic oscillations of the hub angular speed. The macro fiber composite (MFC) active element is used to suppress beam vibrations. In the mathematical formulation of the problem the non-classical effects like material anisotropy and mode coupling due to an arbitrary stacking sequence of the laminate as well as the transverse shear deformations of the material are taken into account. Derived in previous research governing equations of the considered system are solved numerically by the finite difference method. Results of a numerical simulation are compared with experimental data including frequencies and mode shapes of natural vibrations and responses to unit step function excitations. Finally, the effectiveness of the piezoelectric actuator and the tested cubic velocity feedback control algorithm in order to suppress system vibrations is evaluated.
3
Content available remote Optimum weight design of multilayered fiber composite plates with discrete ply angles and uncertainty in ply thicknesses
Latalski J.
Composites Theory and Practice
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2014
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R. 14, nr 4
183--188
EN
The presented paper discusses the minimum weight design of multilayered fiber composite plates with tolerances in individual ply thicknesses. These tolerances are given by the maximum acceptable deviation of every individual ply thickness from its nominal value. The robustness of the design is achieved by diminishing the design state variable (buckling load factor) by the product of arbitrary assumed tolerances and appropriate sensitivities. The proposed approach is illustrated with examples of a simply supported rectangular laminated plate design under uni- and bi-axial compression. The minimum weight identified by the total number of layers is found to assure plate stability. For the discussed analysis, buckling load sensitivity formulas with respect to ply thicknesses are given. Based on these relations, the impact of the discussed variations on the optimal laminate stacking sequence and buckling mode shape is studied in detail. The achieved results emphasize the importance of robust design opposed to merely nominal approaches.
PL
Przedstawiono zagadnienie optymalizacji wielowarstwowych płyt kompozytowych z włóknami ukierunkowanymi dyskretnie z uwzględnieniem występowania tolerancji grubości poszczególnych lamin. Rozważane tolerancje zostały zdefiniowane jako maksymalne dopuszczalne odchylenia rzeczywistej grubości każdej z warstw od jej wartości nominalnej. W zaproponowanym podejściu do zagadnienia rozwiązanie optymalne uzyskano poprzez zmniejszenie zmiennej stanu zadania o wartość iloczynu przyjętych arbitralnie tolerancji i odpowiednich wrażliwości tej zmiennej stanu. Metodę rozwiązania zilustrowano przykładami ściskania jedno- i dwuosiowego płyty prostokątnej, swobodnie podpartej czterostronnie. Jako kryterium optymalizacji przyjęto minimum ciężaru (grubości) płyty. Zapisano rekurencyjne zależności na wrażliwość siły krytycznej względem grubości poszczególnych warstw laminatu. Następnie, na podstawie tych zależności, wyznaczono zmodyfikowaną wartość siły krytycznej obciążenia. Szczegółowo omówiono wpływ badanych tolerancji na układ i kolejność warstw w laminacie wielowarstwowym. Uzyskane wyniki w pełni potwierdzają zasadność stosowania optymalizacji odpornościowej jako metody projektowania gwarantującej lepsze (bezpieczniejsze) rozwiązania niż standardowe ujęcie nominalne zagadnienia.
4
Content available Control of Bending-Bending Coupled Vibrations of a rRotating Thin-Walled Composite Beam
Latalski J., Bocheński M., Warmiński J.
Archives of Acoustics
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2014
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Vol. 39, No. 4
605--613
EN
The paper presents a study of a possible application of structure embedded piezoelectric actuators to enhance the performance of a rotating composite beam exhibiting the coupled flexural-flexural vibrations. The discussed transversal and lateral bending modal coupling results from the directional properties of the beam’s laminate and ply stacking distribution. The mathematical model of the beam is based on an assumption of cross-sectional non-deformability and it incorporates a number of non-classical effects. The final 1-D governing equations of an active composite beam include both orthotropic properties of the laminate and transversely isotropic properties of piezoelectric layers. The system’s control capabilities resulting from embedded Macro Fiber Composite piezoelectric actuators are represented by the boundary bending moment. To enhance the dynamic properties of the composite specimen under consideration a combination of linear proportional control strategies has been used. Comparison studies have been performed, including the impact on modal coupling magnitude and cross-over frequency shift.
5
Content available Ply thickness tolerances in stacking sequence optimization of multilayered laminate plates
Latalski J.
Journal of Theoretical and Applied Mechanics
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2013
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Vol. 51 nr 4
1039--1052
EN
The paper deals with the impact of manufacturing tolerances of plies thicknesses on optimal design of multi-layered laminated plates in compression. It is assumed that the considered tolerances are represented by the maximum acceptable deviation of every individual ply thickness from its nominal design value. The robustness of the optimum is achieved diminishing the buckling load amplitude factor by the product of arbitrary assumed tolerances and appropriate sensitivities. The discussed optimization problem is solved numerically by the direct enumeration method. The proposed approach is illustrated with examples of the rectangular multi-layered laminated plate design under uni- and biaxial compression. The achieved results emphasise the robustness of the proposed method compared to the approaches with ignored tolerances.
6
Content available Numerical analysis of composite structures with embedded piezoelectric active elements
Dębski H., Latalski J.
Journal of KONES
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2012
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Vol. 19, No. 1
51-69
EN
The paper presents a numerical simulation of active multiple layer composite beams in bending test. Within framework of performed analysis glass-epoxy and carbon-epoxy laminates with integrated piezoelectric actuators were considered. In the research macro fiber composite (MFC) type transducers exhibiting d33 effect were used. The numerical models and further calculations were done in ABAQUS/Standard FEM software. Discrete models of the considered composite beam structures were formulated according to the Layup-Ply technique. In performed tests nonlinear geometric effects corresponding to large structural deflections were taken into account. The resulting state equations were solved by means of Newton-Raphson iterative method. Finally, the findings of numerical simulations were compared to the outcomes of laboratory experiments. A very good agreement of numerical and experimental results was achieved; this confirmed the assumptions made to the numerical model and further modelling technique. Numerical model of the piezoelement, analysis of a composite beam with piezoelectric patch, numerical tests for the separated M-8503-P1 piezoelement, electric boundary conditions for the examined actuator, strain state of a glass-epoxy laminate, laboratory test-stand, numerical and laboratory experiment results are presented.
7
Content available Mode shapes variation of a composite beam with piezoelectric patches
Georgiades F., Latalski J., Warmiński J.
Prace Instytutu Lotnictwa
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2011
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Nr 9 (218)
36-43
EN
In this paper the modal shapes of a light, thin laminate beam with active elements were evaluated. Cases with one or two Macro Fiber Composite (MFC) active elements adhered onto a glassepoxy cantilever beam were analyzed. The systems under consideration were modeled in ABAQUS finite element software to derive mode shapes numerically. Next, the modes were compared to each other to estimate the influence of PZT patches. First 20 modes of natural vibrations were examined including bending, torsion and axial ones. The comparisons of mode shapes were performed according to Modal Assurance Criterion (MAC) analysis. The examination of changes of mode shapes of the original beam with placement of active elements is the starting point in prior of optimal placements of PZTs with final goal the control of dynamics of helicopter blades.
PL
W pracy przedstawiono wyniki analizy modalnej lekkiej, cienkiej belki kompozytowej, jednostronnie utwierdzonej, z osadzonymi elementami aktywnymi. Na wstępie przeanalizowano belkę wzorcową – tj. wykonaną z laminatu żywiczno-szklanego bez elementów aktywnych. Następnie zbadano tę samą belkę z dodanym jednym, a w dalszej kolejności także z dwoma kompozytowymi elementami aktywnymi typu MFC (Macro Fiber Composite). Częstości i postacie drgań własnych badanych układów określono numerycznie za pomocą metody elementów skończonych – wykorzystano w tym celu oprogramowanie ABAQUS. Wyznaczono i zbadano 20 pierwszych postaci drgań zawierających zarówno mody giętne oraz skrętne, jak i jedną modę wzdłużną. Do oceny wpływu elementów aktywnych na uzyskane postacie drgań badanej belki wykorzystano kryterium dopasowania modalnego (ang. Modal Assurance Criterion, MAC). Zaprezentowana praca stanowi wstępny etap badań, których celem jest wyznaczenie optymalnego położenia elementów aktywnych sterujących dynamiką łopat wirnika śmigłowca.
8
Content available Modelowanie w systemie ABAQUS piezoelektrycznych elementów aktywnych typu MFC
Latalski J.
Eksploatacja i Niezawodność
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2011
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nr 4
72-78
PL
W pracy przedstawiono sposób efektywnego modelowania kompozytowych elementów piezoelektrycznych metodą elementów skończonych. W systemie ABAQUS przygotowano makroskopowy model elementu aktywnego typu MFC wykorzystującego efekt piezoelektryczny d33. W dalszej kolejności przeanalizowano wielowarstwową belkę kompozytową z naklejonym badanym elementem aktywnym. Numerycznie zbadano prosty i odwrotny efekt piezoelektryczny, wyznaczając odpowiednio wartości napięć na zaciskach elementu aktywnego przy wymuszonym odkształceniu układu oraz ugięcia statyczne przy różnych wartościach napięcia zasilającego. Rezultaty tych analiz porównano z wynikami rzeczywistych pomiarów przeprowadzonych na stanowisku laboratoryjnym. Opracowany model numeryczny wykorzystano do próby wykrycia symulowanego uszkodzenia materiału kompozytowego.
EN
The paper presents an approach to effective modelling of piezoelectric transducers in finite element method based software. A macroscopic model of an active element made of macro fiber composite (MFC type) exhibiting d33 effect is developed in ABAQUS system. Next, a multilayer composite beam with the discussed piezoelectric actuator is analysed. Both a direct and a converse piezo effects are analyzed numerically, calculating respectively charge on transducer's poles subject to forced displacements and beam static deflections with respect to assumed supply voltage. The outcomes of the numerical simulations are compared to the laboratory test results. Next, the worked-out FEM model of MFC actuator/sensor is used to detect the simulated defect in composite material.
9
Content available remote Laminate ply stacking sequence optimization with fibers orientation imperfections
Latalski J.
Engineering Transactions
|
2004
|
Vol. 52, iss.1-2
57-69
EN
The paper discusses the fiber orientations imperfections effect on the optimum design of a laminate plate to compressive load. It is assumed that fibers angular imperfection for each design variable can not exceed maiximum allowable deviation form variable's nominal value. These maximal accepted deviations are called tolerances. The incorporation of tolerances into the design algorithm is achieved by diminishing the limiting values of state variables by the product of assumed tolerances into appropriate sensitivities. Therefore, the given method allows to introduce tolerances into the design in a relatively simple way and ensures safe results. The paper is illustrated by examples of the rectangular laminate plate minimum thickness design. Numerical results show the reliability-based design to be important for structural safety compared the approach where tolerances are not taken into account.
10
Content available remote Manufacturing tolerances of truss members' lengths in minimum weight design
Bauer J., Latalski J.
Computer Assisted Mechanics and Engineering Sciences
|
2000
|
Vol. 7, No. 4
461-469
EN
In most cases a safety of optimal construction may be limited by the violation of stress, buckling or displacement constraints. An unexpected exceed of these constraints may be caused by manufacturing tolerances of structural elements (differences between assumed and obtained dimensions). This requires an incorporation of tolerance problem in optimum design. One may deal with two different tolerances - the first case is when it's related to the members' cross-section variations, whereas the second notion represents the variation of elements' lengths. Considering operation conditions and manufacturing techniques the second case of tolerance seems to be more important. This approach states the problem of minimum weight design of a structure with initial distortions. A standard solution algorithm with the Kuhn-Tucker theorem was used with the adjoint variable method. Necessary optimality conditions have the form of equations and inequalities. The equality constraints were put forward for the average values of design variables l, while tolerances t_j were introduced into inequality equations i.e. the limit values of stresses and displacements were diminished by the positive products of appropriate sensitivities and tolerances. The method was next illustrated by an example of a ten bar bench-mark problem - a typical one for testing algorithms in structural optimization. The idea presented in this paper may be used not only for truss structures but it can be easily extended to other kinds of structures like frames, composites etc.
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