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1

PZT Asymmetrical Shape Optimization in Active Vibration Reduction of Triangular Plates

Brański Adam, Kuras Romuald

Archives of Acoustics

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2023

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Vol. 48, No. 3

425--432

EN

The article presents the new 2D asymmetrical PZT (a-PZT) and its effectiveness in the active reduction of triangular plate vibrations. The isosceles right triangular plate with simply supported edges was chosen as the research object. To determine the a-PZT asymmetry and its distribution on the plate, a maximum bending moment criterion for the beam was used. First of all, this criterion points out exact center location of the a-PZT. It was at the point, at which the plate bending moment has reached its maximum value. Next, at this point, it was assumed that the piezoelectric consists of active fibers located radially from the center. Each fiber acted on the plate as a separate actuator. Next, at each direction, the actuator asymmetry was found mathematically by minimizing the amplitude of the vibrations. By connecting the outer edges of individual fibers, the 2D a-PZT was obtained. It was quantitatively confirmed that the effectiveness of the new a-PZT was the best compared with the effectiveness of the standard square and the circular PZTs, adding the same exciting energy to the PZTs.

2

Asymmetrical PZT Applied to Active Reduction of Asymmetrically Vibrating Beam – Semi-Analytical Solution

Brański Adam, Kuras Romuald

Archives of Acoustics

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2022

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Vol. 47, No. 4

555--564

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.

3

Effectiveness of the active pneumatic suspension of the operator’s seat of the mobile machine in depend of the vibration reduction strategies

Chwastek S., Pobędza J.

Journal of KONES

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2018

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Vol. 25, No. 4

43--48

EN

Low speeds of heavy mobile machines combined with large inertia result in the excitation of low frequency vibrations. Dissipation of vibration energy in the case of unsprung machines is performed only through tires, which slightly reduces the intensity of vibrations. Effective reduction of vibrations of mobile machines is possible only with active or semi-active methods. In unsprung mobile machines, on the way of propagation of vibrations between the source of vibrations and the protected object (machine operator), are vibroisolation systems located. These are most often controlled seat suspensions. In the case of the active suspensions, it is necessary to provide external energy, e.g. in the form of compressed air. The compressed air has the advantage that it is generally available in working machines as the working fluid and has its environmentally friendly properties (leaks do not contaminate the environment). This article is the result of the continuation of work on active methods of vibro-activity lowering in mobile machines, which resulted in, among others, elaboration of simulation model of the active operator’s seat suspension with controlled pneumatic actuator and its experimental identification. In particular, it was verifying the effectiveness of the adopted solution made the identification the friction model and thermodynamic phenomena in the controlled pneumatic cylinder. The aim of this work is parametric optimization of the suspension system and searching for the optimal control strategy. Experimental tests were carried out under conditions of harmonic excitations, coming from the electromechanical vibration exciter with controllable pitch and frequency. Data acquisition system and control circuit of the proportional directional control valve, supplying compressed air to the actuator were implemented using MATLAB-Simulink Real-Time software.

4

Effectiveness of the active pneumatic suspension of the operator’s seat of the mobile machine in depend of the vibration reduction strategies

Chwastek S., Pobędza J.

Journal of KONES

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2018

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Vol. 25, No. 3

93--98

EN

Low speeds of heavy mobile machines combined with large inertia result in the excitation of low frequency vibrations. Dissipation of vibration energy in the case of unsprung machines is performed only through tires, which slightly reduces the intensity of vibrations. Effective reduction of vibrations of mobile machines is possible only with active or semi-active methods. In unsprung mobile machines, on the way of propagation of vibrations between the source of vibrations and the protected object (machine operator), are vibroisolation systems located. These are most often controlled seat suspensions. In the case of the active suspensions, it is necessary to provide external energy, e.g. in the form of compressed air. The compressed air has the advantage that it is generally available in working machines as the working fluid and has its environmentally friendly properties (leaks do not contaminate the environment). This article is the result of the continuation of work on active methods of vibro-activity lowering in mobile machines, which resulted in, among others, elaboration of simulation model of the active operator’s seat suspension with controlled pneumatic actuator and its experimental identification. In particular, it was verifying the effectiveness of the adopted solution made the identification the friction model and thermodynamic phenomena in the controlled pneumatic cylinder. The aim of this work is parametric optimization of the suspension system and searching for the optimal control strategy. Experimental tests were carried out under conditions of harmonic excitations, coming from the electromechanical vibration exciter with controllable pitch and frequency. Data acquisition system and control circuit of the proportional directional control valve, supplying compressed air to the actuator were implemented using MATLAB-Simulink Real-Time software.

5

Comparison of Formulas Obtained for Analytical and LQ Idea Approaches to Determine the Optimal Actuator Location in Active Multimodal Beam Vibration Reduction

Żołopa E., Brański A.

Archives of Acoustics

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2014

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Vol. 39, No. 4

599--603

EN

In this paper an active multimodal beam vibration reduction via one actuator is considered. The optimal actuator distribution is analyzed with two methods: an exact mathematical principles and the LQ problem idea. It turned out that the same mathematical expressions are derived. Thus, these methods are equivalent.

6

Czynna redukcja drgań identyfikowanych układów napędowych maszyn w postaci wielostopniowej przekładni

Dzitkowski T., Dymarek A.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

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2013

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z. 101

29--30

PL

Procesy dynamiczne zachodzące w układach napędowych maszyn związane są z występowaniem drgań w układzie. Mają one bezpośredni wpływ na emitowany hałas, wytrzymałość zmęczeniową, sterowalność i stabilność. Dlatego jednym z podstawowych kryteriów stosowanych w projektowaniu współczesnych konstrukcji mechanicznych, są właściwości dynamiczne konstrukcji opisywane w postaci częstotliwościowych funkcji przejścia. Ich znajomość pozwala uniknąć pracy układu w strefach rezonansowych, które mogą wpłynąć na trwałość i prawidłowe działanie urządzenia. Identyfikacja strukturalna i parametryczna układów ze względu na własności dynamiczne maszyny jest jedną z metod zwiększenia jej trwałości i niezawodności. Zadanie to może być zrealizowane przy wykorzystaniu algorytmów syntezy biernej i czynnej. W pracy zaprezentowana zostanie metoda wyznaczenia struktury i parametrów dynamicznych układów napędowych maszyn przy wykorzystaniu algorytmu syntezy czynnej. Metoda ta umożliwia taki dobór parametrów układu oraz siły sterującej, aby w danych warunkach pracy uzyskać obciążenia w granicach nominalnych.

7

Study operation of the active suspension system of a heavy machine cab

Tora G.

Journal of Theoretical and Applied Mechanics

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2010

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Vol. 48 nr 3

715-731

EN

This study is a part of research on active suspension systems of cabs in heavymachines and trucks, used for suppressing low-frequency and large- amplitude vibrations. The suspension system incorporates two platform mechanisms placed one upon the other. The lower mechanism is responsible for maintaining the cab in the vertical position whilst the upper mechanism controls the cab movements in the vertical direction. Motion of the cab is described using versors associated with the mechanism links. Relationships are derived that yield the instantaneous velocities of the drives that lead to reduction of the cab vibrations in selected DOFs. The procedure is shown for calculating the loads acting on the drives of the active suspension during the specified movement of the machine frame. The mathematical model is further utilised in simulations of the suspension operation.

PL

Artykuł stanowi etap prac dotyczących aktywnego zawieszenia kabiny maszyny roboczej, służącego do redukcji drgań niskoczęstotliwościowych o dużej amplitudzie. Zawieszenie składa się z dwóch mechanizmów platformowych umieszczonych jeden na drugim. Dolny mechanizm jest odpowiedzialny za utrzymanie kabiny w pionie. Górny mechanizm odpowiada za ruch kabiny w kierunku pionowym. Do opisu ruchu wykorzystano wersory związane z ogniwami mechanizmu. Wyprowadzono zależności na chwilowe prędkości napędów, powodujących redukcję drgań kabiny maszyny w wybranych stopniach swobody. Przedstawiono sposób obliczania obciążeń napędów aktywnego zawieszenia kabiny dla znanego ruchu ramy maszyny. Na podstawie matematycznego modelu wykonano symulacje pracy zawieszenia.

8

Quasi-optimal PZT distribution in active vibration reduction of the triangular plate with P-F-F boundary conditions

Brański A., Szela S.

Archives of Control Sciences

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2010

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Vol. 20, no. 2

209-226

EN

An active reduction of transverse vibration of the triangular plate with P-F-F boundary conditions is considered. The cracked plate is idealized research model as partially clamped on one edge with varying clamped length. The active reduction is realised with PZTs. In the paper, assuming the detached base clamped length, the influence of PZTs distribution on the bending moment and the shearing force at the clamped edge is investigated. To realize the purpose two cases are considered. At the former the PZTs are attached at points in which the curvatures of the surface locally take their maximum (MC sub-areas or quasi-optimal ones). At the latter, the PZTs are somewhat shifted. The plate is excited with harmonic plane acoustic wave. The second mode is considered only. The active vibration reduction study with a finite element method (FEM) is carried out. The numerical calculations show that better results are obtained for MC distribution of the PZTs.

9

Improvement of effectiveness in active triangular plate vibration reduction

Brański A., Szela S.

Archives of Acoustics

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2008

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Vol. 33, No. 4

521-530

EN

In the paper, a new method of the effectiveness increase of the active asymmetrical structure vibration reduction via PZTs is proposed. The new method is based on adding successive PZTs to quasi-optimal sub-areas (QO) in the determined order. A triangular plate with the C-F-F boundary conditions is chosen for this purpose. Only the second mode of the plate is taken into consideration in this study. To realise the aim, first the QO are determined. To each QO, PZTs are bonded from one to seven according to the following rule; namely, the consecutive PZT takes up free surface with locally maximal curvature on the QO. The effectiveness of the vibration reduction is measured in particular sense. Numerical experiments are performed to confirm the validity of this idea.

10

On the quasi optimal distribution of PZTs in active reduction of the triangular plate vibration

Branski A., Szela S.

Archives of Control Sciences

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2007

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Vol. 17, no. 4

427-437

EN

Active reduction of transverse vibration of the triangular plate is considered. The C-F-F boundary conditions are imposed. The plate is excited with harmonic acoustic wave. Since it is unsymmetrical boundary problem, the places of bonded PZTs are not obvious. To solve the problem it is based on an idea, that PZTs should be attached at points in which the curvatures of the surface locally take their maximum (quasi-optimal places). Numerical experiments are performed to confirm the validity of the idea. The bending moment and shearing force at the clamped side are calculated for two cases. First case when PZTs are attached at quasi-optimal places and second one, when PZTs are somewhat shifted. The numerical calculations show that better results are obtained at the first case. It confirms the validity of the idea of quasi-optimal distribution of PZTs on the triangular plate surface in the vibration reduction problem.