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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

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.

3

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.

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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.