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Suppression of vibration with optimal actuators and sensors placement

Starek L., Starek D., Solek P., Starekova A.

Archives of Control Sciences

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2010

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Vol. 20, no. 1

99-120

EN

It is proposed to place the actuators to maximize the mean value of energy transmitted from or dissipated by the actuators, while the sensor location should maximize the mean square value of system output, which also maximizes the signal-to-noise ratio. By using explicit expressions for controllability and observability grammians as well as modal energies, it is shown that the approaches based on the system responses to transient and persistent disturbances are closely related, and are equivalent for structures which damping is small and the natural frequencies of which are well spaced. The method of actuator and sensor optimal location via grammians was proposed and compared it with results given by the method of matrix norms.

2

Transient thermal analysis of functionally graded shallow shells by the MLPG

Sladek J., Sladek V., Solek P.

Computer Methods in Materials Science

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2009

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Vol. 9, No. 2

171-177

EN

In recent years the demand for construction of huge and lightweight shell and spatial structures is increasing. To minimize the weight of shell structures a layered profile of the shell is utilized frequently. In such a case a delaminating of individual layers may occur due to a jump change of the material properties. To remove this phenomenon the functionally graded materials (FGMs) has been introduced recently. FGMs are multi-phase materials with a pre-determined property profile, where the phase volume fractions are varying gradually in space. This results in continuously nonhomogenous material properties at the macroscopic structural scale. Often, these spatial gradients in the material behaviour render FGMs as superior to conventional composites because of their continuously graded structures and properties. FGMs may exhibit isotropic or anisotropic material properties, depending on the processing technique and the practical engineering requirements. Many linear bending studies are focused only to a lateral pressure load with assumption of uniformly distributed temperature in the whole shell. However, in shells with FGM properties the role of thermal loading is more imperative. Therefore, it is interesting to analyze shells under a general thermal load. Literature sources on this subject are poor and they are mostly restricted to analyses of plates. Due to the high mathematical complexity of the boundary or initial-boundary value problems, analytical approaches for FGMs are restricted to simple geometry and boundary conditions. The choice of an appropriate mathematical model together with a consistent computational method is important for such kind of structures. Most significant advances in shell analyses have been made using the finite element method (FEM). It is well known that numerical results by standard displacement-based type shell element are over stiff with yielding the shear locking phenomena in thin shells. Locking problems arise due to inconsistencies in discrete representations of the transverse shear energy and the membrane energy. The boundary element method (BEM) has emerged as an alternative numerical method to solve plate and shell problems. It is a very powerful computational method if a fundamental solution is available for considered problem. However, the fundamental solution for a thick orthotropic shell wit continuously varying material properties is not available according to the best of the author?s knowledge. Meshless approaches for solution of problems of continuum mechanics have attracted much attention during the past decade. One of the most rapidly developed meshfree methods is the Meshless Local Petrov-Galerkin method (MLPG). The solution of the uncoupled problem in the present paper is split into two tasks. In the first task the temperature distribution in the shell has to be obtained by solving the diffusion equation. The temperature distribution in shell has to be analyzed as 3-D problem. The MLPG is applied to transient heat conduction equations in a continuously nonhomogeneous solid. The Laplace transform technique is used to eliminate the time variable. Several quasi-static boundary value problems must be solved for various values of the Laplace-transform parameter. The Stehfest?s inversion method is applied to obtain the time-dependent solution. In the second task, the set of governing differential equations for Reissner-Mindlin shell bending theory with Duhamel-Neumann constitutive equations is solved. Since thermal changes in solids are relatively slow with respect to elastic wave velocity, the inertial terms in Reissner-Mindlin governing equations are not considered. The problem is considered as quasi-static with time dependent thermal forces. The MLPG method is applied again to solution of that problem with the meshless Moving Least-Squares (MLS) approximation of primary field variables. The nodal points are spread freely in the analyzed domain and on its boundary. The essential boundary conditions are satisfied by collocation of approximated fields at nodes with prescribed values. In other nodes, the governing PDEs are considered on subdomains around these nodes in the local weak-form with using unit test functions. The resulting local integral equations are discretized within the assumed approximation of field variables. Numerical results for simply supported and clamped square shells are presented to illustrate the efficiency of the present computational method.

PL

Tematem niniejszej pracy jest wykorzystanie lokalnej beziastkowej metody Petrova-Galerkina (MLPG) do problemu odkształceń termicznych powłok Reissnera-Mindlina. W studium wykorzystano model funkcjonalnych materiałów gradientowych z założeniem ciągłej zmiany własności na grubości elementu powłokowego. Forma słaba równań występujących w teorii Reissnera-Mindlina została przeniesiona na zbiór równań całkowych rozwiązywanych w obszarze zdefiniowanych poddomen. Cylindryczne poddomeny losowo otaczają wygenerowane punkty węzłowe. W rozwiązaniu wykorzystano beziatkową aproksymację metody Moving Least-Squares (MLS).

3

Suppression of vibration of a clamped beam via piezoceramics

Starek L., Solek P., Starek D., Starekova A., Blesak P.

Mechanics / AGH University of Science and Technology

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2007

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Vol. 26, no. 4

187-194

EN

Contribution deals with the suppression of the resonance vibration of a clamped beam with sensors and actuators made of piezoceramics material. It will be discussed the problem of influencing of a response of vibration by higher frequencies so called control and observation spillover. The model of a beam with piesoceramics was designed in environment ANSYS. The properties of the model have been identified from the response on an unit step impuls (voltage). The control was realized by controller with PPF method. Simulation of control has been realized on the clamped beam in environment MATLAB. There was designed an experimental test bed for verification of the simulation results.

PL

Artykuł dotyczy tłumienia drgań rezonansowych jednostronnie zamocowanej belki z czujnikiem i aktuatorem wykonamym z materiału piezoelektrycznego. Omówiono problem wpływu odpowiedzi w postaci drgań o częstotliwościach większych od częstotliwości Nyquista na sterowanie i sprzężenie zwrotne, nazywanego w literaturze angielskiej: control and observation spillover. Model belki z piezoelektrykiem został zaimplementowany w programie ANSYS. Właściwości modelu zostały zidentyfikowane na podstawie odpowiedzi układu na wymuszenie w postaci skoku jednostkowego (skoku napięcia). Sterowanie układem zostało zrealizowane przy wykorzystaniu regulatora z dodatnim sprzężeniem zwrotnym od przemieszczenia. Symulacja sterowania jednostronnie zamocowanej belki zrealizowana została w środowisku MATLAB. Zaprojektowano również eksperymentalne stanowisko badawcze do weryfikacji badań symulacyjnych.

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Suppression of vibration of a clamped beam with embedded self-sensing piezoceramic actuator

Starek L., Solek P., Starekova A., Blesak P.

Elektronika : konstrukcje, technologie, zastosowania

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2004

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Vol. 45, nr 8-9

22-24

EN

A performance study of a clamped beam with embedded self-sensing piezoceramic actuator will be presented. We will explore a problem in vibration suppress on for the free and forced vibration of the clamped beam. The both, the experimental implementation of the clamped beam with embedded self-sensing piezoceramic and the FEM model are developed and the comparison between experimental and simulation results for free and forced vibration is given.

PL

W artykule przedstawione zostaną badania dotyczące działania belki wspornikowej z wbudowanym inteligentnym siłownikiem piezoceramicznym. Przebadano problem tłumienia swobodnych i wymuszonych drgań belki. Opracowano zarówno doświadczalną realizację belki wspornikowej z wbudowanym inteligentnym siłownikiem piezoceramicznym jak i model MES. Na tej podstawie dokonano porównania pomiędzy wynikami uzyskanymi na drodze doświadczalnej a rezultatami symulacji w przypadku drgań swobodnych oraz wymuszonych.