Wyniki wyszukiwania - BazTech

1

On nonexistence of global in time solution for a mixed problem for a nonlinear evolution equation with memory generalizing the Voigt-Kelvin rheological model

Pukach P., Il'kiv V., Nytrebych Z., Vovk M.

Opuscula Mathematica

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2017

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Vol. 37, no. 5

735--753

EN

The paper deals with investigating of the first mixed problem for a fifth-order nonlinear evolutional equation which generalizes well known equation of the vibrations theory. We obtain sufficient conditions of nonexistence of a global solution in time variable.

2

A study on natural frequencies of Timoshenko beam with rapidly varying stiffness

Świątek M., Domagalski Ł., Jędrysiak J.

Vibrations in Physical Systems

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2016

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Vol. 27

369--376

EN

Vibrations of Timoshenko beams with properties periodically varying along the axis are under consideration. The tolerance method of averaging differential operators with highly oscillating coefficients is applied to obtain the governing equations with constant coefficients. The dynamics of Timoshenko beam with the effect of the cell length is described. A asymptotic model is then constructed, which is further studied in analysis of the low order natural frequencies. The proposed model is able to describe dynamics of beams made of non-slender cells.

3

Dynamic response of a simply supported viscoelastic beam of a fractional derivative type to a moving force load

Freundlich J.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 4

1433--1445

EN

In the paper, the dynamic response of a simply supported viscoelastic beam of the fractional derivative type to a moving force load is studied. The Bernoulli-Euler beam with the fractional derivative viscoelastic Kelvin-Voigt material model is considered. The RiemannLiouville fractional derivative of the order 0 < α ¬ 1 is used. The forced-vibration solution of the beam is determined using the mode superposition method. A convolution integral of fractional Green’s function and forcing function is used to achieve the beam response. Green’s function is formulated by two terms. The first term describes damped vibrations around the drifting equilibrium position, while the second term describes the drift of the equilibrium position. The solution is obtained analytically whereas dynamic responses are calculated numerically. A comparison between the results obtained using the fractional and integer viscoelastic material models is performed. Next, the effects of the order of the fractional derivative and velocity of the moving force on the dynamic response of the beam are studied. In the analysed system, the effect of the term describing the drift of the equilibrium position on the beam deflection is negligible in comparison with the first term and therefore can be omitted. The calculated responses of the beam with the fractional material model are similar to those presented in works of other authors.

4

Numerical Investigation of Piezoelectric Element Coupling Degradation in Active Beam Systems

Freundlich J. K., Pietrzakowski M.

Machine Dynamics Research

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2013

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Vol. 37, No. 4

13-26

EN

The objective of the present study is to develop modelling of the piezoelectric element edge delamination process and analysis of effects of the progressive adhesive interlayer damage on active beam dynamic behaviour. In the considered system piezoelectric patches are mounted to both opposite sides of the beam and operate as a collocated sensor/actuator pair with velocity feedback. Herein, the actuator coupling damage is described as a large reduction of the adhesive interlayer shear stiffness. It is assumed that the damaged zone of the decreased stiffness extends uniformly across the actuator from its edges to the centre. In the analysis, the beam is divided into sections due to its geometry and the supposed delaminated regions. The calculations are performed using the FE analysis. In the first step, the cantilever beam with piezoelectric elements bonded to the beam surface by a thin glue layer of uniform properties is analysed. The beam is excited by a time varying force. In order to validate the arranged FE model, the analytical and FE calculations of open and closed loop dynamic responses are performed. The compared results show quite good agreement and prove that the applied FE model of the considered system is correct and can be accepted for further numerical analysis. In the next step, FE simulations of the beam forced vibration suppressed by piezoelectric control system with velocity feedback are accomplished. The influence of the length of damaged zone on the dynamic characteristics and the control effectiveness is investigated. As expected, the size, type and location of the coupling damage influence on the dynamic characteristics of the examined beam and cause reduction of the system control efficiency.

5

Model based predictive control of beam with magnetorheological fluid

Snamina J.

Mechanics and Control

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2011

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Vol. 30, no. 3

164-169

EN

In the work a model predictive control method was applied to control the beam vibrations. Model predictive control (MPC) is widely used as advanced control methodology. The considered beam consists of two outer layers made of aluminium and MR fluid layer in between. Activation of the MR fluid is realized by magnetic field. The analysis of strain and stress in three-layered beam were done. Then the equation of forced vibration of beam in the vicinity of the first resonances was derived. Based on this equation the simulation of MPC application was performed for the sinusoidal and random excitation.

PL

W pracy zastosowano algorytm sterowania predykcyjnego przy wykorzystaniu modelu do redukcji drgań belki z cieczą magnetoreologiczną (MR). Rozważana belka składa się z dwóch zewnętrznych warstw wykonanych z aluminium oraz umieszczonej pomiędzy nimi warstwy cieczy MR. Zmiana własności cieczy MR następuje w wyniku wytworzenia przez elektromagnes pola magnetycznego obejmującego część belki. Przedstawiono analizę stanu odkształcenia i stanu naprężenia w poszczególnych warstwach belki. Wyprowadzono równania opisujące drgania w otoczeniu pierwszego rezonansu. Na podstawie zbudowanego modelu zaproponowano algorytm sterowania predykcyjnego, którego celem była redukcja drgań belki. Wykonano symulację drgań belki dla wymuszenia sinusoidalnego oraz stochastycznego.

6

Experimental Analysis of Beam Vibrations Damping with the Special ABS Granular Structure

Zalewski R., Bajkowski J. M.

Machine Dynamics Research

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2011

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Vol. 35, No. 3

98-106

EN

The analysis and generalization of experimental data obtained for the steel beam covered with hermetic sleeve with granular material, were used to determine the influence vacuum effect on beam vibrations. Increasing the underpressure value leads to clustering and interlocking of the grains, thus the so called jammed state and force chains occur. Experimental results confirmed that the granular-filled vacuum structure can be used for easily controlled significant increase in damping ratio of the system.

7

New possibilities of the active damping of vibrations

Bajkowski J., Tadzik P., Zalewski R.

Mechanics / AGH University of Science and Technology

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2007

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Vol. 26, no. 4

156-158

EN

In presented paper a new proposition of granular structure, composed on the basis of granular materials placed in hermetic space with underpressure, as a damping material for vibrated steel beam has been described. Three different types of laboratory tests have been described: fundamental strength properties of granular testing specimen, bending of granular beam and damping of the steel beam vibrations using special granular structures. Obtained results revealed that the behavior of such a structure could be easily controlled by underpressure parameter. Also damping characteristics of vibrated steel beam could be controlled by changing internal underpressure value.

PL

W artykule zaprezentowano zastosowanie struktury, zbudowanej na bazie luźnego granulatu umieszczonego w szczelnej przestrzeni z podciśnieniem, do tłumienia drgań belki stalowej. Omówiono trzy typy badań eksperymentalnych: podstawowe badania wytrzymałościowe próbki struktury granulowanej, badania zginania belek granulowanych oraz badania tłumienia drgań belki stalowej za pomocą wspomnianych materiałów. Wyniki przeprowadzonych eksperymentów jednoznacznie potwierdzają możliwość wpływania na parametry fizyczne granulowanych konglomeratów za pomocą parametru podciśnienia i tym samym na postacie charakterystyk tłumienia drgań swobodnych belki stalowej.

8

Control system of beam vibration using piezo elements

Gosiewski Z., Sochacki A.

Archives of Control Sciences

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2003

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Vol. 13, no. 3

375-385

EN

In modern mechanical contructions active damping seems to be essential. But real mechanical contructions are complicated in shape and are composed of components with distributed parameters. That is why advanced modeling techniques should be implemented in the process of designing of vibration control system. In this paper we design a vibration control system for cantilever beam. As a sensor of the beam movement and as an actuator we use piezoelectric elements coupled with hardware of dSpace and software of Matlab-Simulink. The relations describing influence of piezo-actuator on the beam bending has been found. Measurement equation for piezo sensor was also prepared. Control system was designed for a few controlled modes. The influence of control system on non-controlled modes is considered.

9

Experimental and analytical investigation of actively damped beam vibrations

Pietrzakowski M

Mechanics and Mechanical Engineering

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2001

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Vol. 5, nr 2

111-120

EN

The problem of active damping of cantilever beam transverse vibrations is considered, by using a collocated piezoceramic sensor and actuator. Experimental results of free vibrations confirmed the effectiveness of the control circuit with the analog derivative controller for suppression of a low-frequency beam motion. Theoretical analysis is based on the simplified pure bending model of interaction between the piezoactuator and the beam with a constant equivalent stiffness. The viscoelastic material parameters of the tested beam are estimated considering the fundamental frequency and logarithmic decrement of transient vibrations. The results of simulation, even for the applied simplified model of the system, are in a good agreement with the experiment.