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

100%

Freundlich J.

tom Vol. 54 nr 4

1433--1445

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.

Experimental and analytical investigation of actively damped beam vibrations

75%

Pietrzakowski M.

tom Vol. 5, nr 2

111-120

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.

Model based predictive control of beam with magnetorheological fluid

75%

Snamina J.

tom Vol. 30, no. 3

164-169

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.

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.