Bifurcation, chaos and active control of piezoelectric sandwich beams

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Journal of Vibration and Shock ›› 2011, Vol. 30 ›› Issue (10) : 260-264.

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Bifurcation, chaos and active control of piezoelectric sandwich beams

ZHANG Peng; JIA Zhong-yin

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Abstract

The paper investigated the bifurcation, chaotic dynamics and active control of simply supported piezoelectric sandwich beams with axial loading. Based on the piezoelectric materials constitutive relations and von Karman type geometrically nonlinear strain-displacement relations, considering a proportional and derivative potential feedback laws coupling the direct and inverse piezoelectric coefficients, the nonlinear partial differential equation of motion of the beams is derived by Hamilton’s principle and then discretize it using Galerkin approach. Numerical simulation is carried out to investigate the dynamic bifurcation of the beams. The results show that the oscillation of the piezoelectric sandwich beams can be controlled with the gain proportional and derivative potentials of the considered feedback control.

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piezoelectric sandwich beams / bifurcation / chaotic motion / active control

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ZHANG Peng; JIA Zhong-yin. Bifurcation, chaos and active control of piezoelectric sandwich beams[J]. Journal of Vibration and Shock, 2011, 30(10): 260-264