Two-dimensional analysis of simply supported piezoelectric beams with variable thickness.

*(English)*Zbl 1225.74059Summary: A two-dimensional analysis is presented for piezoelectric beam with variable thickness which is simply supported and grounded along its two ends. According to the governing equations of plane stress problems, the displacement solutions, which exactly satisfy the governing differential equations and the simply-supported boundary conditions at two ends of the beam, are derived. The unknown coefficients in the solution are then determined by using the Fourier sinusoidal series expansion to the boundary equations on the upper and lower surfaces of the beams. The present solutions show a good convergence and the numerical results are presented and compared with those available in the literature. The method could be applied to control engineering and other projects with highly accurate demand on stress and displacement analysis such as the design of micro-mechanical apparatuses.

##### MSC:

74M05 | Control, switches and devices (“smart materials”) in solid mechanics |

74F15 | Electromagnetic effects in solid mechanics |

35Q74 | PDEs in connection with mechanics of deformable solids |

74G10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

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\textit{Y. Xu} and \textit{D. Zhou}, Appl. Math. Modelling 35, No. 9, 4458--4472 (2011; Zbl 1225.74059)

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