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Exact Analytical Solution of Shear-Induced Flexural Vibration of Functionally Graded Piezoelectric Beam

机译:功能梯度压电梁剪切抗弯曲振动的精确分析解

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The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d_(15) effect. In piezoelectric actuators, the potential use of d_(15) effect has been of particular interest for engineering applications since shear piezoelectric coefficient d_(15) is much higher than the other piezoelectric coupling constants d_(31) and d_33. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thickness direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton's principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.
机译:本文的优先级是通过D_(15)效应来获得FGPM光束的自由弯曲振动的精确分析解决方案。在压电致动器中,D_(15)效应的潜在使用对于工程应用已经特别令人兴趣,因为剪切压电系数D_(15)远高于其他压电耦合常数D_(31)和D_33。剪切致动器的应用是诱导和控制光束和板的弯曲振动。在该研究中,使用改进的Timoshenko光束理论,其中假设电势沿厚度方向变化正弦潜力。假设材料特性根据电力法分布横跨厚度分级。汉密尔顿的原则受雇于获得运动方程以及FGPM光束的相关边界条件。由此获得了精确的分析解,因此获得了运动方程。提出了夹紧夹紧和夹紧边界条件的结果。所提出的结果和方法壳作为比较从其他近似方法获得的结果的基准。

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