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Two-Dimensional Free Vibration Analysis of Axially Functionally Graded Beams Integrated with Piezoelectric Layers: An Piezoelasticity Approach
International Journal of Applied Mechanics ( IF 3.5 ) Pub Date : 2020-06-10 , DOI: 10.1142/s1758825120500374
Agyapal Singh 1 , Poonam Kumari 1
Affiliation  

For the first time, a two-dimensional (2D) piezoelasticity-based analytical solution is developed for free vibration analysis of axially functionally graded (AFG) beams integrated with piezoelectric layers and subjected to arbitrary supported boundary conditions. The material properties of the elastic layers are considered to vary linearly along the axial ([Formula: see text]) direction of the beam. Modified Hamiltons principle is applied to derive the weak form of coupled governing equations in which, stresses, displacements and electric field variables acting as primary variables. Further, the extended Kantorovich method is employed to reduce the governing equation into sets of ordinary differential equations (ODEs) along the axial ([Formula: see text]) and thickness ([Formula: see text]) directions. The ODEs along the [Formula: see text]-direction have constant coefficients, where the ODEs along [Formula: see text]-direction have variable coefficients. These sets of ODEs are solved analytically, which ensures the same order of accuracy for all the variables by satisfying the boundary and continuity conditions in exact pointwise manner. New benchmark numerical results are presented for a single layer AFG beam and AFG beams integrated with piezoelectric layers. The influence of the axial gradation, aspect ratio and boundary conditions on the natural frequencies of the beam are also investigated. These numerical results can be used for assessing 1D beam theories and numerical techniques.

中文翻译:

与压电层集成的轴向功能梯度梁的二维自由振动分析:一种压电弹性方法

首次开发了一种基于二维 (2D) 压电弹性的解析解,用于对与压电层集成并受到任意支撑边界条件的轴向功能梯度 (AFG) 梁进行自由振动分析。弹性层的材料特性被认为沿梁的轴向([公式:见文本])线性变化。改进的哈密顿原理用于导出耦合控制方程的弱形式,其中应力、位移和电场变量作为主要变量。此外,采用扩展 Kantorovich 方法将控制方程简化为沿轴向([公式:参见文本])和厚度([公式:参见文本])方向的常微分方程 (ODE) 组。[公式中的常微分方程:见文本]-方向具有恒定系数,其中沿 [公式:见文本]-方向的 ODE 具有可变系数。这些 ODE 集通过解析求解,通过以精确的逐点方式满足边界和连续性条件,确保所有变量的精度相同。为单层AFG梁和与压电层集成的AFG梁提供了新的基准数值结果。还研究了轴向级配、纵横比和边界条件对梁的固有频率的影响。这些数值结果可用于评估一维光束理论和数值技术。通过以精确的逐点方式满足边界和连续性条件,确保所有变量的精度相同。为单层AFG梁和与压电层集成的AFG梁提供了新的基准数值结果。还研究了轴向级配、纵横比和边界条件对梁的固有频率的影响。这些数值结果可用于评估一维光束理论和数值技术。通过以精确的逐点方式满足边界和连续性条件,确保所有变量的精度相同。为单层AFG梁和与压电层集成的AFG梁提供了新的基准数值结果。还研究了轴向级配、纵横比和边界条件对梁的固有频率的影响。这些数值结果可用于评估一维光束理论和数值技术。还研究了梁的固有频率的纵横比和边界条件。这些数值结果可用于评估一维光束理论和数值技术。还研究了梁的固有频率的纵横比和边界条件。这些数值结果可用于评估一维光束理论和数值技术。
更新日期:2020-06-10
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