Approximate analytical solutions of smart composite mindlin beams
Approximate analytical solutions of smart composite mindlin beams
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DOI：
10.1006/jsvi.2000.3475
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发表时间：
2001-07
影响因子：
4.7
通讯作者：
D. Huang;Bohua Sun
中科院分区：
文献类型：
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作者：
D. Huang;Bohua Sun
本文给出了压电层合梁的精细理论和近似解析解。该理论的运动方程是利用能量原理建立的。该公式基于线性压电性和Mindlin层合理论，考虑了机械变形和静电学中的电荷方程之间的耦合。利用MatLab和MATHEMICA软件进行了近似解析解的求解，研究了压电传感器和执行器对智能层合梁横向响应的主动控制效果。这项工作的一个主要特点是引入了位移势函数来简化控制方程。提出了一种新的简谐振动假设和复数变换方法。它可用于同时包含正弦函数和余弦函数以及奇数阶微分系数的微分方程。还研究了传感器层的输出电压和作用在执行器层上的输入电压的行为。图形结果表明，闭环系统具有主动控制叠层梁振动的能力。本方法在这一研究领域具有普遍的应用价值。
In this paper, a refined theory and approximate analytical solutions of laminated composite beams with piezoelectric laminae are developed. The equations of motion of the theory are developed using an energy principle. This formulation is based on linear piezoelectricity and Mindlin lamination theory, and includes the coupling between mechanical deformations and the charge equations of electrostatics. The approximate analytical solutions, using software package MATLAB and MATHEMATICA, are to study the effectiveness of piezoelectric sensors and actuators in actively controlling the transverse response of smart laminated beams. A main feature of this work is that it introduces the displacement potential function to simplify the governing equation. A new assumption of harmonic vibration and the transformation method of complex numbers are introduced. It can be used in differential equations that include both items of the functions sin and cosine, and the odd-order differential coefficient. The behaviour of the output voltage from the sensor layer and the input voltage acting on the actuator layer is also studied. Graphical results are presented to demonstrate the ability of a closed-loop system to actively control the vibration of laminated beams. The present method has a general application in this field of study.