An analytical solution has been developed developed in this research for electro-mechanical flexural response of smart laminated piezoelectric composite rectangular plates encompassing flexible-spring boundary conditions at two opposite edges. Flexible-spring boundary structure is introduced to the system by inclusion of rotational springs of adjustable stiffness which can vary depending on changes in the rotational fixity factor of the springs. To add to the case study complexity, the two other edges are kept free. Three advantages of employing the proposed analytical method include: (1) the electro-mechanical flexural coupling between the piezoelectric actuators and the plate’s rotational springs of adjustable stiffness is addressed; (2) there is no need for trial deformation and characteristic function—therefore, it has higher accuracy than conventional semi-inverse methods; (3) there is no restriction imposed to the position, type, and number of applied loads. The Linear Theory of Piezoelectricity and Classical Plate Theory are adopted to derive the exact elasticity equation. The higher-order Fourier integral and higher-order unit step function differential equations are combined to derive the analytical equations. The analytical results are validated against those obtained from Abaqus Finite Element (FE) package. The results comparison showed good agreement. The proposed smart plates can potentially be applied to real-life structural systems such as smart floors and bridges and the proposed analytical solution can be used to analyze the flexural deformation response.

在这项研究中已经开发出一种分析解决方案，用于智能层压压电复合矩形板的机电弯曲响应，该矩形板在两个相对的边缘处都包含弹性弹簧边界条件。通过包括可调节刚度的旋转弹簧将挠性弹簧边界结构引入系统，该弹簧可以根据弹簧的旋转固定系数的变化而变化。为了增加案例研究的复杂性，另两个方面保持自由。采用所提出的分析方法的三个优点包括：（1）解决了压电致动器和刚度可调的板旋转弹簧之间的机电弯曲耦合；（2）无需尝试变形和特征函数-因此，它比传统的半反方法具有更高的精度；（3）对施加载荷的位置，类型和数量没有限制。采用压电线性理论和经典板理论推导精确的弹性方程。将高阶傅立叶积分和高阶单位阶跃函数微分方程组合起来，得出解析方程。分析结果相对于从Abaqus有限元（FE）软件包获得的结果进行了验证。结果比较表明吻合良好。所提出的智能板可以潜在地应用于诸如智能地板和桥梁的现实生活结构系统，并且所提出的分析解决方案可以用于分析挠曲变形响应。和施加的载荷数。采用压电线性理论和经典板理论推导精确的弹性方程。将高阶傅立叶积分和高阶单位阶跃函数微分方程组合起来，得出解析方程。分析结果相对于从Abaqus有限元（FE）软件包获得的结果进行了验证。结果比较表明吻合良好。所提出的智能板可以潜在地应用于诸如智能地板和桥梁的现实生活结构系统，并且所提出的分析解决方案可以用于分析挠曲变形响应。和施加的载荷数。采用压电线性理论和经典板理论推导精确的弹性方程。将高阶傅立叶积分和高阶单位阶跃函数微分方程组合起来，得出解析方程。分析结果相对于从Abaqus有限元（FE）软件包获得的结果进行了验证。结果比较表明吻合良好。所提出的智能板可以潜在地应用于诸如智能地板和桥梁的现实生活结构系统，并且所提出的分析解决方案可以用于分析挠曲变形响应。将高阶傅立叶积分和高阶单位阶跃函数微分方程组合起来，得出解析方程。分析结果相对于从Abaqus有限元（FE）软件包获得的结果进行了验证。结果比较表明吻合良好。所提出的智能板可以潜在地应用于诸如智能地板和桥梁的现实生活结构系统，并且所提出的分析解决方案可以用于分析挠曲变形响应。将高阶傅立叶积分和高阶单位阶跃函数微分方程组合起来，得出解析方程。分析结果相对于从Abaqus有限元（FE）软件包获得的结果进行了验证。结果比较表明吻合良好。所提出的智能板可以潜在地应用于诸如智能地板和桥梁的现实生活结构系统，并且所提出的分析解决方案可以用于分析挠曲变形响应。