In this technical note, we consider a dynamic linear, cantilevered rectangular plate. The evolutionary PDE model is given by the fourth order plate dynamics (via the spatial biharmonic operator) with clamped-free-free-free boundary conditions. We additionally consider damping/dissipation terms, as well as non-conservative lower order terms arising in various applications. Dynamical numerical simulations are achieved by way of a finite difference spatial approximation with a MATLAB time integrator. The rectangular geometry allows the use of standard 2D spatial finite differences, while the high spatial order of the problem and mixed clamped-free type boundary conditions present challenges. Dynamic energies are also computed. The relevant code is presented, with discussion of the model and context.

翻译：在本技术说明中,我们考虑的是动态线性、可裂变的长方形板块。进化式PDE模型由第四顺序板块动态(通过空间双调操作器)提供,具有无限制的无边界条件。我们另外考虑的是各种应用中产生的阻隔/分散条件以及非保守性较低顺序条件。动态数字模拟是通过与MATLAB时间集成器进行有限的空间近距离近似而实现的。矩形几何学允许使用标准的2D空间限制差异,而问题高度空间顺序和混合的无限制类型边界条件则构成挑战。还计算了动态能量。提出了相关的代码,并讨论了模型和背景。