论文标题
通用kirchhoff-love板的稳定而准确的数值方法
Stable and accurate numerical methods for generalized Kirchhoff-Love plates
论文作者
论文摘要
开发了有效且准确的数值算法来解决符合三个常见物理边界条件的广义kirchhoff-love板模型：（i）夹紧； （ii）只是支持； （iii）免费。我们通过使用二阶有限差分方案离散空间衍生物来解决模型方程，然后使用显式预测器 - 校正器或隐式newmark-beta-beta time-stepppepting algorithm及时推进半混凝土问题。对方案进行了稳定分析，结果用于确定实践中稳定的时间步骤。 解决了一系列精心选择的测试问题，以证明我们的数值方法的特性和应用。数值结果证实了该算法的稳定性和二阶精度，并且与相似的薄板的实验也可比。作为应用程序，我们说明了一种策略，即使用我们的数值方法与计算数据的快速傅立叶变换（FFT）功率谱分析结合使用我们的数值方法来识别板的固有频率。然后，我们利用一个计算的固有频率之一来模拟有趣的物理现象，称为共鸣，并为广义的Kirchhoff-love板击败。
Efficient and accurate numerical algorithms are developed to solve a generalized Kirchhoff-Love plate model subject to three common physical boundary conditions: (i) clamped; (ii) simply supported; and (iii) free. We solve the model equation by discretizing the spatial derivatives using second-order finite-difference schemes, and then advancing the semi-discrete problem in time with either an explicit predictor-corrector or an implicit Newmark-Beta time-stepping algorithm. Stability analysis is conducted for the schemes and the results are used to determine stable time steps in practice. A series of carefully chosen test problems are solved to demonstrate the properties and applications of our numerical approaches. The numerical results confirm the stability and 2nd-order accuracy of the algorithms, and are also comparable with experiments for similar thin plates. As an application, we illustrate a strategy to identify the natural frequencies of a plate using our numerical methods in conjunction with a fast Fourier transformation (FFT) power spectrum analysis of the computed data. Then we take advantage of one of the computed natural frequencies to simulate the interesting physical phenomena known as resonance and beat for a generalized Kirchhoff-Love plate.
