标题： 紧凑差分方法在具有非线性非局部强阻尼的欧拉-伯努利梁和板中的应用 显示英文标题

标题： Compact difference method for Euler-Bernoulli beams and plates with nonlinear nonlocal strong damping

摘要： 我们研究了数值逼近带有非线性非局部强阻尼的欧拉-伯努利（E-B）梁和板问题，这描述了实际应用中梁和板的阻尼力学行为。 我们将阻尼项分别通过梁和板问题中的复合辛普森法则和六点辛普森公式进行离散化，然后为这些问题构建全离散紧差分格式。 为了处理非线性和非局部项，我们设计了若干新颖的离散范数以促进阻尼项和数值格式的误差估计。 证明了所提出格式的稳定性、收敛性和能量耗散性质，并进行了数值实验以验证理论发现。 显示英文摘要

摘要： We investigate the numerical approximation to the Euler-Bernoulli (E-B) beams and plates with nonlinear nonlocal strong damping, which describes the damped mechanical behavior of beams and plates in real applications. We discretize the damping term by the composite Simpson's rule and the six-point Simpson's formula in the beam and plate problems, respectively, and then construct the fully discrete compact difference scheme for these problems. To account for the nonlinear-nonlocal term, we design several novel discrete norms to facilitate the error estimates of the damping term and the numerical scheme. The stability, convergence, and energy dissipation properties of the proposed scheme are proved, and numerical experiments are carried out to substantiate the theoretical findings.