Periodic solutions of a semilinear Euler-Bernoulli beam equation with variable coefficients

Periodic Solutions to Nonlinear Euler-Bernoulli Beam Equations

Bending vibrations of thin beams and plates may be described by nonlinear Euler-Bernoulli beam equations with $x$-dependent coefficients. In this paper we investigate existence of families of time-periodic solutions to such a model using Lyapunov-Schmidt reduction and a differentiable Nash-Moser iteration scheme. The results hold for all parameters $(ε,ω)$ in a Cantor set with asymptotically full measure as $ε\rightarrow0$.

On the Calculation of Differential Parametrizations for the Feedforward Control of an Euler-Bernoulli Beam

This contribution is concerned with the motion planning for underactuated Euler-Bernoulli beams. The design of the feedforward control is based on a differential parametrization of the beam, where all system variables are expressed in terms of a free time function and its infinitely many derivatives. In the paper, we derive an advantageous representation of the set of all formal differential parametrizations of the beam. Based on this representation, we identify a well-known parametrization, for the first time without the use of operational calculus. This parametrization is a flat one, as the …

A-PINN：辅助物理信息神经网络用于连续爱因斯坦-伯努利梁的结构振动分析

A-PINN: Auxiliary Physics-informed Neural Networks for Structural Vibration Analysis in Continuous Euler-Bernoulli Beam

A-PINN通过改进的自适应优化器提升结构振动分析的预测精度和稳定性，实验结果表明模型性能比基准提高至少40%。

The topology of Bott integrable fluids

We construct non-vanishing steady solutions to the Euler equations (for some metric) with analytic Bernoulli function in each three-manifold where they can exist: graph manifolds. Using the theory of integrable systems, any admissible Morse-Bott function can be realized as the Bernoulli function of some non-vanishing steady Euler flow. This can be interpreted as an inverse problem to Arnold's structure theorem and yields as a corollary the topological classification of such solutions. Finally, we prove that the topological obstruction holds without the non-vanishing assumption: steady Euler fl…