This paper addresses the model reduction and the simulation of a damped Euler–Bernoulli–von Kármán pinned beam excited by a distributed force. This nonlinear problem is formulated as a PDE and reformulated as a well-posed state-space system. The model order reduction and simulation are derived by combining two approaches: a Volterra series expansion and truncation and a pseudo-modal truncation defined from the eigenbasis of the linearized problem. The interest of this approach lies in the large class of input waveshapes that can be considered and in the simplicity of the simulation structure. This structure only involves cascades of finite-dimensional decoupled linear systems and multilinear functions. Closed-form bounds depending on the model coefficients and the truncation orders are provided for the Volterra convergence domain and the approximation error. These theoretical results are generalized to a large class of nonlinear models, and refinement of bounds are also proposed for a large sub-class. Numerical experiments confirm that the beam model is well approximated by the very first Volterra terms inside the convergence domain.

本文讨论了由分布力激发的阻尼 Euler-Bernoulli-von Kármán 钉扎梁的模型简化和仿真。这个非线性问题被表述为一个偏微分方程，并被重新表述为一个适定的状态空间系统。模型降阶和模拟是通过结合两种方法得出的：Volterra 级数展开和截断以及从线性化问题的本征基定义的伪模态截断。这种方法的兴趣在于可以考虑的大类输入波形以及仿真结构的简单性。这种结构只涉及有限维解耦线性系统和多线性函数的级联。为 Volterra 收敛域和近似误差提供了取决于模型系数和截断阶数的封闭形式边界。这些理论结果被推广到一大类非线性模型，并且还为大子类提出了边界的细化。数值实验证实，光束模型很好地由收敛域内的第一个 Volterra 项近似。