In this paper, the dynamic modelling and adaptive boundary control of a three-dimensional Timoshenko beam are presented for vibration suppression. In order to ensure that no modal information is left out, partial differential equations (PDEs) are employed to describe the nonlinear dynamic characteristics of the system by applying the extended Hamilton’s principle. Based on the established model, barrier Lyapunov functions (BLFs) are utilised for dealing with system output restrictions. For practical consideration, parameter uncertainties and external disturbances are also taken into account. Under the proposed neural adaptive control scheme, undesirable elastic vibration of the three-dimensional Timoshenko beam is restricted and constrained within given bounds even subject to external perturbations, without needing to know any system parameters. The system stability is proved by the Lyapunov’s direct method. The control performance is verified via using numerical simulations.

在本文中，提出了用于振动抑制的三维 Timoshenko 梁的动力学建模和自适应边界控制。为了确保不遗漏任何模态信息，通过应用扩展的哈密顿原理，采用偏微分方程 (PDE) 来描述系统的非线性动态特性。在建立的模型的基础上，利用障碍李雅普诺夫函数（BLFs）来处理系统输出限制。出于实际考虑，还考虑了参数不确定性和外部干扰。在提出的神经自适应控制方案下，即使受到外部扰动，三维 Timoshenko 梁的不良弹性振动也被限制和约束在给定的范围内，而无需知道任何系统参数。系统稳定性由李雅普诺夫直接法证明。通过使用数值模拟验证控制性能。