The present work presents a model for nonlocal and viscoelastic Euler-Bernoulli beams and aspects of its calibration are addressed. The nonlocal feature of the model is described by the nonlocal elasticity theory proposed by Eringen and its viscoelastic behaviour is modelled by means of internal variables. Parametric analyses are performed to determine the impact of the nonlocal and viscoelastic parameters on the modal properties of the system. Inverse analyses are performed under the Bayesian framework and samples of the posterior density function are obtained by means of the Delayed Rejection Adaptive Metropolis (DRAM). The inverse analyses consider a nonlocal viscoelastic beam model with one internal variable and they address three aspects, namely: the impact of a misspecification of the beam diameter, the impact of modelling the beam diameter as an unknown but uninteresting model parameter and the model calibration when synthetic experimental data comes from a model containing two internal variables. The model parameters were chosen such that the system resembles a Single-Walled Carbon Nanotube (SWCNT).

目前的工作提出了非局部和粘弹性 Euler-Bernoulli 梁的模型，并解决了其校准方面的问题。该模型的非局部特征由 Eringen 提出的非局部弹性理论描述，其粘弹性行为通过内部变量建模。执行参数分析以确定非局部和粘弹性参数对系统模态特性的影响。在贝叶斯框架下进行逆向分析，并通过延迟拒绝自适应大都会（DRAM）获得后验密度函数的样本。逆向分析考虑具有一个内部变量的非局部粘弹性梁模型，它们涉及三个方面，即：梁直径指定错误的影响，当合成实验数据来自包含两个内部变量的模型时，将光束直径建模为未知但无趣的模型参数和模型校准的影响。选择模型参数以使系统类似于单壁碳纳米管 (SWCNT)。