Abstract A Timoshenko functionally graded (TFG) imperfect microscale beam is considered and the coupled viscoelastic mechanics is analysed in a nonlinear regime. Based on the Timoshenko beam theory, incorporating geometric imperfections, the Kelvin-Voigt method is used for internal viscosity, the rotary inertia is automatically generated due to the Timoshenko theory, and the Mari-Tanaka scheme is used for the mixture. After utilising the constitutive stress/strain relations, Hamilton’s principle is used giving three sets of coupled motion equations. A discretisation is performed using Galerkin’s method and numerical simulations, for mechanical behaviour analysis, are built upon a continuation method.

中文翻译：

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Timoshenko 功能梯度不完美微梁的粘弹性力学

摘要 考虑了Timoshenko 功能梯度(TFG) 缺陷微尺度梁，并在非线性状态下分析了耦合粘弹性力学。基于Timoshenko梁理论，结合几何缺陷，内部粘度采用Kelvin-Voigt方法，由于Timoshenko理论自动产生转动惯量，混合采用Mari-Tanaka方案。利用本构应力/应变关系后，利用哈密顿原理给出三组耦合运动方程。离散化是使用 Galerkin 方法进行的，而用于力学行为分析的数值模拟则建立在连续法的基础上。