The thick bar model, accounting for the lateral deformation, shear stiffness, and lateral inertia effect, is the most comprehensive structural theory to study the axial deformation of carbon nanotubes. Physically motivated definition of the axial force field and associated higher order boundary conditions are determined applying a consistent variational framework. The effects of long-range interactions are suitably realized in the framework of the nonlocal integral elasticity. The integral convolutions of the nonlocal constitutive law are determined and suitably resorted with the equivalent nonlocal differential model equipped with non-standard boundary conditions. Preceding contributions on the elastodynamic analysis of the elastic thick bar are, therefore, amended by properly taking into account the higher order and non-standard boundary conditions. The established size-dependent thick bar model is demonstrated to be exempt from the inherent drawbacks of the nonlocal differential formulation and leads to well-posed elastodynamic problems. The wave desperation response and free vibrational behavior of elastic thick bars with kinematic constraints of nano-mechanics interest are rigorously investigated by making recourse to a viable solution approach. New numerical benchmarks are detected for the elastodynamic response of nonlocal thick nano-bars. A consistent approach for nanoscopic study of the field quantities in the nonlocal mechanics is proposed that is capable of properly confirming the smaller-is-softer phenomenon.

中文翻译：

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非局部厚纳米棒的动力学

粗杆模型考虑了横向变形、剪切刚度和横向惯性效应，是研究碳纳米管轴向变形最全面的结构理论。应用一致的变分框架来确定轴向力场的物理驱动定义和相关的高阶边界条件。长程相互作用的影响在非局部整体弹性的框架中得到了适当的实现。非局部本构律的积分卷积由配备非标准边界条件的等效非局部微分模型确定并适当采用。因此，对弹性粗杆的弹性动力学分析的先前贡献是，通过适当考虑高阶和非标准边界条件进行修正。已建立的与尺寸相关的粗棒模型被证明可以避免非局部微分公式的固有缺点，并导致适定的弹性动力学问题。通过求助于可行的解决方案，对具有纳米力学运动学约束的弹性粗杆的波浪绝望响应和自由振动行为进行了严格研究。检测到非局部厚纳米棒的弹性动力学响应的新数值基准。提出了一种在非局部力学中对场量进行纳米级研究的一致方法，该方法能够正确地确认越小越软的现象。已建立的与尺寸相关的粗棒模型被证明可以避免非局部微分公式的固有缺点，并导致适定的弹性动力学问题。通过求助于可行的解决方案，对具有纳米力学运动学约束的弹性粗杆的波浪绝望响应和自由振动行为进行了严格研究。检测到非局部厚纳米棒的弹性动力学响应的新数值基准。提出了一种在非局部力学中对场量进行纳米级研究的一致方法，该方法能够正确地确认越小越软的现象。已建立的与尺寸相关的粗棒模型被证明可以避免非局部微分公式的固有缺点，并导致适定的弹性动力学问题。通过求助于可行的解决方案，对具有纳米力学运动学约束的弹性粗杆的波浪绝望响应和自由振动行为进行了严格研究。检测到非局部厚纳米棒的弹性动力学响应的新数值基准。提出了一种在非局部力学中对场量进行纳米级研究的一致方法，该方法能够正确地确认越小越软的现象。通过求助于可行的解决方案，对具有纳米力学运动学约束的弹性粗杆的波浪绝望响应和自由振动行为进行了严格研究。检测到非局部厚纳米棒的弹性动力学响应的新数值基准。提出了一种在非局部力学中对场量进行纳米级研究的一致方法，该方法能够正确地确认越小越软的现象。通过求助于可行的解决方案，对具有纳米力学运动学约束的弹性粗杆的波浪绝望响应和自由振动行为进行了严格研究。检测到非局部厚纳米棒的弹性动力学响应的新数值基准。提出了一种在非局部力学中对场量进行纳米级研究的一致方法，该方法能够正确地确认越小越软的现象。