ABSTRACT Analysis of nonlocal axial vibration in a nanorod is a crucial subject in science and engineering because of its wide applications in nanoelectromechanical systems. The aim of this paper is to show how these vibrations can be modelled within the framework of port-Hamiltonian systems. It turns out that two port-Hamiltonian descriptions in physical variables are possible. The first one is in descriptor form, whereas the second one has a non-local Hamiltonian density. In addition, it is shown that under appropriate boundary conditions these models possess a unique solution which is non-increasing in the corresponding ‘energy’, i.e., the associated infinitesimal generator generates a contraction semigroup on a Hilbert space, whose norm is directly linked to the Hamiltonian.

中文翻译：

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粘弹性纳米棒中非局部纵向振动的 Port-Hamiltonian 模型

摘要 由于纳米棒在纳米机电系统中的广泛应用，纳米棒中非局部轴向振动的分析是科学和工程中的重要课题。本文的目的是展示如何在 port-Hamiltonian 系统的框架内对这些振动进行建模。事实证明，物理变量中的两种波特-汉密尔顿描述是可能的。第一个是描述符形式，而第二个具有非局部哈密顿密度。此外，结果表明，在适当的边界条件下，这些模型具有唯一的解，该解不增加相应的“能量”，即相关的无穷小生成元在希尔伯特空间上生成一个收缩半群，其范数直接与哈密​​顿量。