本文探討矩形奈米梁與單層(Single-Walled, SW)、雙層(Double-Walled, DW)、乃至於多層(Multi-Walled, MW)奈米碳管(Carbon Nanotubes, CNTs)在不同的邊界條件束制下的自然振動行為，其邊界條件包含簡支承、自由端、固定端等組合邊界，該CNT結構亦考慮嵌入或非嵌入於彈性介質之中。文中分別基於虛位移原理(The Principle of Virtual Displacements, PVD)和Reissner混合變分理論(Reissner’s Mixed Variational Theorem, RMVT)推衍非局部Timoshenko梁理論下相應之強型式和弱型式Euler-Lagrange運動方程式並將其應用於SW、DW和MWCNT之自然振動分析。

This article is intended to present free vibration analysis of single-, double-, and multi-walled (SW-, DW-, and MW-) carbon nanotubes (CNTs) with combinations of simply-supported, free, and clamped edge conditions embedded or non-embedded in an elastic medium. Based on the principle of virtual displacements (PVD) and Reissner’s mixed variational theorem (RMVT), the corresponding strong- and weak-form formulations of the local Timoshenko beam theory(TBT) are reformulated for the free vibration analysis of SW-, DW-, and MW-CNTs, and presented for illustrative purposes.

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