Abstract
This review paper deals with two problems in structural engineering dynamics; one is deterministic, the other is of stochastic nature. One problem is linear, the other is nonlinear. Authors have a biased preferential view on these problems because of their active involvement in the discussed research topics. Still, these two problems reflect, at least in a small manner, some developments in this vast and fascinating field. The first part deals with deterministic linear vibrations of double-walled carbon nanotubes either in classical or refined setting; the second part is devoted to the nonlinear random vibrations of structures.
Highlights
As Qian et al [1] mention that “the discovery of multi-walled carbon nanotubes (MWCNTs) in 1991 has stimulated ever-broader research activities in science and engineering devoted entirely to carbon nanostructures and their applications
Xu et al [4,5] and Ru [6] studied the free vibrations of a double-walled carbon nanotubes (DWCNTs) which is composed of two coaxial single-walled CNTs interacting with each other by the interlayer van der Waals forces
The results showed that DWCNTs have frequencies in the range of terahertz (THz)
Summary
Nanotechnology became recently a very active field of research. This section deals with evaluation of fundamental natural frequencies of double-walled carbon nanotubes under various boundary conditions. The Bubnov-Galerkin and Petrov-Galerkin methods are applied to derive the expressions for natural frequencies. For the first time in the literature explicit expressions are obtained for the natural frequencies. These can be useful for the designer to estimate the fundamental frequency in each of two series
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