Some Modern Problems in Structural Engineering Dynamics

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. 1. Fundamental natural frequencies of double-walled carbon nanotubes 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. Apparently 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.