Nonlinear Vibration and Stability Analysis of Nano-scale Elastic Beam-type Structures

点击翻译按钮获取中文摘要

Nanobeams and Nanotubes are considered nowadays to have wide range of applications in modeling of biosensors, medicine carriers, resonators, artificial tiny blood vessels, Nano-switches and Nano-power generators. Mechanical and electronic properties of almost all the nanostructures are highly influenced by their nonlinear vibration signatures and resonant frequencies. This research is aimed to develop a reliable model to consistently simulate the large-amplitude nonlinear vibration of elastically surrounded nanotubes and nanobeams. A comprehensive study is sought to investigate the unexplored aspects of nonlinear vibration of nanostructures, since the type and strength of nonlinearities are fundamentally different from those of the macro-scale structures. In this research program I will investigate four main issues under a unified framework of: a) Introducing accurate modeling and new analytical solutions for vibration analysis of nanotubes and nanobeams, b) Sensitivity analysis of nanostructure parameters considering different types of nonlinearities, c) Stability analysis and performance study of vibrating nanostructures, and d) Chaos prediction and control of potential chaotic behavior in nanostructures. The essential foundation of this proposal is based on my recent contributions in the modeling and analysis of nonlinear vibrating systems and also performance verification with recent reported experimental results by other researchers in this field. One of the goals of this research is to investigate the interactions of different types of nonlinearities in Nano-scale and also determine the potential of either resonance magnification or cancelation. A general variational-based approach will be developed for the straight, curved and wrinkled nanobeams. Modeling of a wrinkled nanostructures employing the theory of non-uniform rational basis spline (NURBS) is another objective and contributions of this research. The undiscovered dynamic behavior of nanostructures is identified when the geometrical nonlinearities tend to combine with other nonlinear phenomena such as the fringing and Casimir effects. Free vibration, as well as, the harmonic and stochastic vibrations of such nanostructures will be simulated. Different types of possible resonant conditions, including the primary and secondary resonances, as well as the internal resonant cases are considered. The main harmonics together with the sub-harmonic and super-harmonic responses are obtained. A bifurcation analysis is carried out and the stability of periodic and quasi-periodic solutions for nanobeams and nanotubes will be investigated. The effects of interactive nonlinear forces, size, surface and the geometrical conditions on the vibration behaviors of these structures will thoroughly be examined. The outcome of this research will not only enhance the frontier of knowledge for more realistic models and solutions, but also greatly benefit the Canadian and international industries especially in three categories of electric circuits, tissue engineering and regenerative medicine.