Guided Circumferential Waves In Multi-layered Hollow Cylinders

The guided circumferential wave propagation in layered hollow cylinders is an important research area in elastodynamics. It can offer a theoretical foundation for the non-destructive testing (NDT) technology by the use of guided circumferential waves to detect the defects in the adjacent interfacial layer. The complexity of the guided circumferential wave propagation leads the researches to merely concentrate on single-layered hollow cylinders and cylinders with an interior shaft and an exterior hollow cylinder. The properties of the guided circumferential wave propagation in the two-layered and multi-layered hollow cylinders are still unknown.Based on the two-dimensional linear theory of elasticity, the guided circumferential wave propagation in double-layered hollow cylinders, multi-layered hollow cylinders, double-walled carbon nanotubes, and multi-walled carbon nanotubes have been studied theoretically and numerically in the present doctoral dissertation. The main content of this thesis can be briefly described as follows:(1) The theoretical solution of guided circumferential wave propagation is derived for two-layered hollow cylinders and multi-layered hollow cylinders.(2) Adopting the continuum model of thick-walled hollow cylinder, the theoretical solution of guided circumferential wave propagation is derived for double-walled carbon nanotubes, and multi-walled carbon nanotubes by considering the van der Waals forces between the walls.(3) According to the boundary conditions and the interfacial surface continuity conditions of two-layered hollow cylinders, the non-dimensional frequency equation and the expressions of displacement modes are given. The numerical results show that the propagations of the guided circumferential waves generate the frequency dispersion phenomenon, the mode interference phenomenon and the high frequency Rayleigh surface wave phenomenon. The numerical results also showed that the present method can determine the suitable modes and excitation frequency for NDT by the use of guided circumferential waves.(4) According to the boundary conditions and the interfacial surface continuity conditions of multi-layered hollow cylinders, the non-dimensional frequency equation and the expressions of displacement modes are given. The numerical results show that the propagations of the guided circumferential waves generate the frequency dispersion phenomenon, the mode interference phenomenon and the high frequency Rayleigh surface wave phenomenon. The frequency dispersion phenomenon and the mode interference phenomenon will be more serious by comparing to those of two-layered hollow cylinders. The numerical results also showed that the present method can determine the suitable modes and excitation frequency for NDT by the use of guided circumferential waves.(5) Derived from the boundary conditions and the effects of the van der Waals forces between the layers of double-walled carbon nanotubes, the non-dimensional frequency equation is obtained. The numerical results show that the propagations of the guided circumferential waves generate the frequency dispersion phenomenon, the mode interference phenomenon and the high frequency Rayleigh surface wave phenomenon. More complicated frequency dispersion and more interference phenomena of wave modes perhaps are caused by the van der Waals forces between the layers. Especially, a new wave phenomenon, a couple of wave modes may disappear at a frequency and another new couple of wave modes are excited at the same wave number, has been found. It can been called "mode disappearance and restarting" phenomenon.(6) Derived from the boundary conditions and the effects of the van der Waals forces between the layers of multi-walled carbon nanotubes, the non-dimensional frequency equation is obtained. The numerical results show that the propagations of the guided circumferential waves generate the frequency dispersion phenomenon and the mode interference phenomenon, which are more complicated than those in double-walled carbon nanotubes. The so-called "mode disappearance and restarting" phenomenon also takes place. It might be a common wave phenomenon in multi-walled carbon nanotubes.(7) A new investigation, the influence of the physical properties of interfacial surfaces between layers on the propagations of guided circumferential wave, is made. The numerical examples for the interfacial surfaces with the same thickness of 1mm and the different materials of carbon, carborundum and titanium are investigated on the frequency dispersion phenomenon and the suitable excitation frequency for NDT. It is found that different physical properties of interfacial surfaces will make different frequency characteristics relative to the Lame constants mostly.