Primena nelokalne teorije kontinuuma u analizi dinamičkog ponašanja i stabilnosti sistema spregnutih nano-struktura

Abstract

This dissertation investigates vibration and stability behavior of complex nano-scale systems composed of single and multiple carbon nanotubes and graphene sheets. Based on the assumptions introduced through the nonlocal continuum theory, the nanotubes are modeled as nanobeams and graphene sheets are represented as nanoplates where the influence of inter-atomic forces and the discrete nature of nanomaterials are introduced as material parameters. To such mechanical models of nanostructures one can apply the second Newton’s law of motion or Hamilton’s principles to derive the governing equation of motion of the system. In order to obtain solutions of partial differential equations, the analytical and approximation methods will be employed. Special attention is devoted to determining the analytical solutions for natural frequencies and critical buckling load of systems with multiple nanostructures (nanorods, nanobeams and nanoplates) and special cases of such systems. Thus obtained analytical solutions are validated by using the numerical methods as well as the results from molecular dynamics simulations, where excellent agreement of the results is confirmed. In addition, the longitudinal vibration of systems with a single or multiple coupled nanorods will be analyzed using nonlocal elasticity and viscoelasticity theories. What should be noted are the effects of temperature changes and magnetic fields on the dynamic behavior of a cracked carbon nanotube embedded in an elastic medium. It is shown that the possibility of change in the overall system stiffness by changing the parameters of external physical fields leads to certain changes in natural frequencies without any change in other parameters of the model. The case of the free nonlinear vibration and dynamic stability of carbon nanotubes subjected to variable axial force and external magnetic field will be presented in the example of a single nanobeam embedded in a viscoelastic medium by considering the geometric nonlinearity. Analytical approximation results are determined for nonlinear frequencies, amplitude-frequency curve by using the multiple scales method. It is shown that it is possible to avoid resonant states as well as changes in stability and instability regions by changing the external magnetic field parameter without any change in other parameters of the system. A parametric study is performed for all presented systems, and effects of different physical and geometrical parameters on the dynamic behavior and stability are examined in detail.