Nonlinear Dynamics Analysis Of Fluid-conveying Nanotubes Considering Effects Of The Surface Energies

With the development of science and technology, micro-electro-mechanical systems (MEMS) and its technology has been widely used in the fields of science, also caught the attention of scholars and their research interests. When the dimension of MEMS comes to nano-scale we usually call it nano-electro-mechanical systems (NEMS). The fluid-conveying micro/nanotubes are the important component of the MEMS and the NEMS'technology development. The size of micro/nanotubes is extremely small and suitable for micro fluid sensor because of small mass inertia and heat inertia, high response speed, easy integration and low power consumption. It has very important application prospect in the micro mechanical field. In this paper, the fluid-conveying micro/nanotubes are the research object, the linear and nonlinear dynamic behavior bas been researched, which has very important theoretical and practical significance.In recent years, the study of the mechanical properties of fluid-conveying nanotubes has had a fine pedigree, while, most of these study based on the classical continuum beam/shell theoretical models and the nonlocal theoretical models. Research showed that when the micro-structure dimension equal to or smaller than the characteristic scale, material properties is different from neither the macro scale properties nor the atomic scale properties because of the quantum effect, small scale effect and surface energies effect. When structure dimension reduced to the nano scale, the proportion of surface atoms increases rapidly, then the surface energies effect will seriously affect the structure's physical, chemical and mechanical properties, which represent as surface stress from macroscopic view. Therefore, the surface energies can not be ignored when the structure is nano-scale. In this paper, based on the Euler-Bernoulli beam theory, a modified beam model by incorporating surface energies effect is presented. Based on the fluid-structure interaction theory and geometrical nonlinear, the equation of nonlinear dynamics of fluid-conveying nanobeam and corresponding boundary conditions are established, in which the effect of surface energies are taken into account. The main contents of this paper are as follows:First of all, based on the Euler-Bernoulli beam theory, the nonlinear dynamics governing equation of fluid-conveying nanobeam is formulated, in which the effect of surface energies are taken into account. Galerkin method and incremental harmonic balance method are adopted to solve the equations and get the relationship of the nonlinear free vibration frequency and amplitude. Discussed the case of different pipe radius, the influence of increasing flow velocities on the frequency, and got how the surface energies affect the dynamic stability of the fluid-conveying nanotubes. There is obvious size-dependence phenomenon in the analysis.Furthermore, the next chapter is about nonlinear dynamic response analysis of the fluid-conveying nanotubes considering surface effect. In the condition of considering the geometric nonlinearity, the Galerkin method was used to turn the partial differential equation into ordinary differential equation, and then using the multiple scales perturbation method to get the semi-analytical solution of the system. Finally, discuss the effect of the surface energies and the internal fluid flow to the dynamic responses of the fluid-conveying nanoturbes.Finally, based on the Euler-Bernoulli beam theory, considering the surface energies effect, the nonlinear dynamic stability of the fluid-conveying nanoturbes by parametric load is studied. In the numerical calculation section, the influences of the surface energies effect, the internal fluid velocity, the aspect ratio to the principal region of stability and instability are discussed.