# Effect of Coriolis Force on Vibration of Annulus Pipe
## 1 Introduction and Background  
Fluid conveying pipes [1] are attractive form an engineering point of view because the instability effects can be a dangerous structural weakness. These systems interact with axial flows in flexible conduits with prevalent applications in the oil and gas production industries. Examples of these practical applications can be found in [2]. However, the examples found in the literature are not only limited to the field of engineering but cut across other areas of human endeavor, such as the study of pulmonary and urinary tract systems or even hemodynamics within human physiology. A lot of research interest is now focused on models for studying the stability of certain classes of dynamical systems, finding novel numerical and analytical methods for solving such problems. Thus, for linear dynamics for axial flows along slender structures, the pipe conveying fluid is regarded as the main paradigm. Direct applications in technical fields can be found in the behavior of aspirating pipes for ocean mining and Liquefied Natural Gas (LNG) in situ production, as well as for the offshore mining of methane liquid-crystal deposits and carbon sequestration. Flow-induced vibrations and instabilities are seeking to be resolved by simple, fast, and robust models. Many researchers developed different methodologies to study the problem [3, 4, 5]. In particular, the Coriolis force became important in the analysis of stability, due to its role in the energy equation. Studies can be found in [6, 7, 8]. Helped by the experiments described in [9, 10] it was possible to assume that the contribution of both the Coriolis force and the centrifugal force lead to flutter effects that can be dangerous for the strength of the structure. In [11], [PERSON] et al. investigated the impact of the Coriolis force on the long distance wake behind wind farms by using Large Eddy Simulations (LES) combined with a Forced Boundary Layer (FBL) technique. The results indicate that FBL can be used for studies of long distance wakes without including a Coriolis correction, but efforts need to be taken to use a wind shear with a correct mean wind veer. The subject of piping vibration has attracted a lot of attention from various researchers in recent times, due to vast applications. In [12] [PERSON] et al. described a vibration analysis and mathematicalmodel using Euler-Bernoulli and Hamilton's energy expressions for fluid conveying a welded galvanized iron pipe with a clamped-clamped boundary condition. Many other attempts concerning the fluid conveying pipe vibrations were made and different analytical methods were applied and compared to numerical solutions by software. [PERSON] et al. [13], studied the vibrational characteristics of pipe conveying fluid and FE simulation to evaluate velocity and pressure distribution in a single phase fluid flow. [PERSON] et al. [14] obtained the element standard equation for natural frequencies by the Lagrangian interpolation function, the first order Hermite interpolation function, and the Ritz method. [PERSON] et al. [15] used the Lagrangian interpolation function, the first order Hermit interpolation function, and the Ritz method to obtain the element standard equation for the nonlinear vibration response and then integrated a global matrix equation, obtaining the response of a conveying fluid pipe with the New Mark method and Matlab. [PERSON] et al. [16] compared results obtained by experimental verification with the aid of Smart Materials with the results performed by using analytical solution for equation of motion and also, with the results performed by using ANSYS Software. The field of nanostructures is currently turning to vibration issues and their formulation as well. Carbon nanotubes (CNTs) have been extensively used in numerous areas, due to their excellent mechanical properties. As an important mechanical property, the vibration characteristics of a CNT have become another hot topic for research in recent years.