Flexoelectric and surface effects on size-dependent flow-induced vibration and instability analysis of fluid-conveying nanotubes based on flexoelectricity beam model

摘要

Fluid-conveying micro/nano tubes are key tools, which have great applications in biological devices and especially smart drug delivery in order to target the cancer cells. Furthermore, exploiting the smart materials and their combination with drug delivery systems may positively affect the instability control and improve the efficiency and adaptability of design. Recently a specific size-dependent behavior for piezoelectric materials, known as flexoelectric effect, has drawn a great deal of attention. It is proven that this effect, which is resulted by coupling between the strain field and electric polarization, is of significant importance in structures with nano dimensions. This paper is carried out to investigate the vibrations and instability analysis of fluid-conveying piezoelectric nanotubes on the basis of flexoelectricity approach. The fluid-conveying nanotubes made for drug delivery targets are commonly in contact with soft tissues, which could be modeled as a Kelvin-Voigt foundation. The nonlocal strain gradient theory (NSGT) constitutive relations are employed in order to model the problem. An appropriate electric potential distribution is determined using the Maxwell's equation and Gauss's law. The Euler-Bernoulli beam theory and slip boundary conditions are exploited to derive the governing fluid-structure interaction (FSI) equation, which contains flexoelectric and surface effect terms. Galerkin's principle is hired to discretize the equation leading to an eigenvalue problem. Afterwards, the obtained characteristic equation is solved straightforwardly to gain the eigenvalues. The instability of the nanotube is investigated throughout presenting the eigenvalue diagrams. Some illustrations are employed to analyze the effect of different involved parameters on the vibrations and instability behavior of the system. The reported results in the numerical section of the paper may be helpful to achieve an efficient and accurate design of fluid-conveying nanotubes.