Application and dynamical behavior of CNTs as fluidic nanosensors based on the nonlocal strain gradient theory

Abstract In this paper, the dynamical characteristics of CNT sensors with an encapsulated liquid is studied. The governing equation with nonlocal and strain gradient parameters is first derived by Hamilton’s principle, and the classical and higher-order boundary conditions of a simply supported beam are then obtained by a weighted residual approach. A differential quadrature method was used to obtain the numerical solutions of the sixth-order governing differential equation. The effects of the fluid, moment of inertia, non-classical boundary conditions, vibrational mode, nonlocal parameter, and strain gradient parameters on the frequency were studied. Although it is showed that it was difficult to identify the fluid type or density only based on the frequencies of the nanosensors, the results further verified that relative frequency shift percent (RFSP), nonlocal frequency shift percent (NFSP), and strain gradient frequency shift percent (SFSP) which depend on the fluid type, the nonlocal and strain gradient parameters can provide complementary information. It is concluded that measurements of the RFSP, NFSP, and/or SFSP can effectively be used to determine the density of the fluid in the nanosensors. It is hoped that our models can be effectively used to predict sensors’ responses and can allow the optimization of parameters before experiments.