Application of hetero junction CNTs as mass nanosensor using nonlocal strain gradient theory: An analytical solution

Abstract

This paper aims to propose an analytical solution for dynamic analysis of the hetero junction carbon nanotubes (HJCNTs)-based mass nanosensors using a nonlocal strain gradient Timoshenko beam model. To have a more precise nanosensor, it is necessary to have deep information about the vibration characteristics of the nanostructure. So, two main goals are followed in this paper. At first, the vibration of HJCNTs with general (elastic) boundary conditions and without attached mass are studied using a proposed analytical solution. Afterwards, the HJCNT is applied as a cantilever mass sensor for sensing light as well as heavy masses attached to its tip. For the large and heavy masses, the rotary inertia of the attached mass is also considered in the analysis. The governing differential equations are derived based on the Hamilton\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\'s principle and solved by an analytical method, which is based on the modified Fourier series. The weighted residual method is employed for obtaining the variationally consistent boundary conditions using the known equations of motion of the structure. The field quantities are obtained in the closed forms. The convergence and accuracy of the proposed solution are validated through some special cases available in the literature. The effects of small scale parameters and the elastic boundaries on the frequency and mode shapes of HJCNTs are studied. Moreover, the factors that affect the frequency shift of HJCNT-mass sensor are discussed. The obtained results introduce HJCNTs as new mass nanosensors that can operate more efficiently than uniform CNTs. This paper can be greatly useful in designing HJCNT-mass sensors and may serve as a benchmark for the future research in this field.