Effective stiffness and effective mass of the double-walled carbon nanotube mass sensor

In this study, the effective stiffness of the double-walled carbon nanotube sensor is determined by both the Bubnov–Galerkin method and the finite difference technique. It is shown that in addition to the familiar expression of the effective stiffness of the clamped-free beam, there is an additional term for the double-walled carbon nanotube's effective stiffness. Additionally, it is demonstrated that there are two effective stiffness expressions, depending on where the load is applied, at the inner tube or at the outer tube. Additionally, effective mass is evaluated in the context of the Galerkin method.