Nonlinear performance analysis of forced carbon nanotube-based bio-mass sensors

In this effort, an analytical solution is proposed for the large amplitude nonlinear vibrations of doubly clamped carbon nanotube (CNT)-based nano-scale bio-mass sensors. The single walled CNT is modeled as an elastic Euler–Bernoulli nano-scale beam and the size effects are introduced into the mathematical model of the system through Eringen’s nonlocal elastic field theory. The nonlinearity arises due to mid-plane stretching of the bridged CNT, and is accounted for as the von Kármán nonlinearity. The impacts of deposited nano-scale bio-object, its geometrical properties, and its landing position along the longitudinal axis of the CNT-based resonator are considered. The nonlinear equations of motion are derived based on Hamilton’s principle and then the Method of Multiple Scales is employed to derive an analytical approximate solution for the system’s response. To verify the analytical solution and show its limits of applicability, the equations of motion are discretized by multi-mode Galerkin’s method and then the obtained set of equations are numerically solved by Runge–Kutta method and compared with those obtained by analytical solution. The potential applications of the CNT-based resonators for both of nonlinear frequency-/amplitude-based mass sensing are investigated and discussed. The obtained results show that the amplitude-based mass sensing has higher performance than frequency-based one in high quality-factor environments, such as in vitro biological mass sensing in the air or vacuum and inversely the frequency-based mass sensing method has higher mass sensibility in low quality factor environments, such as in vivo biological mass sensing in the liquid solution samples.