Vibration Analysis of Mass Sensing Nanobeams at Higher Modes with Consideration of Size Effects in Nano-Scales

In Nano-scales, the application of nanobeams as sensors of infinitesimal masses is widespread and they been studied by many researchers in nanotechnology. This paper analyzes dynamics and vibration of mass sensing nanobeams in various vibrational modes, taking into account the size effects in nano-scales. To do this, the governing equations for the transverse vibration of a nanotube are derived by considering size effects and an added mass at the arbitrary distance from the beam using the nonlocal elasticity theory. Employing the Hamilton principle, final equations and boundary conditions of the mass sensing nanobeam are obtained. Using the exact method, the frequency characteristics of the mass sensing nanobeam are obtained. Then, The size effects and mass sensing on the frequency behavior of the nonlocal nanobeam are simulated especially at higher modes of vibration. The obtained results show that the mass sensor feature of the nanobeam has increased at higher modes and therefore higher vibrational modes should be carefully studied. It is also observed that size effects at the higher vibrational modes are inventible, and these effects on the frequency are greater than the mode shapes of the nanobeam.