Vibration of Beam-Type Resonant Biosensors With Time-Varying Mass Density

Abstract

This paper investigates the dynamic response of a uniform beam with varying density. The governing equation of motion is derived using the Euler-Bernoulli model of the beam considering the dynamic effect of the change of the beam’s density. The dynamics of a beam-type resonant biosensor is investigated to demonstrate the effect of time-varying beam’s density. In this type of sensors, the density of the resonant beam changes with time due to the nature of absorption process. The absorption is modeled as an asymptotic exponential function of time. It is shown that the adsorption leads to a viscous damping force with a time-varying coefficient. The approximate solution of the governing equation of motion is derived for comparing with the exact solution. The response of the system is presented for several combinations of the system parameters. It is shown that two factors govern the viscous damping effect of the absorption process, namely the time constant of the process and the total change of the mass density over time. In general, a faster absorption process and greater change in mass density lead to more damping in the system. This is significant because a fast absorption rate and greater mass change are desirable design goals while damping is generally considered undesirable.