Amplitude dependent frequency shift of vibrating wires

On the nonlinear interpretation of a vibrating wire viscometer operated at large amplitude

“…It is worth noting that other researchers have investigated the nonlinear behavior of the vibrating wire, but no interpretation was developed to account for this nonlinearity and to accurately calculate fluid viscosity [5,6]. The amplitude of the wire motion investigated by these researchers was on the order of a millimeter where the mechanical properties of the wire should no longer be linear.…”

“…Higher order corrections can be developed for the solution of the nonlinear equation (6). We will proceed with the next highest terms and then develop a general framework for a series solution of the full equations.…”