عنوان مقاله [English]
Piezoelectric microbeams are special types of beams applicable to the atomic force microscope (AFM). Having piezoelectric layers, they are capable of selfactuating using the voltage imposed on the piezoelectric layer. The present paper discusses the vibrating behavior of piezoelectric microbeams, with respect to the hydrodynamic forces imposed by a fluid. To do so, considering Hamiltons principle and assumptions of the Euler-Bernoulli theory, the dynamic modeling of a microbeam was carried out and the differential equation of vibrating motion was extracted. As it is very difficult to determine the exact amount of hydrodynamic force imposed on a beam, the hydrodynamic forces were approximated using string sphere modeling. The results obtained from dynamic modeling were compared with experimental ones. The results show that sphere string modeling can favorably model natural frequency and the resonance amplitude of piezoelectric microbeams in a liquid environment. The
results show that the vibrating motion (natural frequency and resonance amplitude) of a microbeam in liquid is under the influence of fluid density, due to the damping of liquid and additional mass; it is also seen in the higher
vibrating modes. By approaching the microbeam to the sample surface and intensifying squeeze force, the results show further amplitude decrease. The amplitude reduction at higher densities and low angles of the microbeam to the horizon is due to the intensification of compression force. When the interaction force between the probe tip and sample surface is intensified, and when there is a very short distance between the probe tip and sample surface (as small as a nanometer), amplitude is affected. According to the DMT model, there is a direct relationship between the interaction force between the tip and sample surface and the radius of the probe tip. Therefore, the more the radius of the probe tip, the more the interaction force will be. The increase of this force will be followed by a decrease in vibrational motion amplitude.