Dynamic modeling of oblique non-uniform piezoelectric MC in liquid with various percentages of glycerin in the presence of rough surface

One of the most useful applications of an AFM is imaging of biological particles in a liquid medium. The increase of the topography accuracy in a liquid medium requires accurate dynamic modeling of a Microcantilever (MC). This article investigates the accurate dynamic modeling of the non-uniform AFM piezoelectric MC with rectangular geometry in the amplitude mode in liquid medium for rough surfaces. To increase the accuracy of the modeling, the Modified couple stress (MCS) theory in the liquid medium according to the Timoshenko beam model has been used. Moreover, the differential quadrature (DQ) method has been used for solving equations, because in comparison with the other methods it has a high speed in solving equations and is accurate in the number of fewer elements. In addition, the accurate force modeling has been established by considering the shear forces caused by liquid on the sides of the piezoelectric MC by solving the Navier-Stokes equations, and by considering the hydrodynamic force, squeeze force and applied forces between the sample surface and the MC tip. The results illustrate that utilizing higher vibration modes affect the quality of rough surface topography with the step roughness in the liquid medium and increase the quality of surfaces topography in the tapping mode, especially in the second MC vibration mode. Moreover, it should be noted that the sensitivity of the MC vibration amplitude to the piezoelectric MC angle is higher in comparison with other investigated parameters.