Piezoelectric microcantilevers (MCs) are a new generation of microbeams used in atomic force microscopes (AFMs). Due to their miniaturization of AFMs as well as their increased imaging precision and speed, these MCs are more popular than their classical counterparts. Given the widespread application of these beams in nanoparticle topography, analysis of their vibrating motion has attracted much attention in research circles. Exact vibratiing analysis as well as study of the vibrating motion of these beams plays a key role in increasing their measuring accuracy in topography, and contribute to their optimum design. To this end, the nonlinear differential equation of vibratiing motion of a MC was initially derived through Lagrange’s method. Subsequently, the modal analysis and multiple time scale (MTS) methods were implemented to obtain an analytical solution to this equation. The effect on the nonlinear vibrational motion of the interaction between the nanoparticle and the probe was studied. The extended Fourier amplitude sensitivity test (eFAST) was conducted to analyze the nonlinearity sensitivity of the motion. The results obtained from this analysis made it possible to determine optimal geometric dimensions for the MC to increase its sensitivity to motion nonlinearity. Simulation results showed that, at higher inclined angles, the MC sensitivity to vibrational motion nonlinearity increased. The sensitivity analysis results revealed that the MC thickness and the length of its tip had the greatest effect on the MC sensitivity to the nonlinear force of interaction.