Study on dynamics of an atomic force microscope V-shaped microcantilever in liquids based on the finite difference method

V-shaped microcantilevers exhibit high sensitivity and low stiffness characteristics, making them suitable for use as atomic force microscopy probes that enable high-resolution surface imaging and nanomechanical characterization of soft biological samples in liquid environments. However, due to the complex geometry of the V-shaped microcantilever and the effects of fluid–structure coupling and nonlinear tip–sample interactions when operating in liquids, it is generally difficult to study its dynamic characteristics analytically. This study establishes a computational framework based on the finite difference method (FDM) to analyze the dynamic response of a V-shaped microcantilever in liquids by equivalently modeling fluid effects as added mass and damping. The resonance frequencies and the time-varying displacement of the V-shaped microcantilever are calculated and compared with those obtained by the finite element method to validate the accuracy and efficiency of FDM. The effects of the cantilever–sample separation, the free amplitude, and the sample modulus on the dynamic responses of the V-shaped microcantilever are further analyzed. Results demonstrate that nonlinear tip–sample interactions excite higher harmonics, amplified by internal resonance of higher modes. Reducing free amplitude or employing phase imaging enhances measurement sensitivity in liquids. This method offers a computationally efficient tool for dynamic analysis and structural optimization of V-shaped microcantilevers in fluid environments.