The modal decomposition of tapping mode atomic force microscopy microcantilevers in air and liquid environment was experimentally investigated to identify their complex responses. In experiment, the flexible microcantilevers and a flat HOPG sample were used. The responses of the microcantilevers were obtained to extract the linearized modes and orthogonal values using the methods for the proper orthogonal decomposition and the smooth orthogonal decomposition. The influence of the tapping setpoints and the hydrodynamic damping forces were investigated with the multi-mode response of microcantilevers. The results show that the first mode is dominant under normal operating conditions in tapping mode. However, at lower setpoint, the flexible microcantilever behaved uncertain modal distortion near the tip on the sample. The dynamics tapping effect and the damping between microcantilever and liquid influenced their responses.

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