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The prediction and understanding of structural resonances are required to optimize scanning probe microscope (SPM) design. Here, Euler beam theory is applied to the beetle-style SPM to derive analytic functions for the natural frequencies of three significant modes of vibration as a general function of the microscope shape, materials, and dimensions. In the first mode, the three piezoelectric legs vibrate transversely and the scanhead moves from side to side. In the second, the legs bend circumferentially and the scanhead rotates about its center. These modes have been identified previously, but here the mechanics analysis is presented in an improved form where the inertia of the piezo legs is considered, constraints on the shape of the central supporting disk are lifted, and appropriate boundary conditions are defined and enforced. In addition, we discuss a third mode that has not been previously identified. In this lowest frequency mode, two legs pivot about the stationary third leg. The predictions are...

Vibrations of the “beetle” scanning probe microscope: Identification of a new mode, generalized analysis, and characterization methodology