Nonlinear analysis of microresonators under the influence of processing errors
During the machining process of the microbeam,the limitations of the machining accuracy and the biased machining method lead to the deformation of its shape and the appearance of a shallow arch morphology.This machining error exists in the way that can be attributed to the deformation in the thickness direction of the microbeam and the initial deformation which will affect the nonlinear characteristics of the microresonator.In this paper,both the initial deformation and thickness morphology errors of the microresonator model are considered to investigate their effects on the dynamic frequency response of the system.A mathematical model of the microbeam is constructed using D'Alembert's principle,and the model is downscaled by the Galliakin method,and the soft and stiff characteristics of the system are analyzed using the multiscale method as well as the Runge-Kutta method.The system is made to achieve linear vibration by analyzing the variation relationship between the cross-sectional coefficient,the initial rise coefficient and the DC voltage,thus providing a theoretical basis for the improvement of the resonator performance.
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