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Micro-beam resonators are widely used as key components for sensing and actuation systems.Their relatively simple geometries make them very advantageous both from design and microfabrication point of view.In the wide range of applications ranging from the mean residual stress measurement, microscopy, mass flow sensors to bio-medical or DNA analysis, their sensing mechanism depends upon the sensitivity or response of the MEMS beam to some applied excitation.As we know, it is desired to design and construct systems with loss of energy as little as possible for micro-resonators.