Solutions to the Vibrating Silicon Nitride Membrane Problem

Rectangular silicon nitride membranes, supported by silicon substrates, are commonly used in the fabrication of MEMS (Micro Electro Mechanical Systems). Thus being able to accurately model their behaviour is desirable. The vibrational modes of a rectangular membrane were theoretically determined by an analytical solution derived from Newton’s principles and Hooke’s law and a finite element solution determined by means of ANSYS. Experimental results were obtained from a membrane excited with a piezoelectric element whilst being scanned with a laser vibrometer. The agreement between the three sets of results provides a high level in confidence in using ANSYS to predict the behaviour of more complex structures where an analytical solution would be difficult to obtain and/or experimentation would require high fabrication and manpower costs.

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