Fixed-fixed flexures




Overview


The fixed-fixed flexure, shown in the figure above, has a very stiff nonlinear spring constant, because of extensional axial stress in the beams. Approximate analytic expressions for nonlinear fixed-fixed spring constants have been derived by Pisano. Residual stress in the polysilicon film increases the stiffness. Compressive residual stress can cause buckling of the structure. Analytic spring constant equations are given below. A mathematica file is also available.

Spring Constants


Linear spring constants: The spring constant of the flexure is four times that of the guided-end beam:
Except for the substitution of I_x for I_z, an identical derivation provides the spring constant in the z-direction:

The spring constant in the axial direction is found directly from Hooke's Law:

The flexure is very stiff in the y-direction because there is no beam bending.

Definition of terms used in flexure equations:




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Revised: July 3, 1996 by fedder@ece.cmu.edu