The decoupling of the Cartesian stiffness matrix in the design of microaccelerometers

Abstract

The 6×6 Cartesian stiffness matrix obtained through finite element analysis for compliant mechanical structures may lead to spurious coupling that stems from discretization error. The coupling may lead, in turn, to inaccurate results of the translational and rotational displacement analysis of the structure, for which reason a reliable decoupling technique becomes essential. In this paper, the authors resort to a decoupling technique of the Cartesian stiffness matrix, reported elsewhere, which is applied to the stiffness matrix of a class of accelerometers. In doing this, the generalized eigenvalue problem is first recalled as a powerful tool that is pertinent to the design task at hand (Ding and Selig in Int. J. Mech. Sci. 46(5): 703–727, 2004). The decoupled submatrices are then investigated by means of eigenvalue analysis. As a consequence, the translational and rotational stiffness matrices can be analyzed independently. Meanwhile, the decoupled stiffness matrices reveal compliance along the sensitive axes and high off-axis stiffness, thereby satisfying the ultimate design objectives for microaccelerometers with isotropic, monolithic structure.