Page 84 - Mechanics of Microelectromechanical Systems
P. 84
2. Microcantilevers, microhinges, microbridges 71
sectional amounts in Eq. (2.13) take into account that the thickness t of the
microcantilever is constant, whereas the width w(x) varies along the length.
The stiffness matrix [K] of Eq. (2.2) can be calculated either as:
or by applying Castigliano’s first theorem, as presented in Chapter 1. The
compliance-based approach is computationally simpler, compared to the
direct evaluation of stiffness properties, especially in the case of variable
cross-section micromembers. In addition, the compliance expressions can be
used to formulate/solve problems where the loads/deformations are required
at locations other than the free end of the microcantilever. The stiffness
matrix is expressed as:
where:
and
Evidently, the stiffness submatrices of Eqs. (2.16) and (2.17) are the inverses
of the compliance submatrices of Eqs. (2.6) and (2.7), respectively. Also:
and:
