  Using a thermodynamic approach based upon the fluctuation-dissipation theorem
we quantify the stochastic dynamics of rectangular and V-shaped microscale
cantilevers immersed in a viscous fluid. We show that the stochastic cantilever
dynamics as measured by the displacement of the cantilever tip or by the angle
of the cantilever tip are different. We trace this difference to contributions
from the higher modes of the cantilever. We find that contributions from the
higher modes are significant in the dynamics of the cantilever tip-angle. For
the V-shaped cantilever the resulting flow field is three-dimensional and
complex in contrast to what is found for a long and slender rectangular
cantilever. Despite this complexity the stochastic dynamics can be predicted
using a two-dimensional model with an appropriately chosen length scale. We
also quantify the increased fluid dissipation that results as a V-shaped
cantilever is brought near a solid planar boundary.
