  Black phosphorus (P), a layered material that can be isolated down to
individual 2D crystalline sheets, exhibits highly anisotropic mechanical
properties due to its corrugated crystal structure in each atomic layer, which
are intriguing for 2D nanomechanical devices. Here we lay the framework for
describing the mechanical resonant responses in free-standing black P
structures, by using a combination of analytical modeling and numerical
simulation. We find that thicker devices (>100nm) operating in the elastic
plate regime exhibit pronounced signatures of mechanical anisotropy, and can
lead to new multimode resonant characteristics in terms of mode sequences,
shapes, and orientational preferences that are unavailable in nanomechanical
resonators made of isotropic materials. In addition, through investigating
devices with different geometries, we identify the resonant response's
dependence on crystal orientation in asymmetric devices, and evaluate the
effects from the degree of anisotropy. The results suggest a pathway towards
harnessing the mechanical anisotropy in black P for building novel 2D
nanomechanical devices and resonant transducers with engineerable multimode
functions.
