  Pentamode materials are elastic solids with vanishing shear modulus, and can
be used cloak underwater sound with solid state and broadband merits. However,
pentamode materials realized with real microstructure have inevitable small
shear modulus. This paper systematically studies the impact of shear rigidity
and inner surface constraints on acoustic cloak with unideal pentamode
material. The shear rigidity introduces a new kind of resonance in the radial
direction, which is different from the traditional whispering-gallery resonance
along the circumference. Totally fixed, radially fixed or free boundaries on
the cloak inner surface are found to show significant difference on the
cloaking function. To realize a broadband cloak with suitable boundary for
practice, we propose to attach an elastic thin shell on the inner surface to
virtually tune the boundary constraint. The proposed strategy is also validated
with microstructure cloak simulation. This study will provide valuable guidance
for the practical applications of pentamode acoustic cloak.
