  To study shape fluctuations of nuclei in transitional regions, the collective
Hamiltonian method has often been employed. We intend to construct the
quadrupole collective Hamiltonian with the collective inertial functions given
by the local quasiparticle random-phase approximation (QRPA) based on the
Skyrme energy density functional. For this purpose, we first construct a
practical framework of Skyrme QRPA for triaxial nuclear shapes with the finite
amplitude method (FAM). We show quadrupole strength functions for a triaxial
superfluid nucleus $^{188}$Os and the Thouless-Valatin rotational moment of
inertia by the local FAM-QRPA for $^{106}$Pd.
