  It has been estimated that a significant proportion of binary neutron star
merger events produce long-lived massive remnants supported by differential
rotation and subject to rotational instabilities. To examine formation and
oscillation of rapidly rotating neutron stars (NS) after merger, we present an
exploratory study of fully general-relativistic hydrodynamic simulations using
the public code Einstein Toolkit. The attention is focused on qualitative
aspects of long-term postmerger evolution. As simplified test models, we use a
moderately stiff Gamma=2 ideal-fluid equation of state and unmagnetized
irrotational equal-mass binaries with three masses well below the threshold for
prompt collapse. Our high resolution simulations generate postmerger "ringdown"
gravitational wave (GW) signals of 170 ms, sustained by rotating massive NS
remnants without collapsing to black holes. We observe that the high-density
double-core structure inside the remnants gradually turns into a
quasi-axisymmetric toroidal shape. It oscillates in a quasi-periodic manner and
shrinks in size due to gravitational radiation. In the GW spectrograms,
dominant double peaks persist throughout the postmerger simulations and slowly
drift to higher frequencies. A new low-frequency peak emerges at about 100 ms
after merger, owing to the growth of GW-driven unstable oscillation modes. The
long-term effect of grid resolution is also investigated using the same initial
model. Moreover, we comment on physical conditions that are favorable for the
transient toroidal configuration to form, and discuss implication of our
findings on future GW observation targeting rapidly rotating NSs.
