  We theoretically investigate the Floquet generation of second-order
topological superconducting (SOTSC) phase in the high-temperature platform both
in two-dimension (2D) and three-dimension (3D). Starting from a $d$-wave
superconducting pairing gap, we periodically kick the mass term to engineer the
dynamical SOTSC phase within a specific range of the strength of the drive.
Under such dynamical breaking of time-reversal symmetry (TRS), we show the
emergence of the \textit{weak} SOTSC phase, harboring eight corner modes \ie
two zero-energy Majorana per corner, with vanishing Floquet quadrupole moment.
On the other hand, our study interestingly indicates that upon the introduction
of an explicit TRS breaking Zeeman field, the \textit{weak} SOTSC phase can be
transformed into \textit{strong} SOTSC phase, hosting one zero-energy Majorana
mode per corner, with quantized quadrupole moment. We also compute the Floquet
Wannier spectra that further establishes the \textit{weak} and \textit{strong}
nature of these phases. We numerically verify our protocol computing the exact
Floquet operator in open boundary condition and then analytically validate our
findings with the low energy effective theory (in the high-frequency limit).
The above protocol is applicable for 3D as well where we find one dimensional
(1D) hinge mode in the SOTSC phase. We then show that these corner modes are
robust against moderate disorder and the topological invariants continue to
exhibit quantized nature until disorder becomes substantially strong. The
existence of zero-energy Majorana modes in these higher-order phases is
guaranteed by the anti-unitary spectral symmetry.
