  We analytically calculate phase boundaries of tunable spin-orbit coupled BECs
with effective two-body interactions by using variational method. Phase
diagrams for periodically driving $^{87}\rm{Rb}$ and $^{23}\rm{Na}$ systems are
presented, respectively, which display several characteristic features contrast
with those of undriven systems. In the $^{87}\rm{Rb}$ BECs, the critical
density $n_{c}$ (density at quantum tricritical point) can be dramatically
reduced in some parameter regions, thus the prospect of observing this
intriguing quantum tricritical point is greatly enlarged. Moreover, a series of
quantum tricritical points emerge quasi-periodically with increasing the Raman
coupling strength for fixed $^{87}\rm{Rb}$ density. In the $^{23}\rm{Na}$ BECs,
two hyperfine states of $^{23}\rm{Na}$ atoms can be miscible due to driving
under proper parameters. As a result, $^{23}\rm{Na}$ systems can stay in the
stripe phase with small Raman frequency at typical density. This expands the
region of stripe phase in the phase diagram. In addition, there is no quantum
tricritical point in such $^{23}\rm{Na}$ system , which is different from
$^{87}\rm{Rb}$ system.
