  Stimulated by the exciting progress in experiments, we carry out a combined
analysis of the masses, and strong and radiative decay properties of the $B$
and $B_s$-meson states up to the second orbital excitations. Based on our good
descriptions of the mass and decay properties for the low-lying
well-established states $B_1(5721)$, $B_2^*(5747)$, $B_{s1}(5830)$ and
$B_{s2}^*(5840)$, we give a quark model classification for the high mass
resonances observed in recent years. It is found that (i) the $B_{J}(5840)$
resonance may be explained as the low mass mixed state $B(|SD\rangle_L)$ via
$2^3S_1$-$1^3D_1$ mixing, or the pure $B(2^3S_1)$ state, or $B(2^1S_0)$. (ii)
The $B_J(5970)$ resonance may be assigned as the $1^3D_3$ state in the $B$
meson family, although it as a pure $2^3S_1$ state cannot be excluded. (iii)
The narrow structure around 6064 MeV observed in the $B^+K^-$ mass spectrum at
LHCb may be mainly caused by the $B_{sJ}(6109)$ resonance decaying into
$B^{*+}K^-$, and favors the assignment of the high mass $1D$-wave mixed state
$B_s(1D'_2)$ with $J^P=2^-$, although it as the $1^3D_3$ state cannot be
excluded. (iv) The relatively broader $B_{sJ}(6114)$ structure observed at LHCb
may be explained with the mixed state $B_s(|SD\rangle_H)$ via $2^3S_1$-$1^3D_1$
mixing, or a pure $1^3D_1$ state. Most of the missing $1P$-, $1D$-, and
$2S$-wave $B$- and $B_s$-meson states have a relatively narrow width, they are
most likely to be observed in their dominant decay channels with a larger data
sample at LHCb.
