  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 our quark model classifications 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 interpreted as the $2S$-wave state $B(2^1S_0)$.
(ii) The $B_J(5970)$ resonance may be assigned as the $1^3D_3$ state in the $B$
meson family. (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 $J^P=2^-$. (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. 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.
