Together[
Cosh[(t Sqrt[(-Subscript[k, 22]) Subscript[m, 1] - Subscript[k, 11]
Subscript[m, 2] + Sqrt[Subscript[k, 22]^2 Subscript[m, 1]^2 +
2 (2 Subscript[k, 12] Subscript[k, 21] - Subscript[k, 11]
Subscript[k, 22]) Subscript[m, 1] Subscript[m, 2] +
Subscript[k, 11]^2 Subscript[m, 2]^2]])/
(Sqrt[2] Sqrt[Subscript[m, 1]] Sqrt[Subscript[m, 2]])]
(Subscript[k, 22] Subscript[m, 1] - Subscript[k, 11]
Subscript[m, 2]) +
Cosh[(t Sqrt[(-Subscript[k, 22]) Subscript[m, 1] -
Subscript[k, 11] Subscript[m, 2] +
Sqrt[Subscript[k, 22]^2 Subscript[m, 1]^2 +
2 (2 Subscript[k, 12] Subscript[k, 21] - Subscript[k, 11]
Subscript[k, 22]) Subscript[m, 1] Subscript[m, 2] +
Subscript[k, 11]^2 Subscript[m, 2]^2]])/
(Sqrt[2] Sqrt[Subscript[m, 1]] Sqrt[Subscript[m, 2]])]
Sqrt[Subscript[k, 22]^2 Subscript[m, 1]^2 +
2 (2 Subscript[k, 12] Subscript[k, 21] - Subscript[k, 11]
Subscript[k, 22]) Subscript[m, 1] Subscript[m, 2] +
Subscript[k, 11]^2 Subscript[m, 2]^2]]
两项的话可以可以使用Factor

但是四项的话无效了

也就是说按照Cosh[#]样式进行合并...