I presume that you wish to eliminate some variables in the last expression in terms of variables defined in the other expressions. Let me begin with two pieces of advice:
- Do not use subscripted variables. They may look nice, but they can cause problems.
- Simplification is in the eye of the beholder. Mathematica's idea of simplification may not agree with the user's.
On this basis, rewrite the expressions as equations, named for convenience
eq1 = ωh^2 == kh/m;
eq3 = μ == m/(π*ρ*b^2);
eq5 = xα == Sα/(m*b);
eq6 = E1 == (m + π*ρ*b^2)*z + kh*w + (Sα - π*ρ*b^3*a)*n + π*ρ*b^2*V*o +
2*π*ρ*b*V*c (y + V*t + b*(1/2 - a)*o);
eliminate what I presume are the unwanted variables, and simplify the result.
FullSimplify[Eliminate[{eq1, eq3, eq5, eq6}, {ρ, kh, Sα}], b != 0 && m != 0]
(* E1 μ == m ((1 + c) o V - a (b n + 2 c o V) + (2 c V (t V + y))/b +
z + μ (b n xα + z + w ωh^2)) *)
If this is not completely simplified in the way you have in mind, you may need to play around with the code a bit, but this should give you some idea of how to proceed. Good luck.