ClearAll["Global`*"]
Er = 150*10^9;
Em = 75*10^9;
vr = 0.3;
vm = 0.25;
am = (0.25)*ar;

wr1111 = (Er/((1 + vr) (1 - 2 vr)))*(1 - vr + 
     e11 (1 - (2 vr^2)/(1 - vr)));
wr3333 = (Er (1 - vr))/((1 + vr) (1 - 2 vr));
wr1313 = wr3113 = Er/(2 (1 + vr));
wr1133 = (Er*vr)/((1 + vr) (1 - 2 vr));
wr1331 = (Er/(2 (1 + vr)))*(1 + 2 e11 (1 + vr)/(1 - vr));
wm1111 = (Em/((1 + vm) (1 - 2 vm)))*(1 - vm + 
     e11 (1 - (2 vm^2)/(1 - vm)));
wm3333 = (Em (1 - vm))/((1 + vm) (1 - 2 vm));
wm1313 = wm3113 = Em/(2 (1 + vm));
wm1133 = (Em*vm)/((1 + vm) (1 - 2 vm));
wm1331 = (Em/(2 (1 + vm)))*(1 + 2 e11 (1 + vm)/(1 - vm));

xim2 = Sqrt[cm + Sqrt[cm^2 - (wm3333*wm3113)/(wm1111*wm1331)]];
xir2 = Sqrt[cr + Sqrt[cr^2 - (wr3333*wr3113)/(wr1111*wr1331)]];
xim3 = Sqrt[cm - Sqrt[cm^2 - (wm3333*wm3113)/(wm1111*wm1331)]];
xir3 = Sqrt[cr - Sqrt[cr^2 - (wr3333*wr3113)/(wr1111*wr1331)]];
cm = (wm1111*wm3333 + wm1331*wm3113 - (wm1133 + wm1313)^2)/(
  2 (wm1111*wm1331));
cr = (wr1111*wr3333 + wr1331*wr3113 - (wr1133 + wr1313)^2)/(
  2 (wr1111*wr1331));

b11 = ((wr1111*wr1313) + (xir2^-2*wr3113*wr1133)) Cosh[ar*xir2^-1];
b31 = (wr1133 + wr1313) xir2^-1 Sinh[ar*xir2^-2];
b12 = ((wr1111*wr1313) + (xir3^-2*wr3113*wr1133)) Cosh[ar*xir3^-1];
b32 = (wr1133 + wr1313) xir3^-1 Sinh[ar*xir3^-2];
b13 = -((wm1111*wm1313) + (xim2^-2*wm3113*wm1133)) Cosh[am*xim2^-1];
b33 = (wm1133 + wm1313) xim2^-1 Sinh[am*xim2^-2];
b14 = -((wm1111*wm1313) + (xim3^-2*wm3113*wm1133)) Cosh[am*xim3^-1];
b34 = (wm1133 + wm1313) xim3^-1 Sinh[am*xim3^-2];
b21 = ((wr1133*wr1133) + (wr1133*wr1313) - (wr1111*wr3333) + (xir2^-2*
       wr3113*wr3333)) xir2^-1 Sinh[ar*xir2^-1];
b22 = ((wr1133*wr1133) + (wr1133*wr1313) - (wr1111*wr3333) + (xir3^-2*
       wr3113*wr3333)) xir3^-1 Sinh[ar*xir3^-1];
b23 = ((wm1133*wm1133) + (wm1133*wm1313) - (wm1111*wm3333) + (xim2^-2*
       wm3113*wm3333)) xim2^-1 Sinh[am*xim2^-1];
b24 = ((wm1133*wm1133) + (wm1133*wm1313) - (wm1111*wm3333) + (xim3^-2*
       wm3113*wm3333)) xim3^-1 Sinh[am*xim3^-1];
b41 = (-wr1111 + xir2^-2 wr3113) Cosh[ar*xir2^-1];
b42 = (-wr1111 + xir3^-2 wr3113) Cosh[ar*xir3^-1];
b43 = (wm1111 - xim2^-2 wm3113) Cosh[am*xim2^-1];
b44 = (wm1111 - xim3^-2 wm3113) Cosh[am*xim3^-1];
bqs = {{b11, b12, b13, b14}, {b21, b22, b23, b24}, {b31, b32, b33, 
    b34}, {b41, b42, b43, b44}} // MatrixForm