To find the first four roots of 50 trancendental equation in a loop, how to do this?

ClearAll
(*befor finding the root for a lower stiffness use NSlove to find , \
then put that value back on the Rootfind and find the beta for \
varying stiffness *)
Y = 2*10^11;
Iyy = 8.333*10^-6;
L = 4;
z = Range[0.01, 0.5, 0.01];
T = Length[z];
k = 10^12;(*1*10^b;*)
a = 1/(4*b^3*(1 - Cosh[b]*Cos[b]));
phi1 = ConstantArray[0, {T, 1}];
phi2 = ConstantArray[0, {T, 1}];
phi3 = ConstantArray[0, {T, 1}];
phi4 = ConstantArray[0, {T, 1}];
eq = ConstantArray[0, {T, 1}];
eq1 = ConstantArray[0, {T, 1}];
S = ConstantArray[0, {T, 1}];
a1 = (Cos[b*x] - Cosh[b*x]);
a2 = (Sin[b*x] - Sinh[b*x]);
For[i = 2, i < T + 1, i++,
phi1[[i]] = (Cos[b] - Cosh[b])*(Sin[b*(1 - z[[i]])] -
Sinh[b*(1 - z[[i]])]);
phi2[[i]] = (Sin[b] - Sinh[b])*(Cos[b*(1 - z[[i]])] -
Cosh[b*(1 - z[[i]])]);
phi3[[i]] = (Sin[b] + Sinh[b])*(Sin[b*(1 - z[[i]])] -
Sinh[b*(1 - z[[i]])]);
phi4[[i]] = (Cos[b] - Cosh[b])*(Cos[b*(1 - z[[i]])] -
Cosh[b*(1 - z[[i]])]);
eq[[i]] =
a ((phi1[[i]] - phi2[[i]])*(a1 /. x -> z[[i]]) + (phi3[[i]] +
phi4[[i]])*(a2 /. x -> z[[i]])); eq1[[i]] = 1 + (k*eq[[i]])];

Plot[eq1[], {\[Beta], 0, 30}]
S = FindRoot[eq1 == 0, {b, 15}]
om = (b/L)^2*Sqrt[(Y*Iyy)/(7850*0.1^2)] /. S[];
fn = om/(2*\[Pi])

I tried with find root, Nsolve, reduce still it is not working. the objective is to find the natural frequencies. is it possible to put frequency equation in the loop, and can we achieve plotting in the loop.

• Have you taken a look at the elements of your eq and eq1? I suspect they are not what you meant them to be. You need to get them right before you try to solve them. – Kiro Nov 21 '17 at 7:50
• I corrected the program.. a bit can u check it now – Vijay Kumar S Nov 21 '17 at 8:04
• Make the following changes: Plot[eq1[], {b, 0, 30}], because eq1 depends on b, not \[Beta], and use S = Quiet@FindRoot[# == 0, {b, 15}] & /@ eq1; Did you get what you wanted? – Kiro Nov 21 '17 at 8:08
• i got it Sir but how to get the plot in loop and how to but the 'b' in loop. – Vijay Kumar S Nov 21 '17 at 8:52
• i need to extract the first four root from every equation in loop. i tried it is not happening – Vijay Kumar S Nov 21 '17 at 8:55