I tried to solve this determinant in MATLAB but the software is proving difficult. In this determinant in most of the elements, the unknown is 'a' and other things are known. The code is as follows.

syms a

A=7.0686*10^-4;

E=2e11;

L=0.360;

I=3.9761*10^-8;

ku=a*7.132*10^-5;

bt=0.25;

gm=0.55;

ky=sqrt(a*3.4234*10^-3);

K11=90.339e9;

K12=-519.329e6;

K21=-519.329e6;

K22=3.0377e6;

K222=K11;

K33=K22;

K32=K12;

K23=K12;

m1=(A*E/(L*K11));

m2=(A*E/(K12));

m3=(E*I/(L*K22));

m4=(E*I/(L*L*K21));

m5=m1;

m6=m2;

m7=m3;

m8=m4;

m12=m1/m2;

m34=m3/m4;

m56=m12;

m78=m34;

t1=sin(ku);

t2=cos(ku);

t3=cos(ku*gm);

t4=sin(ku*gm);

t5=cos(ku*bt);

t6=sin(ku*bt);

g1=cosh(ky*bt);

g2=sinh(ky*bt);

g3=cosh(ky);

g4=sinh(ky);

g5=cos(ky*bt);

g6=sin(ky*bt);

g7=cos(ky);

g8=sin(ky);

g9=cosh(ky*gm);

g10=sinh(ky*gm);

g11=cos(ky*gm);

g12=sin(ky*gm);

s1=t5-(m1*ku*t6);

s2=t6+(m1*ku*t5);

s16=m34*t6;

s15=m34*t5;

s14=ky*g5;

s13=ky*g6;

s12=ky*g1;

s11=ky*g2;

s10=(m3*ky*ky*g6)-s14;

s9=(m3*ky*ky*g5)+s13;

s8=(m3*ky*ky*g2)+s12;

s7=(m3*ky*ky*g1)+s11;

s6=m12*s14;

s5=m12*s13;

s4=m12*s12;

s3=m12*s11;

v1=(t3)-(m5*ku*t4);

v2=(t4)+(m5*ku*t3);

v16=m78*t4;

v15=m78*t3;

v14=ky*g11;

v13=ky*g12;

v12=ky*g9;

v11=ky*g10;

v10=(m7*ky*ky*g12)-v14;

v9=(m7*ky*ky*g11)+v13;

v8=(m7*ky*ky*g10)+v12;

v7=(m7*ky*ky*g6)+v11;

v6=m56*v14;

v5=m56*v13;

v4=m56*v12;

v3=m56*v11;

D=[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0; 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -t1 t2; 0 0 0 0 0 0 0 0 g3 g4 -g7 -g8 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 g4 g3 g8 -g7 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 -t6 t5 t6 -t5 0 0; g1 g2 g5 g6 -g1 -g2 -g5 -g6 0 0 0 0 0 0 0 0 0 0; g1 g2 -g5 -g6 -g1 -g2 g5 g6 0 0 0 0 0 0 0 0 0 0; g2 g1 g6 -g5 -g2 -g1 -g6 g5 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -t4 t3 t4 -t3; 0 0 0 0 g9 g10 g11 g12 -g9 -g10 -g11 -g12 0 0 0 0 0 0; 0 0 0 0 g9 g10 -g11 -g12 -g9 -g10 g11 g12 0 0 0 0 0 0; 0 0 0 0 g10 g9 g12 -g11 -g10 -g9 -g12 g11 0 0 0 0 0 0; -s3 -s4 s5 -s6 s3 s4 -s5 s6 0 0 0 0 s1 -s2 t5 t6 0 0; s7 s8 -s9 -s10 -s11 -s12 s13 -s14 0 0 0 0 s15 s16 -s15 -s16 0 0; 0 0 0 0 v3 v4 -v5 v6 -v3 -v4 v5 -v6 0 0 v1 v2 -t3 -t4; 0 0 0 0 v7 v8 -v9 -v10 -v11 -v12 v13 -v14 0 0 v15 v16 -v15 -v16]

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