- #1

kravky

- 22

- 3

I am trying to anallytically determine natural frequencies ƒ of the tympanic membrane. I am using 2D sectorial annulus membrane as a simplified model of tympanic membrane according to following picture

The parameters that i want to use are following:

The natural frequencies can be calculated from equation

where λ

where Jn and Yn are Bessel functions of first kind and second kind.

I find out using MAT*AB for n=0 (zeroth order) that for m=1: λ

After substituting λ

My equations are derived using Newtons second law.

Maybe some units or dimensions in my equations are messed up?

The parameters that i want to use are following:

**THICKNESS = 0,1 mm**The natural frequencies can be calculated from equation

where λ

_{mn}can be calculated fromwhere Jn and Yn are Bessel functions of first kind and second kind.

I find out using MAT*AB for n=0 (zeroth order) that for m=1: λ

_{m0}= λ_{10}=0,7484 (i used milimeters for R1 and R2)After substituting λ

_{mn}=λ_{10}=0,7484 into first equation for frequncy fmn i get the fundamental freq.**f1=128Hz.**However i am supposed to get**f1=412Hz**approximately. I don't know what am i doing worng. The parameters i chose are based on experiments from colleagues so i don't think they are wrong (although this tension 35MPa seems high to me)My equations are derived using Newtons second law.

Maybe some units or dimensions in my equations are messed up?