Natural frequencies of simplified tympanic membrane model

In summary, the conversation is about analytically determining the natural frequencies of a tympanic membrane using a 2D sectorial annulus membrane as a simplified model. The parameters used are a thickness of 0.1mm and a tension of 35MPa. The natural frequencies can be calculated using equations involving Bessel functions, and the fundamental frequency is expected to be approximately 412Hz. However, the calculated value is 128Hz and it is suspected that there may be an error in the equations or the units/dimensions used. The conversation also mentions that the eardrum is being modeled, not the drumhead of a tympani. The paper being referenced is also mentioned.
  • #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

forum1.JPG


The parameters that i want to use are following:

THICKNESS = 0,1 mm
sn22.JPG


The natural frequencies can be calculated from equation

sn33.JPG


where λmn can be calculated from

sn11.JPG

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: λm0 = λ10=0,7484 (i used milimeters for R1 and R2)

After substituting λmn10=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?
 

Attachments

  • forum1.JPG
    forum1.JPG
    14.1 KB · Views: 671
  • sn22.JPG
    sn22.JPG
    23.5 KB · Views: 434
  • sn33.JPG
    sn33.JPG
    3.4 KB · Views: 334
  • sn11.JPG
    sn11.JPG
    3.9 KB · Views: 338
Physics news on Phys.org
  • #2
kravky said:
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

I'm a little confused- are you modeling the drumhead for a tympani, or are you modeling the 'eardrum'?
 
  • #3
I am modelling eardrum. Simplified eardrum
 

Related to Natural frequencies of simplified tympanic membrane model

1. What is a simplified tympanic membrane model?

A simplified tympanic membrane model is a representation of the eardrum that is used in scientific studies and experiments. It is a simplified version of the actual eardrum and is often used to better understand its behavior and function.

2. How are natural frequencies of the simplified tympanic membrane model determined?

The natural frequencies of the simplified tympanic membrane model are determined through mathematical calculations and simulations. These calculations take into account the physical properties and dimensions of the model to determine its natural frequencies.

3. What factors affect the natural frequencies of the simplified tympanic membrane model?

The natural frequencies of the simplified tympanic membrane model can be affected by various factors such as the thickness and stiffness of the model, the tension in the model, and the material properties of the model. These factors can be adjusted in the model to study their effects on the natural frequencies.

4. How do the natural frequencies of the simplified tympanic membrane model relate to human hearing?

The natural frequencies of the simplified tympanic membrane model can help us understand how the eardrum responds to different sound frequencies. This information can be used to improve our understanding of human hearing and potentially improve treatments for hearing impairments.

5. What are the applications of studying the natural frequencies of the simplified tympanic membrane model?

Studying the natural frequencies of the simplified tympanic membrane model can have various applications, such as improving our understanding of the mechanisms of hearing, developing new treatments for hearing impairments, and designing better hearing aids and other auditory devices.

Similar threads

Replies
3
Views
2K
Replies
10
Views
714
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Other Physics Topics
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
2K
  • Mechanical Engineering
Replies
3
Views
2K
Replies
1
Views
2K
  • Mechanical Engineering
Replies
1
Views
2K
Replies
4
Views
2K
  • Mechanical Engineering
Replies
1
Views
3K
Back
Top