Studying free vibration of tympanic membrane using analytical, finite element and Rayleigh-ritz approaches

Ommatmohammadi, M. Mohammad-Reza; Majdi, Hadi; Keighobadi, Jafar

doi:10.22064/tava.2025.2049943.1260

Studying free vibration of tympanic membrane using analytical, finite element and Rayleigh-ritz approaches

Document Type : Research Article

Authors

M. Mohammad-Reza Ommatmohammadi

Hadi Majdi

Jafar Keighobadi

Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran

10.22064/tava.2025.2049943.1260

Abstract

The tympanic membrane ™ plays a central role in the human hearing mechanism. Located at the entrance to the middle ear, it vibrates in response to changes in air pressure generated by incoming sound waves. The oscillation characteristics—particularly the natural frequencies and associated mode shapes—directly influence auditory perception and hearing sensitivity. This study investigates the TM’s natural frequencies using a simplified yet representative mathematical model, employing both analytical and semi‑analytical approaches. The semi‑analytical analysis is conducted using the Rayleigh–Ritz method with various basis functions to assess their accuracy in predicting frequency and mode shapes. Among these, Chebyshev polynomials exhibit exceptional efficiency, yielding high‑accuracy frequency estimates in close agreement with analytical solutions and validated by finite‑element simulations. In addition, the study examines the sensitivity of TM modes to variations in geometric and material parameters, providing valuable insight into their influence on dynamic behavior. A comparative analysis confirms that Chebyshev polynomials deliver the most accurate results, outperforming the other basis functions considered.

Highlights

The mathematical formulation of tympanic membrane vibration is provided.
Analysis of natural frequency (analytical and semi-analytical methods) is conducted.
Different functions, including the Chebyshev polynomial are used to compare results with analytical solutions.
Modes of vibration, both analytical and semi-analytical are analyzed conceptually.
A deep investigation about variation of parameters affecting natural frequency is performed.

Keywords

Tympanic membrane

Natural frequency acoustics

Mode shapes

Rayleigh-Ritz method

Parameter variation

Subjects