Iranian Society of Acoustics and Vibration and Avecina Journal of Theoretical and Applied Vibration and Acoustics 2423-4761 11 2 2025 07 01 Studying free vibration of tympanic membrane using analytical, finite element and Rayleigh-ritz approaches 142 160 728763 10.22064/tava.2025.2049943.1260 EN M. Mohammad-Reza Ommatmohammadi Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran 0009-0004-5154-7732 Hadi Majdi Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran Jafar Keighobadi Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran Journal Article 2025 02 10 <span style="font-size: 11.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;">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.</span> https://tava.isav.ir/article_728763_f2157cac10f21f8db053e07cf7aff0ce.pdf