Applied Mathematics and Mechanics (English Edition) ›› 2026, Vol. 47 ›› Issue (4): 695-718.doi: https://doi.org/10.1007/s10483-026-3366-8

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Development and application of a lumped parameter model for predicting blast wave effects on middle ear dynamics

Hongge HAN1, Liang WANG1, Zhanli LIU2, Yongtao SUN1,3,4,5,6,(), Anshuai WANG1, Yueting ZHU7, Jie WANG8,9, Haoqiang GAO1, Qian DING1   

  1. 1.Department of Mechanics and Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin University, Tianjin 300350, China
    2.School of Aerospace Engineering, Tsinghua University, Beijing 100084, China
    3.National Key Laboratory of Explosion Science and Safety Protection, Beijing Institute of Technology, Beijing 10008l, China
    4.National Key Laboratory of Vehicle Power System, Tianjin University, Tianjin 300350, China
    5.National Key Laboratory of Strength and Structural Integrity, Xi’an 710065, China
    6.Science and Technology on Transient Impact Laboratory, No. 208 Research Institute of China Ordnance Industries, Beijing 102202, China
    7.Department of Otolaryngology, Head and Neck Surgery, Tianjin Children’s Hospital, Tianjin University, Tianjin 300400, China
    8.Department of Otolaryngology Head and Neck Surgery, Beijing Tongren Hospital, Capital Medical University, Key Laboratory of Otolaryngology Head and Neck Surgery, Ministry of Education, Beijing 100730, China
    9.Beijing Engineering Research Center of Audiological Technology, Beijing 100730, China
  • Received:2025-10-03 Revised:2026-01-21 Published:2026-03-31
  • Contact: Yongtao SUN, E-mail: ytsun@tju.edu.cn

Abstract:

The human ear is one of the most vulnerable organs to blast damage in modern warfare. The accurate prediction of blast wave effects on the ear has become a key challenge in auditory trauma research. A lumped parameter (LP) model, with parameters optimized using a genetic algorithm, is developed to efficiently predict the middle ear’s dynamic response to blast waves. The model accurately predicts tympanic membrane (TM) and stapes responses, particularly the first peak. Frequency-domain displacement and sensitivity analyses show that the middle ear responses are concentrated in a low-frequency range, with the blast wave amplitude significantly influencing the overall responses. TM responses are more sensitive to decay time at higher frequencies, while stapes responses are more sensitive at lower frequencies. This method achieves competitive accuracy and high computational efficiency. Based on this model, a risk index based on stapes displacements is proposed to optimize and evaluate hearing protection systems.

Key words: blast wave, lumped parameter (LP) model, genetic algorithm, middle ear response, hearing protection

2010 MSC Number: 

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