Mechanical modeling of a shell horn for automobiles considering nonlinear stiffness of the diaphragm

Junsu Lee; Jungon Kim; Dongwook Yoo; Incheol Kim; Wonkyu Moon

doi:10.7776/ASK.2026.45.1.033

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2026 Vol.45, Issue 1 Preview Page Next Page

Research Article

Mechanical modeling of a shell horn for automobiles considering nonlinear stiffness of the diaphragm 다이아프램의 비선형 강성을 고려한 자동차용 쉘 혼의 기계 모델링

31 January 2026. pp. 33-40

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Abstract

The shell horn for automobiles is a multiphysics system in which the electromagnetic, mechanical, and acoustic domains interact, and its operating frequency and sound pressure characteristics are highly sensitive to design parameters. Previous studies approximated the horn dynamics using simple linear spring models or focused on predicting the fundamental operating frequency, without providing a systematic analysis of the diaphragm’s nonlinear stiffness. This study aims to characterize the nonlinear mechanical behavior of the diaphragm and to propose an enhanced Lumped Parameter Model (LPM) that incorporates this nonlinearity. Static Force-Displacement (FD) curves were obtained through finite element analysis and universal testing machine measurements, confirming the geometric nonlinear stiffening as displacement increased. Dynamic force–displacement measurements using an impedance sensor further revealed nonlinear responses and hysteresis behavior. These static and dynamic characteristics were integrated into the lumped parameter model to compute the electromagnetic-mechanical-acoustic responses. Surface velocity measurement of the armature, conducted without the acoustic shell under a 12 V Direct Current (DC), showed good agreement with the proposed model, accurately predicting not only the fundamental frequency but also higher-order harmonics. The proposed nonlinear stiffness-based model is expected to serve as a useful foundation for future design and performance optimization of the shell horns.

Keywords

Shell horn

Diaphragm nonlinear stiffness

Force-Displacement (FD) curve

Lumped Parameter Model (LPM)

Harmonics

자동차용 쉘 혼은 전자기부, 기계부, 음향부가 결합된 다중물리 시스템으로, 설계 변수 변화에 따라 작동 주파수 및 음압 특성이 크게 달라진다. 기존 연구에서는 쉘 혼의 동특성을 단순 선형 스프링 기반 모델로 근사하거나, 기본 작동 주파수만을 분석하는 것에 그쳤으며, 다이아프램의 비선형 강성에 대한 체계적 분석은 이루어지지 않았다. 본 연구에서는 쉘 혼 시스템의 핵심 부품 중 하나인 다이아프램의 비선형 기계 특성을 규명하고, 이를 반영한 집중 매개변수 모델을 제안하고자 한다. 이를 위해 유한 요소 기반 정적 해석과 만능재료시험기를 활용한 정적 힘-변위 곡선을 측정하여 다이아프램의 변위 증가에 따른 기하학적 비선형 강성 증가를 확인했다. 또한 임피던스 센서를 활용한 동적 힘-변위 곡선 측정을 통해 비선형 응답과 히스테리시스 특성까지 파악했다. 이러한 정적 및 동적 특성을 집중 매개 모델에 반영하여 쉘 혼의 전자기-기계-음향 모델을 수치적으로 계산했다. 아마추어의 중심 속도는 음향부인 쉘을 제외하고 직류 전압을 12 V 인가하여 실험 결과와 비교했을 때, 기본 주파수뿐 아니라 고차 하모닉스까지 높은 정확도로 예측할 수 있었다. 본 연구에서 제안한 비선형 강성 기반 집중 매개변수 모델은 쉘 혼의 설계 및 성능 개선을 위한 기초 연구 모델로 활용될 수 있을 것으로 기대된다.

키워드

쉘 혼

다이아프램 비선형 강성

힘-변위 곡선

집중 매개변수 모델

하모닉스

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Information

Publisher :The Acoustical Society of Korea
Publisher(Ko) :한국음향학회
Journal Title :The Journal of the Acoustical Society of Korea
Journal Title(Ko) :한국음향학회지
Volume : 45
No :1
Pages :33-40
Received Date : 2025-11-26
Revised Date : 2025-12-11
Accepted Date : 2025-12-14
DOI :https://doi.org/10.7776/ASK.2026.45.1.033

The Journal of the Acoustical Society of KoreaISSN:1225-4428(Print) 2287-3775(Online)한국음향학회

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