Vibration characteristics analysis of barrel type cylindrical shells

Moojoon Kim; Jungsoon Kim

doi:10.7776/ASK.2026.45.2.175

All Issue

2026 Vol.45, Issue 2 Preview Page Next Page

Research Article

Vibration characteristics analysis of barrel type cylindrical shells 베럴형 원통쉘의 진동특성 해석

31 March 2026. pp. 175-185

PDF XML

Abstract

This paper presents an analytical study on the axisymmetric vibration characteristics of barrel-type cylindrical shells. Assuming that the shell thickness is sufficiently small compared to its length, the torsional motion is neglected and two displacement components - normal displacement along the meridional curvature and tangential displacement along the meridian - are considered. The coupled governing equations are derived from the Lagrangian formulation and expressed as a set of ordinary differential equations. A power series expansion with respect to the angular coordinate is introduced to obtain general solutions, which are classified according to the parity of the displacement functions. Resonance conditions are derived in determinant form for clamped-clamped and simply supported boundary conditions. Natural frequencies and corresponding mode shapes are calculated, and the validity of the proposed analytical method is verified through comparison with finite element analysis. The results show good agreement overall. Furthermore, the effects of the surface curvature radius on resonance frequencies are investigated, revealing that the natural frequencies increase as the curvature radius increases for all vibration modes.

Keywords

Barrel type

Cylindrical shell

Vibration characteristic

Boundary condition

Resonant frequency

본 논문에서는 베럴형 원통쉘의 축대칭 진동 특성을 해석적으로 규명하였다. 쉘의 두께가 길이에 비해 충분히 얇다는 가정하에, 접선 방향 변위와 그에 수직한 법선 방향 변위를 고려하여 라그랑지안으로부터 연립 상미분방정식을 유도하였다. 도출된 방정식은 각도에 대한 멱급수 해법을 적용하여 해석적으로 전개하였으며, 변위 함수의 기·우함수 특성에 따라 두 가지 경우로 구분하여 일반해를 구성하였다. 양단 고정 및 단순지지 경계조건에 대해 공진 조건식을 행렬식 형태로 유도하고, 이를 통해 고유진동수와 모드 형상을 계산하였다. 제안된 해석 방법의 타당성을 검증하기 위하여 유한요소해석 결과와 비교하였으며, 두 결과가 전반적으로 잘 일치함을 확인하였다. 또한 곡률반경 변화에 따른 공진주파수의 변화를 분석하여, 곡률반경 증가에 따라 모든 모드의 공진주파수가 증가함을 확인하였다.

키워드

베럴형

원통쉘

진동특성

경계조건

공진주파수

References

L. Meirovitch, Analytical Methods in Vibrations (Macmillan, New York, 1967), pp. 205-273.

H. Chung, “Free vibration analysis of cylindrical shells,” J. Sound Vib. 74, 331-350 (1981).

10.1016/0022-460X(81)90303-5

M. Amabili, “Theory and experiments for large-amplitude vibrations of empty and fluid-filled circular cylindrical shells with imperfections,” J. Sound Vib. 262, 921-975 (2003).

10.1016/S0022-460X(02)01051-9

A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, 4^th ed (Cambridge University, New York, 1944), pp. 487-498.

S. P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, 2^nd ed (McGraw-Hill, New York, 1959), pp. 51-54.

W. Flugge, Stresses in Shells (Springer-Verlag, Heidelberg, 1973), pp. 414-432.

10.1007/978-3-642-88291-3_7

Vibration of Shells, NASA SP-288, https://ntrs.nasa.gov/citations/19730018197/, (Last viewed September 2, 2013).

J. N. Reddy, Theory and Analysis of Elastic Plates and Shells (CRC Press, Boca Raton, London, New York, 2006), pp. 403-378.

10.1201/9780849384165

W. Soedel, Vibrations of Shells and Plates, 3^rd ed (Marcel Dekker, New York, 2004), pp. 301-321.

M. Amabili, Nonlinear Vibrations and Stability of Shells and Plates, (Cambridge University Press, Cambridge, New York, Melbourne, 2008), pp. 242-271.

O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, 5^th ed (Butterworth-Heinemann, Oxford, 2000), pp. 87-111.

K. J. Bathe, Finite Element Procedures (Prentice Hall, New Jersey, 1996), pp. 148-335.

P. T. Thang, H. Kim, C. Kim, H. Jang, T. Kim, and J. Kim, “Free vibration analysis of barrel-shaped sandwich shells with auxetic honeycomb core using modified thick shell theory,” Aerosp. Sci. Technol. 145, 108861 (2024).

10.1016/j.ast.2023.108861

J. Mantari, A. Oktem, and C. Soares, “Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory,” Compos. Struct. 94, 37-49 (2011).

10.1016/j.compstruct.2011.07.020

D. Li, Y. Lan, and T. Zhou, “Numerical and experimental investigation of a variable-curvature shell class I flextensional transducer,” J. Acoust. Soc. Am. 154, 1800-1812 (2023).

10.1121/10.0021071

L. Zhang, “Vibrational behaviour of higher-order cylindrical shells,” J. Korean Soc. Mech. Eng. 15, 137-147 (2023).

X. Sun, W. Sun, D. Du, X. Liu, S. Lv, and K. Xu, “Semi-analytical dynamic modeling and analysis of cylindrical shell with arbitrary variable path curved stiffeners,” MAMS. 33, 2445224 (2026).

10.1080/15376494.2024.2445224

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 :2
Pages :175-185
Received Date : 2026-03-11
Accepted Date : 2026-03-25
DOI :https://doi.org/10.7776/ASK.2026.45.2.175

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

All Issue