전단변형을 고려한 비대칭 박벽 곡선보의 자유진동해석
Free Vibration Analysis of Non-symmetric Thin-Walled Curved Beams with Shear Deformation
본 연구에서는 전단변형을 고려한 비대칭 박벽 곡선보의 자유진동해석을 수행할 수 있는 일반이론을 제시하기 위하여, 3차원 연속체에 대한 가상일의 원리로부터 전단변형 효과를 고려하고 비대칭 박벽단면과 ?(Warping)을 포함하는 변위장을 도심 축에 대해 정의한 후 곡선보의 변형도-변위관계로부터 공간 박벽 곡선보의 일반화된 탄성변형에너지와 운동에너지를 새롭게 유도한다. 또한, 전단변형이 고려된 곡선보의 총포텐셜에너지에 대해 변분을 취함으로써 평형방정식과 힘-변위관계를 제시한다. 한편, 제시된 이론에 대해 등매개 보요소를 도입하여 유한요소 정식화를 수행하였으며 곡선보의 동적 거동특성을 조사하기 위하여 전단변형, 곡률효과 그리고 진동모드에 대한 매개변수 연구를 수행한다. 마지막으로, 본 연구의 타당성을 입증하기 위하여, 다양한 해석예제에 대한 3차원 고유진동수를 산정하고 타 연구자들의 결과 및 ABAQUS의 쉘요소를 이용한 해석결과와 비교ㆍ검증한다.
For spatial free vibration of non-symmetric thin-walled curved beams with shear deformation, an improved formulation is proposed in the present study. The elastic strain and the kinetic energies are first derived by considering constant curvature and shear deformation effects due to shear forces and restrained warping torsion. Next equilibrium equations and force-deformation relations are obtained using a stationary condition of total potential energy. And the finite element procedures are developed by using isoparametric curved beam element with arbitray thin-walled sections. Particularly not only shear deformation and thickness-curvature effects on vibration behaviors of curved beams but also mode transition and crossover phenomena with change in curvatures of beams are parametrically investigated. In order to illustrate the accuracy and the reliability of this study, various numerical solutions for spatial free vibration are compared with results by available references and ABAQUS's shell element.
- Krishnan, A. and Suresh, Y. J., "A simple cubic linear element for static and free vibration analysis of curved beams," Computers & Structures 68, 1998, pp. 473-489.
- Huang, C.S., Tseng, Y. P., Leissa, A. W., and Nieh, K. Y., "An exact solution for in-plane vibrations of an arch having variable curvature and cross section," International Journal of Mechanical Sciences 40, 1998, pp. 1159-1173.
- Issa, M.S., Wang, T. M, and Hsiao, B. T., "Extensional vibrations of continuous circular curved beams with rotary inertia and shear deformation, I: free vibration," Journal of Sound and Vibration 114, 1987, pp. 297-308.
- Cortinez, V. H, Piovan, M. T., and Rossi, R. E., "Out of plane vibrations of thin walled curvEd beams considering shear flexibility," Structural Engineering and Mechanics 8, 1999, pp. 257-272.
- Kang, K, Bert, C. W., and Striz, A. G., "Vibration analysis of shear deformable circular arches by the differential quadrature method," Journal of Sound and Vibration 181, 1995, pp. 353-360.
- Piovan, M T., Cortinez, V. H., and Rossi, R. E., "Out-of-plane vibrations of shear deformable continuous horizontally curved thin-walled beams," Journal of Sound and Vibration 237, 2000, pp. 101-118.
- Tseng, Y. P., Huang, C. S., and Lin, C. J., "Dynamic stiffness analysis for in-plane vibrations of arches with variable curvature," Journal of Sound and Vibration 207,1997, pp. 15-31.
- Charpie, J. P. and Burroughs, C. B., "An analytic model for the free in-plane vibration of beams of variable curvature and depth," Journal of the Acoustical Society of America 94, 1993, pp. 866-879.
- Petyt, M. and Fleischer, C. C, "Free vibration of a curved beam," Journal of Sound and Vibration 18, 1971, pp. 17-30.
- Gendy, A. S. and Saleeb, A. F., "Vibration analysis of coupled extensionaljflexuraljtorsional modes of curved beams with arbitrary thin-walled sections," Journal of Sound and Vibration 174, 1994, pp. 261-274.
- Howson, W. P., Jemah, A K, and Zhou, J. Q., "Exact natural fre- quencies for out-of-plane motion of plane structures composed of curved beam members," Computers & Structures 55, 1995, pp. 989-995.
- Howson, W. P. and Jemah, A K, "Exact out-of-plane natural frequencies of curved Timoshenko beams," Journal of Engineering Mechanics 125, 1999, PF. 19-25.
- Snyder, J. M and Wilson, J. E, "Free vibrations of continuous horizontally curved beams," Journal of Sound and Vibration 157, 1992, pp. 345-355.
- Oh, S. J., Lee, B. K, and Lee, I. W., "Natural frequencies of non-circular arches with rotatory inertia and shear deformation," Journal of Sound and Vibration 219, 1999, pp. 23-33.
- Takahashi, S. and Suzuki, K, "Vibrations of elliptic arc bar perpendicular to its plane," Bulletin of the Japan Society of Mechanical Engineers 20, 1977, pp. 1409-1416.
- Noor, A. K, Peters, I. M, and Min, B. I., "Mixed finite element models for free vibrations of thin-walled beams," Finite Elements in Analysis and Design 5, 1989, pp. 291-305.
- Timoshenko, S. P. and Cere, J. M, Theory of elastic stability, McGraw-Hill, N.Y., 1961.
- Wang, T. M, Nettleton, R. H, and Keita, B., "Natural frequencies for out-of-plane vibrations of continuous curved beams," Journal of Sound and Vibration 68, 1980, pp. 427-436.
- ABAQUS, User's Manual Vol. I and Vol. II. Ver. 5.2, Hibbit, Karlsson, 1992.
- Scott, J. F. M and Woodhouse, J., "Vibration of an elastic strip with varing curvature," Philosophical Transactions of the Rayal Society of London, Physical Sciences and Engineering 339, 1992, pp. 587-625.
- Bathe, K J., Finite Element Procedures, Prentice- Hall, Englewood Giffs, N. J., 1996.
- Anestis S. Veletsos, Austin, Walter J., Lopes, Carlos A, and Wung, Shyr-jen, "Free in-plane vibration of circular arches," Journal of Engineering Mechanics Division 98, 1972, pp. 311-329.
- Irie, T., Yamada, G., and Takahashi, I., "In-plane vibration of a free-clamped slender arc of varying crosssection," Bulletin of the Japan Society of Mchanical Engineers 23, 1980, pp. 567-573.
- Chidamparam, P. and Leissa, A w., "Influence of centerline extensibility on the in-plane free vibrations of loaded circular arches," Journal of Sound and Vibration 183, 1995, pp. 779-795.
- Wang, T. M., "Lowest natural frequency of clamped parabolic arcs," Journal of Structural Division 98, 1972, pp. 407-411.
- Vlasov, V. Z., Thin-walled elastic beams, National Science Foundation, Washington, D.C, 1961.
- Raveendranath, P., Singh, Gajbir, and Pradhan, B., "Free vibration of arches using a curved beam element based on a coupled polynomial displacement field," Computers & Structures 78, 2000, pp. 583-590.
- Suzuki, K, Aida, H, and Takahashi, S., "Vibrations of curved bars perpendicular to their planes," Bulletin of the Japan Society of Mechanical Engineers 21, 1978, pp.162-173.
- Lee, B. K and Wilson, J. F., "Free vibrations of arches with variable curvature," Journal of Sound and Vibration 136, 1989, pp. 75-89.
- Suzuki, K and Takahashi, S., "In-plane vibration of curved bars with varying cross-section," Bulletin of the Japan Society of Mechanical Engineers 25, 1982, pp. 1100-1107.
- Kim, M. Y., Kim, N.I., and Yun, H. T., "Exact dynamic and static stiffness matrices of shear deformable thin-walled beam-columns(accepted for publication)," Journal of Sound and Vibration, 2003.
- Gupta, A. K. and Howson, W. P., "Exact natural frequencies of plane structures composed of slender elastic curved members," Journal of Sound and Vibration 175, 1994, pp. 145-157.
- Wang, T. M. and Brannen, W. F., "Natuarl frequencies for out-of-plane vibrations of curved beams on elastic foundations," Journal of Sound and Vibration 84, 1982, pp. 241-246.
- Tarnopolskaya, T., Hoog, F. R. De, and Fletcher, N. H, "Low-frequency mode transition in the free in-plane vibration of curved beams," Journal of Sound and Vibration 228, 1999, pp. 69-90.
- Tarnopolskaya, T., Hoog, F. R. De, Fletcher, N. H, and Thwaites, S., "Asymptotic analysis of the free in-plane vibrations of beam with arbitrarily varying curvature and cross-section," Journal of Sound and Vibration 196, 1996, pp. 659-680.
- Wang, T. M and Guilbert, M. P., "Effects of rotary inertia and shear on natural frequencies of continuous circular curved beams," International Journal of Solids and Structures 17, 1981, pp. 281-289.
- Kim, M.Y., Kim, N.I., and Min, B. C, "Analytical and numerical study on spatial free vibration of nonsymmetric thin-walled curved beams," Journal of Sound and Vibration 258, 2002, pp. 595-618.
- Kawakami, M, Sakiyama, T., Matsuda, H, and Morita, C, "In-plane and out-of-plane free vibrations of curved beams with variable sections," Journal of Sound and Vibration 187, 1995, pp. 381-401.
저자의 다른 논문
- 1999 "지진력을 받는 해양케이블의 동적 비선형해석" 한국지진공학회논문집 = Journal of the Earthquake Engineering Society of Korea 3 (2): 77~86
- 1999 "파력을 받는 해양케이블의 동적 비선형 해석" 韓國海岸海洋工學會誌 = Journal of Korean society of coastal and ocean engineers 11 (4): 173~188
- 1999 "조류력을 받는 해양케이블의 자유진동해석" 韓國海岸海洋工學會誌 = Journal of Korean society of coastal and ocean engineers 11 (4): 231~237
- 2002 "박벽보의 응력해석을 위한 단면상수의 자동산정" 韓國鋼構造學會 論文集 = Journal of Korean Society of Steel Construction 14 (1): 41~49
- 2004 "박벽 곡선보 구조의 최근 연구현황 및 이론" 전산 구조 공학 = Journal of the Computational Structural Engineering Institute of Korea 17 (1): 7~14
- 2005 "탄성좌굴 고유치 및 2차 탄성해석법을 이용한 평면강절프레임의 개선된 좌굴설계법" 한국전산구조공학회논문집 = Journal of the computational structural engineering institute of Korea 18 (2): 159~168
- 2005 "휨 및 비틀림 거동 및 전단변형 효과를 고려한 차량-현수교의 동적 상호작용 해석" 한국전산구조공학회논문집 = Journal of the computational structural engineering institute of Korea 18 (4): 361~372
- 2005 "Exact dynamic element stiffness matrix of shear deformable non-symmetric curved beams subjected to initial axial force" Structural engineering and mechanics : An international journal 19 (1): 73~96
원문복사신청을 하시면, 일부 해외 인쇄학술지의 경우 외국학술지지원센터(FRIC)에서
무료 원문복사 서비스를 제공합니다.
NDSL에서는 해당 원문을 복사서비스하고 있습니다. 위의 원문복사신청 또는 장바구니 담기를 통하여 원문복사서비스 이용이 가능합니다.
- 이 논문과 함께 출판된 논문 + 더보기