加筋板壳结构振动分析的若干问题研究
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摘要
本文主要讨论加筋板壳结构的振动问题。通过比较加筋平板采用不同类型单元和不同结点数单元时的计算结果与实验数据的误差,发现不同的单元类型适合于不同的振动模型;另一方面,单元的结点数也会通过影响结构刚度来改变固有频率。梁单元是模拟加强筋振动状况的最理想单元类型,但由于采用梁单元时忽略了加强筋的几何特征,因此需要通过考虑平板壳单元结点上转动自由度对相应的梁单元结点位移自由度的影响来改善计算精度。
通过对基于不同参数的模型的相互比较,来进一步研究加强筋的添置对原平板振动特性的影响。对于加强筋横截面尺寸的影响,当固定横截面的宽度或厚度而单独改变另一横截面参数时,对于不同模态振型会产生两种不同的结果。而当横截面宽度和厚度同比增长时,各阶模态振型变化规律一致。更多地,当在平板上采用不同数量的加强筋,或将加强筋安放在不同的位置时,固有频率都会产生相应的变化。
在对圆柱壳的研究中,通过对比基于不同类型单元,不同自由度单元和不同网格密度模型时的计算结果与简单圆柱壳固有频率实验结果,得到了较为合理的有限元模型,并基于此建立了加筋的圆柱壳模型以分析加强筋对圆柱壳固有频率的影响。进一步地,在引入几何非线性的影响后,还分析了在不同内压,不同纵向加速度,不同绕轴心的角速度的情况下,圆柱壳固有频率的变化规律。
This thesis is focused on the study of vibration behaviors of stiffened shell and plane structure. By referring to an experimental data of a stiffened plane, models in the same conditions have been built to study the numerical errors while changed the types of elements or counts of nodes. According to the results, it is better to choose them with attributes of various models. For optimizing the stiffened plane models with beam-element stiffeners, the effect between rotational freedom of shell elements and motional freedom of beam elements has been considered.
The models with different parameters have been investigated for discovering the further effects of stiffeners. There are two distinguished results while fixing the width or thickness of stiffener but changing the lengths of other edges. However, it shows the same tendency while keeping a constant ratio of width over thickness. Moreover, the counts or positions of stiffeners on a plane change, the natural frequencies change accordingly.
In the study of a cylindrical shell, a relative precise model has been built by analyzing the effect of element types, freedoms on nodes and mesh densities. Furthermore, by considering the effect of nonlinear geometry, the cylindrical shell model, in different internal pressures, accelerations and rotational speeds, have been analyzed.
通过对基于不同参数的模型的相互比较,来进一步研究加强筋的添置对原平板振动特性的影响。对于加强筋横截面尺寸的影响,当固定横截面的宽度或厚度而单独改变另一横截面参数时,对于不同模态振型会产生两种不同的结果。而当横截面宽度和厚度同比增长时,各阶模态振型变化规律一致。更多地,当在平板上采用不同数量的加强筋,或将加强筋安放在不同的位置时,固有频率都会产生相应的变化。
在对圆柱壳的研究中,通过对比基于不同类型单元,不同自由度单元和不同网格密度模型时的计算结果与简单圆柱壳固有频率实验结果,得到了较为合理的有限元模型,并基于此建立了加筋的圆柱壳模型以分析加强筋对圆柱壳固有频率的影响。进一步地,在引入几何非线性的影响后,还分析了在不同内压,不同纵向加速度,不同绕轴心的角速度的情况下,圆柱壳固有频率的变化规律。
This thesis is focused on the study of vibration behaviors of stiffened shell and plane structure. By referring to an experimental data of a stiffened plane, models in the same conditions have been built to study the numerical errors while changed the types of elements or counts of nodes. According to the results, it is better to choose them with attributes of various models. For optimizing the stiffened plane models with beam-element stiffeners, the effect between rotational freedom of shell elements and motional freedom of beam elements has been considered.
The models with different parameters have been investigated for discovering the further effects of stiffeners. There are two distinguished results while fixing the width or thickness of stiffener but changing the lengths of other edges. However, it shows the same tendency while keeping a constant ratio of width over thickness. Moreover, the counts or positions of stiffeners on a plane change, the natural frequencies change accordingly.
In the study of a cylindrical shell, a relative precise model has been built by analyzing the effect of element types, freedoms on nodes and mesh densities. Furthermore, by considering the effect of nonlinear geometry, the cylindrical shell model, in different internal pressures, accelerations and rotational speeds, have been analyzed.
引文
[1] K. Sezawa. On the lateral vibration of a rectangular plate clamped at four edges. Report No. 70, Aeronautics Research Institution, Tokyo Univsity, 1931: 124-126 (in Japanese)
[2] S. Tomotika. The transverse vibration of a square plate clamped at four edges. Phil magazine, 1936,21: 745-760
[3] D. Young. Vibration of rectangular plates by the Ritz method. Journal of Application Mechanics, 1950,17: 448-453.
[4] V. V. Bolotin. Dynamic edge effect in the elastic vibration of plates. Inshe. Sbornik., 1961, 31: 3-14. (In Russian)
[5] N. W. Bazley, D. W. Fox. Methods for lower bounds to frequencies of continuous elastic systems. Report TG-609, Application Physics Lab. The Johns Hopkins Univeersity, May 1965
[6] N. Aronszajn. The Rayleigh-Ritz and Weinstein methods for approximation of eigenvalues-III: Application of Weinstein's method with an auxiliary problem of type I. Technology Report, No.3, Project NR 041, 090, Oklahoma A. and M. College, 1950
[7] S. T. A. Odman. Studies of boundary value problems. Part II. Characteristic functions of rectangular plates. Process NR 24, Swedish Cement and Concrete Research Institution, Royal Institution Technology, 1955: 7-62.
[8] C. L. Kirk. Natural frequencies of stiffened plates. Journal of Sound and Vibration, 1970,13:375-388.
[9] R. B. Bhat. Vibration of panels with nonuniformly spaced stringer. Journal of Sound and Vibration, 1982, 84: 449-452.
[10] J. R. Wiu , W. H. Lim. Vibration of rectangular plates with edge restraints and intermediate supports. Journal of Sound and Vibration, 1988, 123: 103-113.
[11] W. H. Liu, W. H. Chen. Free vibrations of restrained cylindrical thin shell panel under axial and transverse stresses. Journal of Sound and Vibration, 1988, 127: 384-390.
[12] S. P. Cheng, C. Dade. Dynamic analysis of stiffened plates and shells using spline Gauss collocation method. Computers and Structures 1990, 36: 623-629.
[13] G. S. Palani, N. R. Iyer, T. V. R. Apparao. An efficient element model for static and vibration analysis of eccentrically stiffened plates/shells. Computers and Structures, 1992,43: 651-661.
[14] T. S. Koko, M. D. Olson. Vibration analysis of stiffened plates by super elements. Journal of Sound and Vibration, 1992,158: 149-167.
[15] P. S. Rao, G. Sinha, M. Mukhopadhyay. Vibration of submerged stiffened plates by the finite element method. International Shipbuilding Progress, 1993, 40: 261-292.
[16] C. S. Chen, W. Liu, S. M. Chern. Vibration analysis of stiffened plate. Computers and Structures, 1994, 50: 471-480.
[17] T. P. Holopanien. Finite element free vibration analysis of eccentrically stiffened plates. Computers and Structures, 1995, 56: 93-1007.
[18] Y. Xiang, C. M. Wang. Exact buckling and vibration solutions for stepped rectangular plates. Journal of Sound and vibration, 2002,250(3):503-517
[19] J. L. Sewall, E. C. Naumann. An experimental and analytical vibration study in thin cylindrical shells with and without longitudinal stiffeners. NASA-'ND-4705, 1968.
[20] S. A. Rinehart, J. T. S. Wang. Vibration of simply supported cylindrical shells with longitudinal stiffeners. Journal of Sound and Vibration, 1972, 24: 151-163.
[21] D. J. Mead, N. S. Bardell. Free vibration of a thin cylindrical shell with discrete axial stiffeners. Journal of Sound and Vibration, 1986, 111: 229-250.
[22] D. J. Mead, N. S. Bardell. Free vibration of a thin cylindrical shell with periodic circumferential stiffeners. Journal of Sound and Vibration, 1987, 115: 499-520.
[23] B. A. J. Mustafa, R. Ali. Prediction of natural frequency of vibration of stiffened cylindrical shells and orthogonally stffened curved panels. Journal of Sound and Vibration, 1987, 113:317-327.
[24] B. A. J. Mustafa, R. Ali. Free vibration analysis of multi-symmetric stiffened shells. Computers and Structures, 1987,27: 803-810.
[25] N. S. Bardell, D. J. Mead. Free vibration of an orthogonally stiffened cylindrical shell, Part I: discrete line simple supports. Journal of Sound and Vibration, 1989, 134:29-54.
[26] N. S. Bardell, D. J. Mead. Free vibration of an orthogonally stiffened cylindrical shell, Part II: Discrete general stiffeners. Journal of Sound and Vibration, 1989, 134: 55-72.
[27] M. L. Accorsi and M. S. Bennett. A finite element based method for the analysis of free wave propagation in stiffened cylinders. Journal of Sound and vibration, 1991,148:279-292.
[28] Z. Mecitoglu, M. C. Dokmeci. Free vibrations of a thin, stiffened, cylindrical shallow shell. AIAA Journal, 1991, 30: 848-850.
[29] R. S. Langley. A dynamic stiffness technique for the vibration analysis of stiffened shell structures. Journal of Sound and Vibration, 1992,156: 521-540.
[30] G. Sinha, M. Mukhopadhyay. Finite element free vibration analysis of stiffened shells. Journal of Sound and Vibration, 1994, 171: 529-548.
[31] G. Sinha, M. Mukhopadhyay. Static, free and forced vibration analysis of arbitrary non-uniform shells with tapered stiffeners. Computers and Structures, 1997, 62: 919-933.
[32] J. Jiang, M. D. Olson. Vibration analysis of orthogonally stiffened cylindrical shells using super mite elements. Journal of Sound and Vibration, 1994, 173: 73-83.
[33] A. J. Stanley, N. Ganesan. Free vibration characteristics of stiffened cylindrical shells. Computers and Structures, 1997, 65: 33-45.
[34] B. Sivasubramonian, G. V. Rao, A. Krishnan. Free vibration of longitudinally stiffened curved panels with cutout. Journal of Sound and Vibration 1999, 226: 41-55.
[35]D.Lee,I.Lee.Vibration analysis of anisotropic plates with eccentric stiffeners.Computers and Structures,1995,57:99-105
[36]M.D.Olson and C.R.Hazell.Vibration studies on some integral rib-stiffened plates.Journal of Sound and Vibration 1977,50:43-61.
[37]A.Mukherjee,M.Mukhopadhyay.Finite element free vibration of eccentrically stiffened plates.Computers and Structures,1988,30:1303-1317.
[38]A.Bhimaraddi,A.J.Carr,P.J.Moss.Finite element analysis of laminated shells of revolution with laminated stiffeners.Computers and Structures,1989,33:295-305.
[39]B.Sivasubramonian,G.V.Rao,A.Krishnan.Free vibration of longitudinally stiffened curved panels with cutout.Journal of Sound and Vibration,1999,226:41-55.
[40]A.N.nayak,J.N.Bandyopadhyay.On the free vibration of stiffened shallow shells.Journal of Sound and Vibration,2002,255(2):357-382.
[41]王勖成.有限单元法.北京:清华大学出版社,2003
[42]H.Krauss.Thin Elastic Shell.New York:Wiley,1967.
[43]R.N.Arnold,G.B.Warburton,Flexuarl vibrations of the walls of thin cylindrical shells having freely supported ends,Proceeding of the Royal Society of London,1997,197:544-550
[44]R.Miserentino,S.C.Dixon,Vibration and flutter tests of a pressurized thin-walled truncated conical shell,National Aeronautics and Space Administration,1971,Va.23365
[2] S. Tomotika. The transverse vibration of a square plate clamped at four edges. Phil magazine, 1936,21: 745-760
[3] D. Young. Vibration of rectangular plates by the Ritz method. Journal of Application Mechanics, 1950,17: 448-453.
[4] V. V. Bolotin. Dynamic edge effect in the elastic vibration of plates. Inshe. Sbornik., 1961, 31: 3-14. (In Russian)
[5] N. W. Bazley, D. W. Fox. Methods for lower bounds to frequencies of continuous elastic systems. Report TG-609, Application Physics Lab. The Johns Hopkins Univeersity, May 1965
[6] N. Aronszajn. The Rayleigh-Ritz and Weinstein methods for approximation of eigenvalues-III: Application of Weinstein's method with an auxiliary problem of type I. Technology Report, No.3, Project NR 041, 090, Oklahoma A. and M. College, 1950
[7] S. T. A. Odman. Studies of boundary value problems. Part II. Characteristic functions of rectangular plates. Process NR 24, Swedish Cement and Concrete Research Institution, Royal Institution Technology, 1955: 7-62.
[8] C. L. Kirk. Natural frequencies of stiffened plates. Journal of Sound and Vibration, 1970,13:375-388.
[9] R. B. Bhat. Vibration of panels with nonuniformly spaced stringer. Journal of Sound and Vibration, 1982, 84: 449-452.
[10] J. R. Wiu , W. H. Lim. Vibration of rectangular plates with edge restraints and intermediate supports. Journal of Sound and Vibration, 1988, 123: 103-113.
[11] W. H. Liu, W. H. Chen. Free vibrations of restrained cylindrical thin shell panel under axial and transverse stresses. Journal of Sound and Vibration, 1988, 127: 384-390.
[12] S. P. Cheng, C. Dade. Dynamic analysis of stiffened plates and shells using spline Gauss collocation method. Computers and Structures 1990, 36: 623-629.
[13] G. S. Palani, N. R. Iyer, T. V. R. Apparao. An efficient element model for static and vibration analysis of eccentrically stiffened plates/shells. Computers and Structures, 1992,43: 651-661.
[14] T. S. Koko, M. D. Olson. Vibration analysis of stiffened plates by super elements. Journal of Sound and Vibration, 1992,158: 149-167.
[15] P. S. Rao, G. Sinha, M. Mukhopadhyay. Vibration of submerged stiffened plates by the finite element method. International Shipbuilding Progress, 1993, 40: 261-292.
[16] C. S. Chen, W. Liu, S. M. Chern. Vibration analysis of stiffened plate. Computers and Structures, 1994, 50: 471-480.
[17] T. P. Holopanien. Finite element free vibration analysis of eccentrically stiffened plates. Computers and Structures, 1995, 56: 93-1007.
[18] Y. Xiang, C. M. Wang. Exact buckling and vibration solutions for stepped rectangular plates. Journal of Sound and vibration, 2002,250(3):503-517
[19] J. L. Sewall, E. C. Naumann. An experimental and analytical vibration study in thin cylindrical shells with and without longitudinal stiffeners. NASA-'ND-4705, 1968.
[20] S. A. Rinehart, J. T. S. Wang. Vibration of simply supported cylindrical shells with longitudinal stiffeners. Journal of Sound and Vibration, 1972, 24: 151-163.
[21] D. J. Mead, N. S. Bardell. Free vibration of a thin cylindrical shell with discrete axial stiffeners. Journal of Sound and Vibration, 1986, 111: 229-250.
[22] D. J. Mead, N. S. Bardell. Free vibration of a thin cylindrical shell with periodic circumferential stiffeners. Journal of Sound and Vibration, 1987, 115: 499-520.
[23] B. A. J. Mustafa, R. Ali. Prediction of natural frequency of vibration of stiffened cylindrical shells and orthogonally stffened curved panels. Journal of Sound and Vibration, 1987, 113:317-327.
[24] B. A. J. Mustafa, R. Ali. Free vibration analysis of multi-symmetric stiffened shells. Computers and Structures, 1987,27: 803-810.
[25] N. S. Bardell, D. J. Mead. Free vibration of an orthogonally stiffened cylindrical shell, Part I: discrete line simple supports. Journal of Sound and Vibration, 1989, 134:29-54.
[26] N. S. Bardell, D. J. Mead. Free vibration of an orthogonally stiffened cylindrical shell, Part II: Discrete general stiffeners. Journal of Sound and Vibration, 1989, 134: 55-72.
[27] M. L. Accorsi and M. S. Bennett. A finite element based method for the analysis of free wave propagation in stiffened cylinders. Journal of Sound and vibration, 1991,148:279-292.
[28] Z. Mecitoglu, M. C. Dokmeci. Free vibrations of a thin, stiffened, cylindrical shallow shell. AIAA Journal, 1991, 30: 848-850.
[29] R. S. Langley. A dynamic stiffness technique for the vibration analysis of stiffened shell structures. Journal of Sound and Vibration, 1992,156: 521-540.
[30] G. Sinha, M. Mukhopadhyay. Finite element free vibration analysis of stiffened shells. Journal of Sound and Vibration, 1994, 171: 529-548.
[31] G. Sinha, M. Mukhopadhyay. Static, free and forced vibration analysis of arbitrary non-uniform shells with tapered stiffeners. Computers and Structures, 1997, 62: 919-933.
[32] J. Jiang, M. D. Olson. Vibration analysis of orthogonally stiffened cylindrical shells using super mite elements. Journal of Sound and Vibration, 1994, 173: 73-83.
[33] A. J. Stanley, N. Ganesan. Free vibration characteristics of stiffened cylindrical shells. Computers and Structures, 1997, 65: 33-45.
[34] B. Sivasubramonian, G. V. Rao, A. Krishnan. Free vibration of longitudinally stiffened curved panels with cutout. Journal of Sound and Vibration 1999, 226: 41-55.
[35]D.Lee,I.Lee.Vibration analysis of anisotropic plates with eccentric stiffeners.Computers and Structures,1995,57:99-105
[36]M.D.Olson and C.R.Hazell.Vibration studies on some integral rib-stiffened plates.Journal of Sound and Vibration 1977,50:43-61.
[37]A.Mukherjee,M.Mukhopadhyay.Finite element free vibration of eccentrically stiffened plates.Computers and Structures,1988,30:1303-1317.
[38]A.Bhimaraddi,A.J.Carr,P.J.Moss.Finite element analysis of laminated shells of revolution with laminated stiffeners.Computers and Structures,1989,33:295-305.
[39]B.Sivasubramonian,G.V.Rao,A.Krishnan.Free vibration of longitudinally stiffened curved panels with cutout.Journal of Sound and Vibration,1999,226:41-55.
[40]A.N.nayak,J.N.Bandyopadhyay.On the free vibration of stiffened shallow shells.Journal of Sound and Vibration,2002,255(2):357-382.
[41]王勖成.有限单元法.北京:清华大学出版社,2003
[42]H.Krauss.Thin Elastic Shell.New York:Wiley,1967.
[43]R.N.Arnold,G.B.Warburton,Flexuarl vibrations of the walls of thin cylindrical shells having freely supported ends,Proceeding of the Royal Society of London,1997,197:544-550
[44]R.Miserentino,S.C.Dixon,Vibration and flutter tests of a pressurized thin-walled truncated conical shell,National Aeronautics and Space Administration,1971,Va.23365