复合材料夹芯圆柱壳水下振动和声辐射的三维弹性解
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摘要
为获得复合材料夹芯圆柱壳的振动声辐射准确解,在厚度方向将壳体分成若干薄层,基于三维弹性理论和状态空间技术,对每一薄层建立状态空间方程,并结合位移和应力连续条件,建立横向位移和应力的传递矩阵。外表面的流体载荷和内表面的点激励通过傅里叶级数展开,并代入状态空间方程,获得了复合材料圆柱壳水下振动和声辐射的弹性准确解。应用具体算例,与有限元仿真和文献计算结果对比。结果表明,本文的三维弹性理论相较于近似的二维壳体理论更加准确。进一步研究了铺层角、表层和芯材厚度分布及材料损耗因子对振动声辐射的影响。计算结果表明,在环频率以下的频段,声功率峰值点数目随铺层角度增加呈"抛物线"型变化趋势;在环频率以上的中高频段,随着铺层角度增加,声功率峰值点数目呈先增加后趋于平缓然后继续增加的趋势。随着芯材损耗因子的增加,声功率峰值逐步降低,但下降幅度减小。
In order to obtain the exact solution for the vibration and sound radiation of composite sandwich cylindrical shell,the shell was divided into several thin layers in the thickness direction,the state space equation was established for each thin layer based on three-dimensional elastic theory and state space technique and the transfer matrix of transversal displacement and stress was built considering the continuous condition of displacement and stress.The fluid load on the outer surface and the point excitation on the inner surface were expanded by Fourier series and introduced into the state space equation,the exact elastic solution of underwater vibration and sound radiation of composite sandwich shell was obtained.In contrast to the results by finite element simulation and that from the previous literature,present theoretical model is more accurate than the approximate two-dimensional shell theories.The effect of ply angle,thickness distribution of face and core and loss factor on vibration and sound radiation were further investigated.The results show that in the frequency range below the ring frequency the peak's number of sound power changes as the parabolic curve,and in the middle and high frequency bands above the ring frequency the peak's number of sound power increases first and tends to be gentle,and then continues to increase.With the increasing of core's loss factor,the peak value of sound radiation power gradually decreases,as well as the extent of decline.
In order to obtain the exact solution for the vibration and sound radiation of composite sandwich cylindrical shell,the shell was divided into several thin layers in the thickness direction,the state space equation was established for each thin layer based on three-dimensional elastic theory and state space technique and the transfer matrix of transversal displacement and stress was built considering the continuous condition of displacement and stress.The fluid load on the outer surface and the point excitation on the inner surface were expanded by Fourier series and introduced into the state space equation,the exact elastic solution of underwater vibration and sound radiation of composite sandwich shell was obtained.In contrast to the results by finite element simulation and that from the previous literature,present theoretical model is more accurate than the approximate two-dimensional shell theories.The effect of ply angle,thickness distribution of face and core and loss factor on vibration and sound radiation were further investigated.The results show that in the frequency range below the ring frequency the peak's number of sound power changes as the parabolic curve,and in the middle and high frequency bands above the ring frequency the peak's number of sound power increases first and tends to be gentle,and then continues to increase.With the increasing of core's loss factor,the peak value of sound radiation power gradually decreases,as well as the extent of decline.
引文
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[18]刘艳红,王炳华,卿光辉.含分层的压电材料层合板的自由振动分析[J].工程力学,2012,29(7):347-352.LIU Y H,WANG B H,QING G H.Free vibration analysis of piezoelectric laminated plates with delamination[J].Engineering Mechanics,2012,29(7):347-352(in Chinese).
[19]YANG T L,HUANG Q B,LI S D.Three-dimensional elasticity solutions for sound radiation of functionally graded materials plates considering state space method[J].Shock and Vibration,2016,DOI:10.1155/2016/1403856.
[20]BERT C W,BAKE J L,EGLE D M.Free vibrations of multilayer anisotropic cylindrical shells[J].Journal of Composite Materials,1969,3(3):480-499.
[21]FAHY F,GARDONIO P.Sound and structural vibration radiation,transmission and response[M].Oxford:Academic Press,2007.
[22]YANG C M,JIN G Y,LIU Z G,et al.Vibration and damping analysis of thick,cylindrical shells with a viscoelastic core under arbitrary boundary conditions[J].International Journal of Mechanical Sciences,2015,92:162-177.
[23]SUN Y,YANG T J,CHEN Y H.Sound radiation modes of cylindrical surfaces and their application to vibro-acoustics analysis of cylindrical shells[J].Journal of Sound and Vibration,2018,424:64-77.
[2]李永强,李峰,何永亮.四边固支铝基蜂窝夹层板弯曲自由振动分析[J].复合材料学报,2011,28(3):210-216.LI Y Q,LI F,HE Y L.Flexural vibration analysis of honeycomb sandwich plate with completely clamped support[J].Acta Materiae Compositae Sinica,2011,28(3):210-216(in Chinese).
[3]王目凯,陈照波,焦映厚,等.敷设约束阻尼薄壁圆柱壳的振动特性[J].哈尔滨工业大学学报,2017,49(1):72-79.WANG M K,CHEN Z B,JIAO Y H,et al.Vibration characteristics of thin cylindrical shell with constrained layer damping[J].Journal of Harbin Institute of Technology,2017,49(1):72-79(in Chinese).
[4]ZHAI Y C,CHAI M J,SU J M,et al.Dynamics properties of composite sandwich open circular cylindrical shells[J].Composite Structures,2018,189:148-159.
[5]DANESHJOU K,TALEBITOOTI R,KORNOKAR M.Vibroacoustic study on a multilayered functionally graded cylindrical shell with poroelastic core and bonded-unbonded configuration[J].Journal of Sound and Vibration,2017,393:157-175.
[6]CHANDRA N,GOPALET K V N,RAJA S.Vibro-acoustic response of sandwich plates with functionally graded core[J].Acta Mechanica,2017,228:2775-2789.
[7]RAKESH K,VIJAY R,AJAY K G,et al.Higher-order closed-form solutions for thick laminated sandwich shells[J].Journal of Sandwich Structures and Materials,2005,7(4):335-358.
[8]刘明.功能梯度材料软夹芯夹层板壳自由振动解析分析方法研究[D].武汉:华中科技大学,2015.LIU M.Analytical method of free vibration of sandwich plates and shells with functionally graded flexible core[D].Wuhan:Huazhong University of Science and Technology,2015(in Chinese).
[9]邸馗,茅献彪.简支边界条件下超椭圆蜂窝夹芯板的自由振动[J].复合材料学报,2017,34(8):1817-1824.DI K,MAO X B.Free vibration analysis of simply supported super elliptical honeycomb panels[J].Acta Materiae Compositae Sinica,2017,34(8):1817-1824(in Chinese).
[10]KHEZRI M,GHARIB M,BRADFORD M A,et al.A state space augmented generalised RKPM for three-dimensional analysis of thick and laminated composite plates[J].Computers and Structures,2015,158:225-239.
[11]KULKARNI S D,KAPURIA S.Free vibration analysis of composite and sandwich plates using an improved discrete Kirchhoff quadrilateral element based on third-order zigzag theory[J].Computational Mechanics,2008,42(6):803-82.
[12]任晓辉,陈万吉.复合材料夹层板振动分析的精化锯齿理论和三角形板单元[J].工程力学,2012,29(2):34-38.REN X H,CHEN W J.Triangular plate element based on refined zig-zag theory for free vibration analysis of sandwich plates[J].Engineering Mechanics,2012,29(2):34-38(in Chinese).
[13]LIU B,FERREIRA A J M,XING Y F,et al.Analysis of functionally graded sandwich and laminated shells using a layer wise theory and a differential quadrature finite element method[J].Composite Structures,2016,136:546-553.
[14]杨少红,王安稳.基于混合分层理论的粘弹层合圆柱壳的阻尼振动和层间应力研究[J].工程力学,2008,25(3):38-42.YANG S H,WANG A W.Damping vibration and inter laminar stresses study using mixed layerwise theories for viscoelastic laminated cylindrical shells[J].Engineering Mechanics,2008,25(3):38-42(in Chinese).
[15]ALIBEIGLOO A,ALIZADEH M.Static and free vibration analyses of functionally graded sandwich plates using state space differential quadrature method[J].European Journal of Mechanics A:Solids,2015,54:252-266.
[16]SHABAN M,ALIBEIGLOO A.Three-dimensional elasticity solution for sandwich panels with corrugated cores by using energy method[J].Thin-Walled Structures,2017,119:404-411.
[17]YE J Q.Laminated composite plates and shells[M].London:Springer,2003.
[18]刘艳红,王炳华,卿光辉.含分层的压电材料层合板的自由振动分析[J].工程力学,2012,29(7):347-352.LIU Y H,WANG B H,QING G H.Free vibration analysis of piezoelectric laminated plates with delamination[J].Engineering Mechanics,2012,29(7):347-352(in Chinese).
[19]YANG T L,HUANG Q B,LI S D.Three-dimensional elasticity solutions for sound radiation of functionally graded materials plates considering state space method[J].Shock and Vibration,2016,DOI:10.1155/2016/1403856.
[20]BERT C W,BAKE J L,EGLE D M.Free vibrations of multilayer anisotropic cylindrical shells[J].Journal of Composite Materials,1969,3(3):480-499.
[21]FAHY F,GARDONIO P.Sound and structural vibration radiation,transmission and response[M].Oxford:Academic Press,2007.
[22]YANG C M,JIN G Y,LIU Z G,et al.Vibration and damping analysis of thick,cylindrical shells with a viscoelastic core under arbitrary boundary conditions[J].International Journal of Mechanical Sciences,2015,92:162-177.
[23]SUN Y,YANG T J,CHEN Y H.Sound radiation modes of cylindrical surfaces and their application to vibro-acoustics analysis of cylindrical shells[J].Journal of Sound and Vibration,2018,424:64-77.