Free vibration of non-circular cylindrical shells with variable circumferential profile

An analysis is presented of the free vibration of non-circular cylindrical shells with a variable circumferential profile expressed as an arbitrary function. The applicability of thin-shell theory is assumed and the governing equations of vibration of a non-circular cylindrical shell are written in a matrix differential equation by using the transfer matrix of the shell. Once the transfer matrix has been determined by numerical integration of the matrix equation, the natural frequencies and mode shapes of vibration are calculated numerically in terms of the matrix elements. The method is applied to cylindrical shells of three or four-lobed cross-section, and the effects of the length of the shell and the radius at the lobed corners on the vibration are studied.     

Free vibration of joined conical-cylindrical shells

An analysis is presented for the free vibration of joined conical-cylindrical shells. The governing equations of vibration of a conical shell, including a cylindrical shell as a special case, are written as a coupled set of first order differential equations by using the transfer matrix of the shell. Once the matrix has been determined, the entire structure matrix is obtained by the product of the transfer matrices of the shells and the point matrix at the joint, and the frequency equation is derived with terms of the elements of the structure matrix under the boundary conditions. The method has been applied to a joined truncated conical-cylindrical shell and an annular plate-cylindrical shell system, and the natural frequencies and the mode shapes of vibration calculated numerically. The results are presented.     

Free vibration of non-circular cylindrical shell panels

In the free vibration analysis of clamped non-circular cylindrical shell panels, a matrix method has been used to solve the governing differential equations, which have variable coefficients. The effect of the curvature, thickness ratio and aspect ratio on the natural frequencies has been studied. The results obtained for circular cylindrical panels are compared with other available results. The convergence of the solution is found to be good.     

Free vibrations of laminated composite cylindrical shells with an interior rectangular plate

The free vibration analysis of a laminated composite cylindrical shell with an interior rectangular plate is performed by the analytical and experimental methods. The frequency equations of vibration of the shell including the plate are formulated by using the receptance method. To obtain the free vibration characteristics before the combination of two structures, the energy principle based on the classical plate theory and Love's thin shell theory is adopted. The numerical results are compared with the results from an experiment, as well as a finite element analysis, to validate the current formulation. The influences of the length-to-radius ratio (L_S/a) and radius-to-thickness ratio (a/h_S) of the shell and fiber orientation angles (Θ) of symmetric cross- and angle-ply composite materials on the natural frequencies of a cylindrical laminated combined shell are also discussed in details.     

Transfer matrix method for internal noise prediction of an arbitrary shell-cavity structure induced by temporal-spatial random surface excitation

Combining structural finite element method(FEM),acoustic finite element and boundary element methods,a model of elastic shell vibration of an arbitrary shell-cavity structure coupled with internal and external sound fields is built.In addition,the transfer matrices from the excitation force to vibration of the shell and internal sound field are calculated.As the fluctuating pressure of turbulent boundary layer(TBL) is a temporal-spatial random surface excitation,the overall shape function matrix is introduced,and then the relationship between power spectral density matrix of the generalized nodal force of the elastic shell and power spectral density of the temporal-spatial random surface excitation is derived.Utilizing the vibro-acoustic coupled transfer matrix,relationships between the power spectral densities of vibration of the elastic shell/internal sound field and the power spectral density matrix of the generalized nodal force are obtained.Thus,the calculation method of vibration and internal sound field of an arbitrary shell-cavity structure induced by temporal-spatial random surface excitation is established.A typical vibro-acoustic coupled model of a rectangular cavity with acoustic media internally and externally,and with elastic rectangular plate on one side,is taken as example.The vibration of the elastic shell and power spectral density of the internal sound field are calculated and compared with the analytical method.The two results generally agree with the analytical one,with deviations of about 1 dB and 2 dB,respectively.The transfer matrix method has good adaptability which is not restricted by the shell-cavity structure and the shape of the inner region.     

传递矩阵法预报时空随机激励下任意薄壳腔体内部噪声

利用结构有限元结合声有限元及边界元方法,建立了任意薄壳腔体弹性壳板振动与内外声场的耦合模型,并计算了激励力与壳板振动和内部声场之间的传递矩阵;湍流边界层脉动压力具有时空随机面激励特性,引入整体形状函数矩阵,进一步推导弹性壳板广义节点力功率谱密度函数矩阵与随机面分布激励力功率谱密度函数的关系,再利用声振耦合传递矩阵,得到弹性壳板振动和内部声场功率谱密度函数与广义节点力功率谱密度函数矩阵的关系,形成随机分布激励下任意薄壳腔体结构振动及内部声场的计算方法。以典型的内外均有声介质且一面为弹性矩形板的矩形腔声振耦合模型为例,计算了弹性壳板振动和内部声场功率谱密度函数,并与解析方法进行了比较,两者基本吻合,偏差分别为1 dB和2 dB左右。传递矩阵法不受腔体结构及其内部区域形状的制约,具有良好的适用性。      

Free vibration of a conical shell with variable thickness

An analysis is presented for the free vibration of a truncated conical shell with variable thickness by use of the transfer matrix approach. The applicability of the classical thin shell theory is assumed and the governing equations of vibration of a conical shell are written as a coupled set of first order differential equations by using the transfer matrix of the shell. Once the matrix has been determined by quadrature of the equations, the natural frequencies and the mode shapes of vibration are calculated numerically in terms of the elements of the matrix under any combination of boundary conditions at the edges. The method is applied to truncated conical shells with linearly, parabolically or exponentially varying thickness, and the effects of the semi-vertex angle, truncated length and varying thickness on the vibration are studied.     

Free vibration analysis of a hanged clamped-free cylindrical shell partially submerged in fluid: The effect of external wall,internal shaft,and flat bottom

The free flexural vibration of a hanged clamped-free cylindrical shell with various boundary conditions partially submerged in a fluid is investigated. Specifically, the effects of the boundary conditions such as the existence of the external wall, internal shaft, and bottom on the natural vibration characteristics of the partially submerged cylindrical shell are investigated both theoretically and experimentally. The fluid is assumed to be inviscid and irrotational. The cylindrical shell is modeled by using the Rayleigh–Ritz method based on the Sanders shell theory. The kinetic energy of the fluid is derived by solving a boundary-value problem related to the fluid motion. The theoretical predictions were in good agreement with the experimental results validating the theoretical approach developed in this study. The effects of the external wall, internal shaft, and bottom on the natural vibration characteristics can be neglected when its boundaries are not very close to the shell structure.     

Structure-borne noise reduction for an infinite, elastic cylindrical shell

A theoretical model was developed to evaluate the reduction of structure-borne noise generated by an axially symmetric ring force which is applied on the interior of the cylindrical shell. The vibrating cylindrical shell is coated with a microvoided elastomer that is acoustically soft material designed for the reduction of the generated noise. The analytical model is a two-layer shell structure comprised of a cylindrical shell and an outer layer (coating) that is perfectly bonded to the cylindrical shell. The outer and inner surfaces of the coated shell are in contact with water and air, respectively. The analysis for this problem is based on the theory of elasticity, acoustic wave equations, and pertinent boundary conditions. Effects of various parameters such as coating thickness and material properties on the noise reductions are presented.     

Mathematical model for characterizing noise transmission into finite cylindrical structures

This work presents a theoretical study of the sound transmission into a finite cylinder under coupled structural and acoustic vibration. Particular attention of this study is focused on evaluating a dimensionless quantity, "noise reduction," for characterizing noise transmission into a small cylindrical enclosure. An analytical expression of the exterior sound pressure resulting from an oblique plane wave impinging upon the cylindrical shell is first presented, which is approximated from the exterior sound pressure for an infinite cylindrical structure. Next, the analytical solution of the interior sound pressure is computed using modal-interaction theory for the coupled structural acoustic system. These results are then used to derive the analytical formula for the noise reduction. Finally, the model is used to predict and characterize the sound transmission into a ChamberCore cylindrical structure, and the results are compared with experimental data. The effects of incidence angle and internal acoustic damping on the sound transmission into the cylinder are also parametrically studied.     

考虑铺层角的复合材料圆柱壳自由振动三维弹性准确解

为了获得任意角度铺层的多层复合材料圆柱壳的自由振动准确解,在三维弹性理论的基础上,结合分层理论和状态空间法,建立横向位移和应力的传递矩阵,轴向和环向位移采用双螺旋模式的位移函数,对任意角度铺层复合材料圆柱壳简支边界条件下的自由振动进行了理论推导,得到了自由振动方程的精确形式。与文献理论解和有限元计算结果对比,结果表明,关注频率在2倍的环频率以下时,薄壳的固有频率计算精度能控制在1%以内,厚壳的固有频率计算精度能控制在2%以内。对于厚壳的计算可将壳体沿厚度方向划分为多层来处理,这样能有效提高计算精度。计算分析了铺层角对壳体固有频率的影响,环向模态数较低时,固有频率随着铺层角的增加呈抛物线变化趋势;环向模态数较高时,固有频率随着铺层角的增大单调递增。该理论方法同样适用于均质各向同性壳和正交各向异性圆柱壳。      

Maxi-element analysis for free vibrations of orthotropic shells of revolution

The theory of free vibration for orthotropic shells of revolution with arbitrary homogeneous boundary conditions is developed. The essence of the method is to decompose the overall shell into a number of so-called cylindrical, conical, and plate “maxi-elements”. Since the eigenfunctions of each of the individual maxi-elements are analytically determined directly from the solution of the governing differential equations, the procedure has the advantage of requiring significantly fewer elements compared with the usual finite element or finite difference procedures. For the conical shell and the plate, the method of solution is novel, while the solution for the cylindrical shell has been published by the first author. The versatility and accuracy of the method is shown through the inclusion of a number of examples which present the excellent correlation with test results and other numerical schemes.     

降低加肋双层圆柱壳辐射噪声线谱的结构声学设计

为降低双层圆柱壳辐射噪声线谱,从控制内壳振动响应和衰减壳间振动传递率进行结构声学设计。采用机械阻抗理论分析了环肋圆柱壳模态响应控制机理;由环肋振动方程推导分析了环肋径向机械阻抗特性;基于阻抗失配、波形转换原理提出一种阻抗加强环肋,分析了振动波阻抑特性;利用阻尼减振技术,综合考虑肋板的刚度、阻尼特性,设计了金属橡胶层叠肋板;结合数值计算实例,分析了设计双层壳模型的声辐射性能。结果表明:设计的双层加肋圆柱壳结构能有效降低辐射噪声线谱,在分析频段内辐射声压线谱平均降低约6.6 dB。研究结果对研制低噪声水下航行器具有良好的工程价值和应用前景。      

径向声子晶体隔声特性*

该文构造了由两种匀质材料交替分布的径向声子晶体柱壳模型。首先,针对声波在其中的轴对称传播情况进行了理论分析,建立了声波由内向外传播的传递矩阵,进而导出了声压透射系数和隔声量表达式。采用数值分析的方法系统地讨论了径向声子晶体柱壳的隔声特性,并与单一材质柱壳的传播规律进行对比分析,其次,借助有限元仿真分析的手段对数值结果进行了验证。最后,详细分析了内外流体的特性阻抗对径向声子晶体柱壳隔声特性的影响,得到了相应的参数影响规律。研究表明,径向声子晶体柱壳存在声波带隙,导致其在带隙范围内的隔声效果远远优于单材质柱壳,并且该结构的固有特性突破了质量定律的限制;声波带隙内表面局域态现象出现与否由内外声场和结构场共同决定。     

柱壳和锥壳结构自由振动特征的数值计算与校验

为了评估柱壳和锥壳结构自由振动特征数值计算的精度,分析不同边界条件、环肋、纵肋以及流体载荷对自由振动特征的影响,计算并校验了典型壳体结构在空气中、浸没以及浸没并充满水情况下的自由振动特征。结果表明,空气中干模态分析在2 kHz内、单面及双面接触水情况下的流固耦合湿模态分析在500 Hz内的计算精度能够控制在10%以内。壳体流固耦合自由振动分析时可以采用实体单元离散也可以采用壳单元离散的方法,前者精度略高,能够有效保证求解收敛的频带范围更宽,但工作量更大。径长比大于0.2时,浸没于水中的自由振动分析可以转换为内部填充水时的自由振动分析,转换时应保证两者流固耦合湿表面积相等,如半浸水和半充满水,能够有效减小计算量;环肋和流体载荷对壳体自由振动特征的影响明显,环肋使柱壳同阶自振频率增加,流体载荷使柱壳同阶自振频率减小且影响幅度更大,两者均会使得柱壳模态振型呈现错序排列;流固耦合效应对无肋柱壳和环肋柱壳自振频率的影响效果相当;柱壳内外有水相对于单面接触水而言,同阶自振频率进一步减小,模态振型基本不变;流体载荷对环肋锥壳的自振频率和模态振型的影响幅度较对环肋柱壳小。      

The receptance method applied to ring-stiffened cylindrical shells: Analysis of modal characteristics

The receptance method is applied to determine the natural frequencies and mode shapes of circular cylindrical shells stiffened by rings. The receptances of cylindrical shell and of a ring to forces in the radial and circumferential directions are derived in terms of the modal characteristics of each. A matrix equation of free vibration, which must be solved by an iterative technique, results by eliminating the angular variable. An iterative solution is practical, since the size of the matrices remains at two times the number of stiffening rings, regardless of the number of modes of the unstiffened cylinder and rings included in the solution. The validity of the method is demonstrated by comparing results for specific cases with the results obtained theoretically and experimentally by others. When various stiffener configurations are being considered for a given cylindrical shell, the modal characteristics of the shell without stiffeners may be calculated once and used repeatedly to calculate the frequencies of the stiffened shell configurations. The form of the results offers potential for simplifications which are presented in a companion paper.     

部分浸没圆柱壳声固耦合计算的半解析法研究

部分浸没圆柱壳-流场耦合系统的声振分析是一种典型的半空间域内声固耦合问题,其振动及声学计算目前主要依赖于数值方法求解,但无论从检验数值法还是从机理上揭示其声固耦合特性,解析或半解析方法的发展都是不可或缺的.本文提出了一种半解析方法,先将声场坐标系建立在自由液面上,采用正弦三角级数来满足自由液面上的声压释放边界条件;接着基于二维Flügge薄壳理论建立了以圆柱圆心为坐标原点的壳-液耦合系统的控制方程;然后再利用Galerkin法处理声固耦合界面的速度连续条件,推导得到声压幅值与壳体位移幅值之间的关系矩阵并求解该耦合系统的振动和水下声辐射.与有限元软件Comsol进行了耦合系统自由、受迫振动和水下辐射噪声计算结的对比分析,表明本文方法准确可靠.本文的研究为解析求解弹性结构与声场部分耦合的声振问题提供了新的思路.     

Sound transmission through layered cylindrical shells with applied damping treatment

Sound transmission through closed circular cylindrical shells with unconstrained damping treatment and sandwich shells with constrained damping treatment is considered in an acoustoelastic formulation in which the full interaction between the structural vibration and the internal cavity pressure field are taken into account. Only the axisymmetric modes of vibration of the shell are considered in an initial formulation. The structural response and the sound transmission characteristics for an external random pressure field are computed through an efficient matrix inversion procedure. Results indicate insensitivity of noise reduction and structural response to variations in core parameters of the sandwich shell. The sandwich shell has better noise transmission characteristics in the higher frequency ranges as compared to an equivalent layered shell with unconstrained damping treatment.     

Acoustic scattering from fluid-loaded stiffened cylindrical shell: analysis using elasticity theory

The acoustic scattering from a fluid-loaded stiffened cylindrical shell is described by using elasticity theory. The cylindrical shell is reinforced by a thin internal plate which is diametrically attached along the tube. In this model, cylindrical shell displacements and constraints expressed from elasticity theory are coupled to those of the plate at the junctions, where plate vibrations are described by using plate theory. The present model is first validated at low frequency range (k1a approximately 5-40) by comparison with a previous model based on the Timoshenko-Mindlin thin shell theory and by experimental results. Theoretical and experimental resonance spectra are then analyzed in a high frequency range (k1a approximately 120-200). Only resonances due to the S0 wave are clearly observed in this frequency range, and their modes of propagation are identified. Furthermore, A0 wave propagation is detected, because of the presence of the reflection of this wave at the shell-plate junctions.     

变厚度圆板、环板振动分析的传递矩阵法*

变厚度圆板和环板是在工程设计中经常遇到的一类构件,与等厚度板相比,通过适当的沿径向厚度的变化,这种变厚度板在振动、失稳、弯曲等方面能起到更好的效果。将沿径向任意变厚度圆板、环板划分为一系列等厚度环板单元,基于Mindlin中厚板理论采用逆向推导的方式推导了其传递矩阵,建立起变厚度圆板、环板的频率方程。通过计算线性变厚度环板自由振动时的频率,并与ANSYS模态分析结果相比较,验证了计算模型的精确性。逆向推导法避免了高阶数传递矩阵推导复杂的问题,是对传递矩阵法的很好推广。