求解水下纵向加肋无限长非圆柱壳声辐射问题的一种新的半解析方法

基于齐次扩容精细积分法和复数矢径虚拟边界谱方法，利用Fourier积分变换和稳相法，提出了一种具有较高效率和精度的新的求解水下纵向加肋无限长非圆柱壳声辐射问题的半解析方法．考虑了非圆柱壳和肋骨之间同时存在多种相互作用力和力偶矩，较已往很多学者仅计及法向相互作用力更加符合实际．不仅比较了该文方法和精确解计算纵向加肋圆柱壳在集中点力激励下的声辐射计算结果，同时还研究了肋骨数量、大小以及椭圆柱壳横截面椭圆度对声辐射特性的影响．数值计算结果表明该文方法较已有的混合FE-BE法更为有效．     

刚性角隅内圆柱壳结构声辐射特性研究

本文对流场中处于刚性角隅内圆柱壳结构振动-声辐射问题进行研究．基于双反射方法，推导了位于两个垂直刚性壁面角隅区内圆柱壳结构的振动-声辐射方程．以此为基础，开展受线环向激励力作用的圆柱壳结构的振动-声辐射特性的数值计算．研究了刚性角隅内圆柱壳结构布置位置及计算频率对声辐射功率、声指向性的影响．计算结果可为分析含复杂声学边界的结构声振问题提供技术支持．     

New matrix method for response analysis of circumferentially stiffened non-circular cylindrical shells under harmonic pressure

Based on the governing equation of vibration of a kind of cylindrical shells written in a matrix differential equation of the first order,a new matrix method is pre- sented for steady-state vibration analysis of a noncircular cylindrical shell simply sup- ported at two ends and circumferentially stiffened by rings under harmonic pressure.Its difference from the existing works by Yamada and Irie is that the matrix differential equation is solved by using the extended homogeneous capacity precision integration ap- proach other than the Runge-Kutta-Gill integration method.The transfer matrix can easily be determined by a high precision integration scheme.In addition,besides the normal interacting forces,which were commonly adopted by researchers earlier,the tan- gential interacting forces between the cylindrical shell and the rings are considered at the same time by means of the Dirac-δfunction.The effects of the exciting frequencies on displacements and stresses responses have been investigated.Numerical results show that the proposed method is more efficient than the aforementioned method.     

变厚度圆柱壳的强度优化设计

对在任意轴对称分布荷载作用下体积保持常数的变厚度圆柱壳的强度优化设计问题进行了研究。当中面形状固定时 ,采用阶梯折算法 ,用传递矩阵导出了变厚度圆柱壳的初参数解的显式表达式。根据Huber-Mises-Hencky强度准则 ,将变厚度圆柱壳的强度优化转化为极小化当量应力的非线性规划问题 ,并采用投影梯度法建立了问题的优化方法。文中对几个典型问题进行了计算。与等厚度圆柱壳相比较 ,优化圆柱壳的最大当量应力得到了显著降低。本文的研究方法和结果可以用于指导大型圆柱壳体的加肋设计     

STRESS CONCENTRATIONS IN CYLINDRICAL SHELLS WITH LARGE OPENINGS

Based on Donnell's shallow shell equation, a new method is given in this paper to ana-lyze theoretical solutions of stress concentrations about cylindrical shells with large openings. With themethod of complex variable function, a series of conformal mapping functions are obtained from dif-ferent cutouts' boundary curves in the developed plane of a cylindrical shell to the unit circle. And,the general expressions for the equations of a cylindrical shell, including the solutions of stress concen-trations meeting the boundary conditions of the large openings' edges, are given in the mapping plane.Furthermore, by applying the orthogonal function expansion technique, the problem can be summa-rized into the solution of infinite algebraic equation series. Finally, numerical results are obtained forstress concentration factors at the cutout's edge with various opening's ratios and different loadingconditions. This new method, at the same time, gives a possibility to the research of cylindrical shellswith large non-circular openings or with nozzles.     

Propagation of harmonic waves along open circular cylindrical shells reinforced with a quasiregular set of discrete longitudinal ribs

We obtain the exact solution describing the propagation of harmonic waves along an open cylindrical shell reinforced with a quasiregular set of discrete longitudinal ribs. Numerical examples are used to examine the effect of discrete ribs on the number and shape of dispersion curves and the effect of the stiffness and inertial characteristics of the ribs on the excitation frequency for given wave parameters     

Effect of the Number of Ribs on a Transient in a Cylindrical Shell under a Disturbing Load*

International Applied Mechanics - A technique to study the transient process of the forced vibrations of a cylindrical shell stiffened with longitudinal ribs is developed. The shell is under an...     

VIBRATION AND ACOUSTIC RADIATION FROM SUBMERGED STIFFENED SPHERICAL SHELL WITH DECK-TYPE INTERNAL PLATE

Based on the motion differential equations of vibration and acoustic coupling system for thin elastic spherical shell with an elastic plate attached to its internal surface, in which Dirac-δ functions are employed to introduce the moments and forces applied by the attachment on the surface of shell, by means of expanding field quantities as Legendre series, a semi-analytic solution is derived for the vibration and acoustic radiation from a submerged stiffened spherical shell with a deck-type internal plate, which has a satisfactory computational effectiveness and precision for an arbitrary frequency range. It is easy to analyze the effect of the internal plate on the acoustic radiation field by using the formulas obtained by the method proposed. It is concluded that the internal plate can significantly change the mechanical and acoustic characteristics of shell, and give the coupling system a very rich resonance frequency spectrum. Moreover, the method can be used to study the acoustic radiation mechanism in similar structures as the one studied here.     

Natural Vibrations of a Cylindrical Shell with Circular Ribs Attached by Means of Discrete Elastic Elements

The vibrations of a cylindrical shell reinforced with circular ribs attached to it by means of discrete elastic elements are studied. The problem is solved by the finite-element method. The shell and ribs are modeled by a plane four-node finite element, which is a combination of a four-node plane stress element and a four-node flexural element. The effect of the stiffness of the elastic elements on the natural frequencies and modes is examined __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 108–113, October 2005.     

Vibroacoustic comparisons of composite laminated cylindrical shells according to three shear deformation shell theories

Whether the first-order and Reddy third-order shear deformation shell theories are able to evaluate the vibroacoustic responses of laminated cylindrical shells with normal deformation in the high frequency range or not is examined by comparison with a 3D higher-order shear deformation shell theory. The implicit governing equations of arbitrary angle-ply laminated cylindrical shells are derived from the 3D higher-order and Reddy third-order shell theories, and solved on the basis of the Fourier transform. The Reddy third-order shell theory can be obtained as a special case from the 3D higher-order shell theory. The first-order and Reddy third-order shell theories almost give rise to the same vibrational and acoustic results. These two simple shear deformation shell theories can be used to study far-field acoustic radiation from laminated cylindrical shells from the low to high frequency range, but they show some differences from the 3D higher-order shell theory in high frequency vibration of shells. Nevertheless, the differences of vibrational responses seem not to be distinct. The helical wave spectra of the higher-order radial displacements are nearly separate from those of the low-order radial displacement and play a minor role in far-field acoustic radiation, which makes the two simple shell theories applicable in prediction of acoustic power of the cylindrical shells in the much higher frequency range. Moreover, it also results in the fact that far-field sound is least sensitive in comparison with near-field sound and vibration of shells.     

Propagation of harmonic waves in longitudinally reinforced cylindrical shells with low shear stiffness

The exact solutions of the equations of motion derived under refined theories of shells and ribs based on the Timoshenko model are used to plot dispersion curves for harmonic waves propagating along a cylindrical shell reinforced with discrete longitudinal ribs __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 37–41, May 2006.     

Natural Vibrations of a Cylindrical Shell Reinforced with Two-Layer Rings

The vibrations of a cylindrical shell reinforced with ring ribs attached to the shell by means of elastic elements are studied. The problem is solved by the finite-element method. The shell and ribs are modelled by a plane four-node finite element, which is a combination of a four-node plane stress element and a four-node flexural element. The effect of the stiffness of the elastic elements on the natural frequencies and modes is examined __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 105–110, August 2005.     

Sound radiation of a functionally graded material cylindrical shell in water by mobility method

Based on the fundamental dynamic equations of functionally graded material (FGM) cylindrical shell, this paper investigates the sound radiation of vibrational FGM shell in water by mobility method. This model takes into account the exterior fluid loading due to the sound press radiated by the FGM shell. The FGM cylindrical shell was excited by a harmonic line radial force uniformly distributing along the generator. The FGM shell equations of motion, the Helmholtz equation in the exterior fluid medium and the continuity equation at fluid-shell interface are used in this vibroacoustic problem. The expressions of sound radiation efficiency and sound field of the FGM shell have been derived by mobility method. Radiation efficiency, modal mobility and the directivity pattern of the sound field are solved numerically. In particular, radiation efficiency and directivity pattern with various power law index are analyzed.     

Nonlinear Deformation and Stability of a Noncircular Cylindrical Shell Under Combined Loading with Bending and Twisting Moments

A previously developed technique is used to solve problems of strength and stability of discretely reinforced noncircular cylindrical shells made of a composite material with allowance for the moments and nonlinearity of their subcritical stress–strain state. Stability of a reinforced bay of the aircraft fuselage made of a composite material under combined loading with bending and twisting moments is studied. The effects of straining nonlinearity, stiffness of longitudinal ribs, and shell thickness on the critical loads that induce shell buckling are analyzed.     

On the deformation of a ribbed cylindrical shell with initial deflection under dynamic loading

The finite-difference method with explicit time coordinate is used to study the dynamic stress-strain state of a cylindrical shell with ribs and initial deflections. A specific numerical example is considered to trace the time evolution of longitudinal and transverse displacements for different parameters of the initial deflection __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 61–66, December 2005.     

离散元与壳体有限元结合的多尺度方法及其应用

在深入研究复杂结构和非均质材料冲击响应和破坏机理的过程中,往往遇到多尺度计算问题。本文尝试建立三维离散元与壳体有限元结合的多尺度方法用于处理圆柱壳问题,该方法采用三维离散元对感兴趣的局域进行局部模拟,利用平板壳体有限元进行整体模拟,采用一种特殊的过渡层使离散元区和有限元区能很好的衔接。我们将这一方法应用于激光辐照下充压柱壳的热/力耦合冲击破坏响应,得到的模拟结果与文献报道有较好的吻合。     

MECHANICAL AND ACOUSTIC RESPONSE OF AN UNDERWATER STRUCTURE SUBJECTED TO MECHANICAL EXCITATION

In this paper, an underwater structure is modeled as a cylindrical shell with internal bulkheads, and closed by a truncated conical shell, and it consists of metal substrate and sound absorbing coating, whose FGM core is considered. Suppose the inner cavity and outer space of the structure are filled with air and fluid mediums, the mechanical response of the underwater structure is calculated with Galerkin method while the acoustic response is investigated by means of the Helmholtz integral. Some numerical examples are given and the effect of geometrical size and material parameters on mechanical and acoustic response is discussed.     

纵横加肋圆柱壳的应力分析

建立了一种纵横加肋圆柱壳有限元分析的正确的力学模型,通过大量数值计算,论证了纵骨尺寸,纵骨间距对壳体应力状态的影响,提出了一种等效各向同性壳的近似解析公式,为开展纵横加肋圆柱壳的结构设计打下了良好的基础。     

ANALYSIS OF SOUND RADIATION FROM THE RING－STIFFENED CYLINDRICAL SHELL COATED WITH VISCOELASTIC LAYER IN FLUID MEDIUM

The Donnell theory of shell is applied to describe shell motion and layer motion is described by means of three-dimensional Navier equations. Using deformation harmonious conditions of the interface, the effects of stiffeners and layer are treated as reverse forces and moments acting on the cylindrical shell. In studying the acoustic field produced by vibration of the submerged ring-stiffened cylindrical coated shell, the structure dynamic equation, Helmholtz equation in the fluid field and the continuous conditions of the fluid-structure interface compose the cou-pling vibration equation of the sound-fluid-structure. The extract of sound pressure comes down to the extract of coupling vibration equation. By use of the solution of the equation, the influences of hydrostatic pressure, physical characters and geometric parameters of the layer on sound radiation are discussed.     

Stress–Strain Analysis of Thin-Walled Shells with Massive Ribs

A multifrontal method is proposed for solving large-scale finite-element problems with a symmetric stiffness matrix. This approach is based on node ordering rather than element ordering as in the traditional frontal or multifrontal methods. This allows us to employ the efficient well-known ordering techniques such as the minimum-degree algorithm or the nested dissection method. A thin-walled cylindrical shell with massive ribs is considered as an example. The efficiency of the method proposed is illustrated against the classical skyline and aggregation multilevel conjugate-gradient iterative solvers