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.     

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.     

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.     

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.     

Dynamic stability of viscoelastic circular cylindrical shells taking into account shear deformation and rotatory inertia

The present work discusses the problem of dynamic stability of a viscoelas- tic circular cylindrical shell,according to revised Timoshenko theory,with an account of shear deformation and rotatory inertia in the geometrically nonlinear statement.Pro- ceeding by Bubnov-Galerkin method in combination with a numerical method based on the quadrature formula the problem is reduced to a solution of a system of nonlinear integro-differential equations with singular kernel of relaxation.For a wide range of vari- ation of physical mechanical and geometrical parameters,the dynamic behavior of the shell is studied.The influence of viscoelastic properties of the material on the dynamical stability of the circular cylindrical shell is shown.Results obtained using different theories are compared.     

Analytical model of sound transmission through laminated composite cylindrical shells considering transverse shear deformation

Composite structures are often used in the aerospace industry due to the advantages offered by a high strength to weight ratio. Sound transmission through an infinite laminated composite cylindrical shell is studied in the context of the transmission of airborne sound into the aircraft interior. The shell is immersed in an external fluid medium and contains internal fluid. Airflow in the external fluid medium moves with a constant velocity. An exact solution is obtained by simultaneously solving the first-order shear deformation theory （FSDT） of a laminated composite shell and the acoustic wave equations. Transmission losses （TL） obtained from numerical solutions are compared with those of other authors. The effects of structural properties and flight conditions on TL are studied for a range of values, especially, the Mach number, stack sequences, and the angle of warp. Additionally, comparisons of the transmission losses are made between the classical thin shell theory （CST） and FSDT for laminated composite and isotropic cylindrical shells.     

THE LARGE DEFLECTION ON PROBLEM OF CIRCULAR PLATE ON ELASTIC FOUNDATION AND IN CONJUNCTION WITH LINEAR ELASTIC STRUCTURE

This paper deals with the axisymmetrical deformation of the circular plate in largedeflection,which is on elastic foundation and in conjunction with a certain linear elasticstructure.The governing integral equations are established by the method of mixedboundary condition I and the simplified form is given.The pertrubation method is used toobtain the solutions and an example of the composite structure made up of a circular plateand a cylindrical shell is presented.     

New matrix method for analyzing vibration and damping effect of sandwich circular cylindrical shell with viscoelastic core

Based on the linear theories of thin cylindrical shells and viscoelastic materials, a governing equation describing vibration of a sandwich circular cylindrical shell with a viscoelastic core under harmonic excitation is derived. The equation can be written as a matrix differential equation of the first order, and is obtained by considering the energy dissipation due to the shear deformation of the viscoelastic core layer and the interaction between all layers. A new matrix method for solving the governing equation is then presented With an extended homogeneous capacity precision integration approach. Having obtained these, vibration characteristics and damping effect of the sandwich cylindrical shell can be studied. The method differs from a recently published work as the state vector in the governing equation is composed of displacements and internal forces of the sandwich shell rather than displacements and their derivatives. So the present method can be applied to solve dynamic problems of the kind of sandwich shells with various boundary conditions and partially constrained layer damping. Numerical examples show that the proposed approach is effective and reliable compared with the existing methods.     

THE EXACT SOLUTION FOR THE GENERAL BENDING PROBLEMS OF CONICAL SHELLS ON THE ELASTIC FOUNDATION

The general bending problem of conical shells on the elastic foundation (Winkler Medium) is not solved. In this paper, the displacement solution method for this problem is presented. From the governing differential equations in displacement form of conical shell and by introducing a displacement function U(s,θ), the differential equations are changed into an eight-order soluble partial differential equation about the displacement function U(s,θ) in which the coefficients are variable. At the same time, the expressions of the displacement and internal force components of the shell are also given by the displacement function U(s θ). As special cases of this paper, the displacement function introduced by V.S. Vlasov in circular cylindrical shell, the basic equation of the cylindrical shell on the elastic foundation and that of the circular plates on the elastic foundation are directly derived. Under the arbitrary load, and boundary conditions, the general bending problem of the conical shell on the elas     

TRANSFER MATRIX METHOD FOR ANALYZING VIBRATION AND DAMPING CHARACTERISTICS OF ROTATIONAL SHELL WITH PASSIVE CONSTRAINED LAYER DAMPING TREATMENT

The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.     

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．     

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...     

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.