Compound strip analysis of ring-stiffened cylindrical shells under hydrostatic pressure

The efficient compound strip method is used to analyse the buckling of ring-stiffened cylindrical shells under hydrostatic pressure. The eccentricity of stiffeners is taken into account. Numerical examples are given to illustrate the efficiency and accuracy of this method.     

ANALYTICAL SOLUTION OF RADIATED SOUND PRESSURE OF RING－STIFFENED CYLINDRICAL SHELLS IN FLUID MEDIUM

ＡＮＡＬＹＴＩＣＡＬＳＯＬＵＴＩＯＮＯＦＲＡＤＩＡＴＥＤＳＯＵＮＤＰＲＥＳＳＵＲＥＯＦＲＩＮＧ－ＳＴＩＦＦＥＮＥＤＣＹＬＩＮＤＲＩＣＡＬＳＨＥＬＬＳＩＮＦＬＵＩＤＭＥＤＩＵＭＸｉｅＧｕａｎｍｏ（谢官员模）ＬｕｏＤｏｎｇｐｉｎｇ（骆东平）（Ｒｅｃｅｉｖ...     

静水压力下环加肋圆柱壳总体与局部失稳分析的复合有限条法

本文提出了一种计算环加肋圆柱壳稳定性的新方法─—复合有限条法。该方法能够在一个复合有限条元中计入若干个横向加肋的影响，井能考虑肋骨的偏心，是一种子结构方法。算例表明，复合有限条法具有很高的求解精度和效率，是一种分析加肋柱壳结构的较理想方法。该方法不仅能够计算环加肋圆柱壳的总体失稳临界载荷，而且可计算其局部失稳临界载荷。     

单层偏心圆柱薄壳的自由振动特性分析研究

论文从偏心圆柱壳截面的几何特性出发,将偏心圆柱壳问题转化为一个周向变厚度圆柱壳问题,随后利用其状态向量之间的传递矩阵将壳体的振动控制方程转化为矩阵微分方程形式,通过Magnus级数法求解传递矩阵得到频率方程.采用Lagrange插值法得到偏心圆柱壳体自由振动状态下的固有频率,并且与圆柱壳的固有频率进行了比较.对影响结构固有频率的主要参数进行了分析,得到了这些参数和固有频率之间的关系.论文不仅提出了一种有效求解偏心圆柱壳固有频率的新方法,同时亦可为检测偏心圆柱壳的偏心距提供一种新的思路和方法.     

The effect of material and geometry on the non-linear vibrations of orthotropic circular cylindrical shells

The extensive use of circular cylindrical shells in modern industrial applications has made their analysis an important research area in applied mechanics. In spite of a large number of papers on cylindrical shells, just a small number of these works is related to the analysis of orthotropic shells. However several modern and natural materials display orthotropic properties and also densely stiffened cylindrical shells can be treated as equivalent uniform orthotropic shells. In this work, the influence of both material properties and geometry on the non-linear vibrations and dynamic instability of an empty simply supported orthotropic circular cylindrical shell subjected to lateral time-dependent load is studied. Donnell׳s non-linear shallow shell theory is used to model the shell and a modal solution with six degrees of freedom is used to describe the lateral displacements of the shell. The Galerkin method is applied to derive the set of coupled non-linear ordinary differential equations of motion which are, in turn, solved by the Runge–Kutta method. The obtained results show that the material properties and geometric relations have a significant influence on the instability loads and resonance curves of the orthotropic shell.     

Analytical solution of radiation sound pressure of double cylindrical shells in fluid medium

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Coupled thermoelasticity of functionally graded cylindrical shells

The coupled thermoelastic response of a functionally graded circular cylindrical shell is studied. The coupled thermoelastic and the energy equations are simultaneously solved for a functionally graded axisymmetric cylindrical shell subjected to thermal shock load. A second-order shear deformation shell theory that accounts for the transverse shear strains and rotations is considered. Including the thermo-mechanical coupling and rotary inertia, a Galerkin finite element formulation in space domain and the Laplace transform in time domain are used to formulate the problem. The inverse Laplace transform is obtained using a numerical algorithm. The shell is graded through the thickness assuming a volume fraction of metal and ceramic, using a power law distribution. The results are validated with the known data in the literature.     

Nonlinear bending analysis of ring-stiffened circular and annular general angle-ply laminated plates with various boundary conditions

In this study, elastic large deflection analysis of axisymmetric ring-stiffened circular and annular general angle-ply laminated plates subjected to transverse uniform load is studied. Based on first order shear deformation theory (FSDT) and large deflection von-Karman relations, the governing equations are derived. The dynamic relaxation (DR) method in conjunction with the central finite difference discretization technique is used to solve the nonlinear equilibrium equations. A detailed parametric study is carried out to investigate the influences of plate thicknesses, stiffener width, stiffener depth, fiber orientation, stacking sequence and different types of boundary conditions. Also, some linear and nonlinear analysis is provided to consider the effect of nonlinearity on the results.     

Solutions to equations of vibrations of spherical and cylindrical shells

ＳＯＬＵＴＩＯＮＳＴＯＥＱＵＡＴＩＯＮＳＯＦＶＩＢＲＡＴＩＯＮＳＯＦＳＰＨＥＲＩＣＡＬＡＮＤＣＹＬＩＮＤＲＩＣＡＬＳＨＥＬＬＳＤｉｎｇＨａｏｄｉａｎｇ（丁浩江）Ｃｈｅｎｗｅｉ－ｑｉｕ（陈伟球）（ＺｈｅｊｉａｎｎＵｎｉｖｅｒｓｉｔｙ．Ｈａｎｇｚｈｏｕ）...     

Free vibration analysis of a hung clamped-free cylindrical shell partially submerged in fluid

The free flexural vibration of a hung clamped-free cylindrical shell partially submerged in a fluid is investigated. The fluid is assumed to be inviscid and irrotational. The cylindrical shell is modelled by using the Rayleigh-Ritz method based on Sanders’ shell theory. The kinetic energy of the fluid is derived by solving the boundary-value problem related to the fluid motion. The natural vibration characteristics of the partially submerged cylindrical shell are discussed with respect to the added virtual mass approach. In this study, the nondimensionalized added virtual mass incremental factor for the partially submerged finite shell is derived. This factor can be readily used to estimate the change in the natural frequency of the shell due to the presence of a fluid.     

An analytical study of the non-linear vibrations of cylindrical shells

The primary resonance response of simply supported circular cylindrical shells is investigated using the perturbation method. Donnell's non-linear shallow-shell theory is used to derive the governing partial differential equations of motion. The Galerkin technique is then employed to transform the equations of motion into a set of temporal ordinary differential equations. Considering only the primary resonance case, the method of multiple scales is used to study the periodic solutions and their stability. The necessary and sufficient conditions for appearance of the so-called companion mode are also discussed. To this end, a range of the possible multi-mode solution is obtained for response and excitation amplitudes and also excitation frequency as a function of damping, geometry and material properties of the shell. Parametric studies are performed to illustrate the effect of different values of thickness, length and material composition on the possibility of the companion mode participation in primary resonance response.     

宏纤维压电层合壳结构非线性屈曲分析

以纤维压电MFC （Micro-Fiber Composite）层合圆柱壳为例,研究了其在准静态屈曲下的非线性振动响应。基于Reissner-Mindlin一阶剪切变形假设,采用大转角几何全非线性理论,建立了带有纤维角度的MFC层合壳结构的非线性屈曲与振动分析模型。采用全拉格朗日方程（Total Lagrange Formulation）对非线性模型进行线性化处理,并结合Riks-Wempner弦长控制迭代法进行准静态求解,然后在每个解点进行自由振动分析。通过与文献数据对比验证了所建模型的准确性。并用该计算模型对MFC-d31层合圆柱壳进行屈曲及自由振动分析,研究了几何参数（曲率、厚度、纤维角度和不同外加电压）对频率的影响。结果表明,厚度、曲率和纤维增强角度对结构的临界载荷有显著的影响,且结构的临界载荷随着上述参数的增大而增大;电场强度可对不同纤维角度壳体的自振频率进行调节,能够提高结构的临界载荷;纤维角度越大,电压对结构自振频率调节的效果越明显。     

Superior aeroelastic behaviors of axially functional graded cylindrical shells in supersonic airflow

It is well known that mode localization occurs in the panel flutter structural systems. Therefore, it is reasonable to expect the aeroelastic stability of the structure to be enhanced by changing the geometrical sizes and material properties of the structure along the airflow direction. In this investigation, an axially functionally graded (AFG) cylindrical shell is designed and its super aeroelastic behaviors in supersonic airflow are studied. The enhanced aeroelastic stability and the excellent capability in the passive flutter suppression are achieved by the present AFG design. For the thickness of the cylindrical shell, three types of functions are analyzed. Numerical results show that all these three functions can increase the flutter bound of the cylindrical shell to some extent. It is also noted that in some situations, local mode coalescence happens. In this study, an effective method is proposed to eliminate the local mode coalescence by adding the lumped mass. For the material properties, two groups of functions are considered. It is found that under suitable parameters of the functions, even if the effective stiffness of the whole structural system decreases, the flutter bound of the structure can still be increased due to the AFG design. In addition, the flutter stability of the AFG cylindrical shell is much better than that of the traditional transversely functionally graded shell. The present study is significant in the aeroelastic design of aerospace vehicles.     

Detection and description of non-linear phenomena in experimental modal analysis via linearity plots

Ground vibration tests (GVTs) on aircraft prototypes are mainly performed to experimentally identify the structural dynamic behaviour in terms of a modal model. This assumes a linear dynamic behaviour of the structure. However, in the practice of ground vibration testing it is often observed that structures do not behave in a perfectly linear manner. Non-linearities can be determined, for example, by free play in junctions, hydraulic systems in control surfaces, or friction. This paper compiles measured, typical, non-linear phenomena from various GVTs on large aircraft. The standard procedure in GVTs nowadays is the application of the Harmonic Balance method which linearizes the dynamic behaviour on the level of excitation. The procedure requires a harmonic excitation of the structure which is usually performed during phase resonance testing. The non-linear behaviour is investigated in terms of linearity plots in which the resonance frequency of a mode is plotted as a function of the excitation level. The experimental data is then compatible with all post-processing procedures for the measured results, e.g. updating of the finite element model or flutter calculations. This paper shows measured linearity plots for some typical non-linear phenomena. In the second part of the paper analytical linearity plots for different non-linear stiffness and damping models are considered in order to investigate whether the type of non-linearity can be identified from measured linearity plots. The analytical linearity plots are discussed with respect to their application limits. The analytical linearity plots are used to interpret the experimental linearity plots stemming from various GVTs on different aircraft prototypes. Finally, the observability of non-linear stiffness and non-linear damping characteristics via linearity plots is assessed.     

Natural frequencies of rotating functionally graded cylindrical shells

Love’s first approximation theory is used to analyze the natural frequencies of rotating functionally graded cylindrical shells.To verify the validity of the present method,the natural frequencies of the simply supported non-rotating isotropic cylindrical shell and the functionally graded cylindrical shell are compared with available published results.Good agreement is obtained.The effects of the power law index,the wave numbers along the x-and θ-directions,and the thickness-to-radius ratio on the natural frequencies of the simply supported rotating functionally graded cylindrical shell are investigated by several numerical examples.It is found that the fundamental frequencies of the backward waves increase with the increasing rotating speed,the fundamental frequencies of the forward waves decrease with the increasing rotating speed,and the forward and backward waves frequencies increase with the increasing thickness-to-radius ratio.     

Stress-strain analysis of elliptic cylindrical shells under local loads

The stress-strain state of elliptic cylindrical shells under local loads is analyzed.Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 113–121, October 2004.     

Experimental modal analysis of a synthetic composite femur

In this paper we describe the experimental characterization of the modal parameters of a synthetic composite femur model widely used in biomechanical research studies. The objective of the experimental procedure was to identify the natural frequencies and mode shapes of an unconstrained (free-free) femur. The experimental data were compared with the same obtained in an analog study performed with a fresh cadaveric femur bone. Other objective of the study was to investigate modal analysis as a technique to validate a finite element model of a composite femur with isotropic material properties.     

Dynamics of the geometrically non-linear analysis of anisotropic laminated cylindrical shells

A general approach, based on shearable shell theory, to predict the influence of geometric non-linearities on the natural frequencies of an elastic anisotropic laminated cylindrical shell incorporating large displacements and rotations is presented in this paper. The effects of shear deformations and rotary inertia are taken into account in the equations of motion. The hybrid finite element approach and shearable shell theory are used to determine the shape function matrix. The analytical solution is divided into two parts. In part one, the displacement functions are obtained by the exact solution of the equilibrium equations of a cylindrical shell based on shearable shell theory instead of the usually used and more arbitrary interpolating polynomials. The mass and linear stiffness matrices are derived by exact analytical integration. In part two, the modal coefficients are obtained, using Green's exact strain-displacement relations, for these displacement functions. The second- and third-order non-linear stiffness matrices are then calculated by precise analytical integration and superimposed on the linear part of equations to establish the non-linear modal equations. Comparison with available results is satisfactorily good.     

Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions

The aim of the present study is to investigate the nonlinear free vibration of spinning cylindrical shells under spinning and arbitrary boundary conditions. Artificial springs are used to simulate arbitrary boundary conditions. Sanders' shell theory is employed, and von Kármán nonlinear terms are considered in the theoretical modeling. By using Chebyshev polynomials as admissible functions, motion equations are derived with the Ritz method. Then, a direct iteration method is used to obtain the nonlinear vibration frequencies. The effects of the circumferential wave number, the boundary spring stiffness, and the spinning speed on the nonlinear vibration characteristics of the shells are highlighted. It is found that there exist sensitive intervals for the boundary spring stiffness, which makes the variation of the nonlinear frequency ratio more evident. The decline of the frequency ratio caused by the spinning speed is more significant for the higher vibration amplitude and the smaller boundary spring stiffness.     

Experimental analysis of the natural vibrations and stability of cylindrical shells reinforced with rectangular plates

The paper presents experimental results on the effect of reinforcing cylindrical shells with rectangular plates on the axial compressive critical loads and the natural frequencies and modes of two sets of shells __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 100–103, May 2008.