Free vibration analysis of joined conical shells: Analytical and experimental study

Natural frequencies and mode shapes of two joined isotropic conical shells are presented in this study. The joined conical shells can be considered as the general case for joined cylindrical–conical shells, joined cylinder–plates or cone–plates, conical and cylindrical shells with stepped thicknesses and also annular plates. Governing equations are obtained using thin-walled shallow shell theory of Donnell and Hamilton׳s principle. The continuity conditions at the joining section of the cones are appropriate expressions among stress resultants and deformations. The equations are solved assuming trigonometric response in circumferential and series solution in meridional directions and all combinations of boundary conditions can be assumed in this method. The results are compared and validated with the available results in other investigations and also modal testing. The effects of semi-vertex angles and meridional lengths on the natural frequency and circumferential wave number of joined shells are investigated.     

Vibration analysis of cylindrical shells in contact with an annular fluid region

An experimental and numerical investigation of the vibratory modal characteristics of a vertical thin-walled cylindrical shell containing water, or oil, in an adjacent coaxial region is presented. A system of two fluid-coupled cylindrical shells is studied. In addition to the effect of increasing liquid level in the shell, the effects of the thickness of the liquid layer in the annular region between the vibrating outer shell and another coaxial rigid cylinder, or between two thin coaxial cylindrical shells, are studied. Experimental results were obtained using the standard modal analysis technique and the time average holographic method. In parallel, computation of natural frequencies and mode shapes of the coupled fluid-structural vibrations were carried out by means of the finite element method operated within the framework of the ANSYS program package. The comparison between experimental results and finite element results was found to be reasonable in most of the cases studied. The fundamental influence of the viscosity of the fluid in the narrow annulus upon the dynamic behaviour of the shell is discussed.     

Effects of modal coupling on the dynamics of parametrically and directly excited cylindrical shells

Cylindrical shells exhibit a dense frequency spectrum, especially in the lowest frequency range. In addition, due to the circumferential symmetry, frequencies occur in pairs. So, in the vicinity of the lowest natural frequencies, several equal or nearly equal frequencies may occur, leading to multiple internal resonances. The aim of the present work is to investigate the dynamic behavior and stability of cylindrical shells under lateral and axial forcing with equal natural frequencies. The shell is modeled using the Donnell nonlinear shallow shell theory. A consistent modal solution for this problem is deduced and used to discretize the equations of motion by applying the Galerkin method. A parametric analysis is conducted to clarify the influence of the modal interaction among these nonlinear vibration modes on coexisting solutions, bifurcations, resonances curves and stability boundaries of the shell.     

Design and analysis of a glass roof structure

The hybrid grid shell, made of quadrangular meshes diagonally stiffened by pre‐tensioned thin cables, is an attractive structural form in the design and construction of long‐span transparent glass roof structures. These hybrid structures are very slender and lightweight, and it is desirable to understand their detailed structural behavior. The mechanical characteristic of the hybrid structure was investigated based on a quadrangle of slats with cross cables. The construction of the design model for the glass roof was firstly described. Then, the static behavior and stability capacity of the hybrid grid dome and the corresponding single‐layer lattice dome were studied based on a finite element model. Moreover, the modal analyses of the two domes were carried out. The natural frequencies and the vibration modes of the domes were given to investigate the dynamic behavior of the hybrid grid dome. Finally, the effects of the asymmetric loads and rise‐to‐span ratios on the structural behavior were studied in detail. Copyright © 2011 John Wiley & Sons, Ltd.     

Natural vibrations of loaded noncircular cylindrical shells containing a quiescent fluid

The paper deals with a solution of three-dimensional problems of natural vibrations and stability of loaded cylindrical shells with circular and arbitrary cross sections containing a quiescent ideal compressible fluid. A mathematical formulation of the problem has been developed based on the variational principle of virtual displacements taking into account the pre-stressed undeformed state caused by the action of static forces on the shell. The motion of potential compressible non-viscous fluid is described by a wave equation, which is transformed using the Bubnov–Galerkin method. The solution of the problem reduces to the computation of complex eigenvalues of a coupled system of two equations. Based on the developed finite element algorithm several numerical examples have been considered to analyze the influence of fluid levels, ratio of ellipse semi-axes, shell thickness and boundary conditions on the natural frequencies and vibration modes of circular and elliptical cylindrical shells loaded by mechanical forces. It has been found that the value of the external uniformly distributed pressure giving rise to instability does not depend on the level of fluid in the shell. The results allow us to conclude that the dynamic characteristics of the system are specified not only by the equivalent added mass of the fluid but also by hydroelastic interaction at the wetted surface.     

Nonlinear free vibration analysis of prestressed circular cylindrical shells on the Winkler/Pasternak foundation

Nonlinear free vibration analysis of prestressed circular cylindrical shells placed on Winkler/Pasternak foundation is investigated in the present paper. The nonlinearity is considered due to large deflections. Simultaneous effects of prestressed condition and elastic foundation on natural frequencies of the shells under various boundary conditions are examined extensively in this study. The nonlinear Sanders–Koiter shell theory is employed in order to derive strain–displacement relationships. The nonlinear classical Love's thin shell theory is also applied in some specific cases due to contrast the results. Beam modal functions are used to approximate spatial displacement field. The governing equations in linear state are solved by the Rayleigh–Ritz procedure. Perturbation methods are used to find the relationship between vibration amplitude and frequency in nonlinear state. Prestress state includes the effects of internal hydrostatic pressure and initial uniaxial tension. Results are compared with published theoretical and experimental data for some specific cases.     

大连极地海洋动物馆屋盖的结构选型及锯齿状锥面网壳的静、动力特性分析

介绍了大连极地海洋动物馆屋盖结构体系及结构选型依据。其屋盖结构根据建筑造型及功能要求选用了双层网架、单层筒壳、单层球面网壳及锯齿状锥面网壳等4种空间结构体系。重点介绍了锯齿状锥面网壳结构构成;并采用大型通用有限元软件ANSYS对锯齿状锥面网壳部分进行了静力分析及几何非线性稳定分析,得到了此类结构的应力分布、位移分布等静力特性及稳定性能;对结构进行了模态分析,获得了其自振频率、振型等自振特性,为后续对结构进行动力分析提供了基础。结果表明,该结构设计符合规范要求,稳定性良好,适于建筑造型呈锯齿状,屋面恒荷载较小的建筑物屋面。可为今后该类结构的设计提供一定理论依据。     

河北省科技馆单层球面网壳结构的抗震分析与设计

结合一工程实例 ,采用子空间迭代法求出了该网壳结构的前 2 0阶自振频率和振型 ,分析了其振动规律 ;应用振型分解反应谱法和时程分析法分析了该网壳结构的地震反应 ;结合现行抗震设计规范对网壳结构进行了“二阶段”抗震验算。     

Free vibration analysis of functionally graded cylindrical shells including thermal effects

Free vibration analysis of simply supported FG cylindrical shells for four sets of in-plane boundary conditions is performed. The material properties are assumed to be temperature-dependant and gradually changed in the thickness direction of the shell. The effects of temperature rise are investigated by specifying arbitrary high temperature on the outer surface and the ambient temperature on the inner surface of the cylinder. Distribution of temperature across the shell thickness is found from steady state heat conduction only in the thickness direction. The equations of motion are based on Love's shell theory and the von Karman–Donnell-type of kinematic nonlinearity. The static analysis is first performed to determine the prestressed state induced by the thermal loadings, using the exact solution of the governing equations and then the equations of motion are solved by Galerkin's method. The results are obtained to indicate the effects of power law index on the natural frequencies and corresponding mode shapes in the thermal environment.     

Free vibration of non-uniformly ring stiffened cylindrical shells using analytical, experimental and numerical methods

In this research, the free vibration analysis of cylindrical shells with circumferential stiffeners, i.e. rings with non-uniform stiffeners eccentricity and unequal stiffeners spacing is investigated using analytical, experimental and finite elements (FE) methods. Ritz method is applied in analytical solution while stiffeners treated as discrete elements. The polynomial functions are used for Ritz functions and natural frequency results for simply supported stiffened cylindrical shell with equal rings spacing and constant eccentricity is compared with other's analytical and experimental results, which showed good agreement. Also, a stiffened shell with unequal rings spacing and non-uniform eccentricity with free–free boundary condition is considered using analytical, experimental and FE methods. In experimental method, modal testing is performed to obtain modal parameters, including natural frequencies, mode shapes and damping in each mode. In FE method, two types of modeling, including shell and beam elements and solid element are used, applying ANSYS software. The analytical and the FE results are compared with the experimental one, showing good agreements. Because of insufficient experimental modal data for non-uniformly stiffeners distribution, the results of modal testing obtained in this study could be as useful reference for validating the accuracy of other analytical and numerical methods for free vibration analysis.     

Experimental study conducted on a liquid-filled combined conical tank model

Elevated water tanks are often built with a superstructure vessel consisting of a truncated cone with a top superimposed cylindrical cap. Such vessels are referred to as ‘combined conical tanks’. This study is motivated by the lack of procedures for the seismic analysis and design of such structures. It reports the first experimental study conducted on a small-scale combined liquid-filled conical shell model. Shake table testing is conducted to determine the fundamental frequencies as well as the frequencies of vibration of the modes during which the cross section of the tank remains circular (cos(θ)-modes). The later are responsible for the base shear force and overturning moment acting on the tank.Results of the experiments are used to validate the assumptions employed in a previously developed analytical model for the free surface sloshing motion and a numerical model for the vibration of the liquid-shell system. In general, excellent agreements are shown between the analytical and the experimental results as well as between the numerical and the experimental findings.     

Analysis and optimization of laminated composite circular cylindrical shell subjected to compressive axial and transverse transient dynamic loads

Optimization is one of the important stages in the design process. In this paper the genetic algorithms method is applied for weight and transient dynamic response and two constraints including critical buckling loads and principle strains optimization of laminated composite cylindrical shells. The multi-objective function seeks the minimum structural weight and transient dynamic response. Nine design variables including material properties (fibre and matrix), volume fraction of fibre, fibre orientation and thickness of each layer are considered. In analytical solution, vibration of composite circular cylindrical shells are investigated based on the first-order shear deformation shell theory. The boundary conditions are assumed to be fully simply support. The dynamic response of the composite shells is studied under transverse impulse and axial compressive loads. The modal technique is used to develop the analytical solution of the composite cylindrical shell. The solution for the shell under the given loading conditions can be found using the convolution integrals. An example of simply supported laminated composite cylindrical shells is given to demonstrate the optimality of the solution obtained by the genetic algorithms technique. Results are shown that the weight coefficient of multi-objective function and the type of the constraints have considerable effect on the optimum weight and dynamic response.     

基于多参考振型的Rayleigh阻尼系数计算方法在单层柱面网壳中的应用

传统的Rayleigh阻尼系数计算法(两参考振型法)并不总是适用于单层柱面网壳的地震时程分析,对基于多参考振型的Rayleigh阻尼系数计算方法在单层柱面网壳中的应用进行了研究.分析结果表明,在某些地震波作用下,主要贡献振型数目较多,分布较为离散,且频率值相差较大,此种情况下基于多参考振型的计算方法比两参考振型法更为合理;而在另外一些地震波下,结构的主要贡献振型数目较少,分布较为集中,且频率值较为接近,此时基于多参考振型的计算方法和两参考振型法都可以应用.     

竖向地震作用下储罐地震力的等效力学模型

圆形截面的储液罐通常由一个包含短锥和叠加顶端圆柱体的组合容器构成。与圆筒形储罐不同,组合储罐的特点是具有锥形部分的倾斜筒壁。通常,由于罐体内所包含液体的静水压力和竖向地震力激发的动水压力,导致壳体内产生压应力。本文目的在于确定充满液体的储藏罐受到竖向地震作用的动态特性。基于一个关于流体结构相互作用的双边界元公式,建立了数值分析。建立了一个等效模型,用于复制液体组合容器受到竖向地震时所产生的力。基于该模型可得到容器壁的弹性。与此同时,容器内的液体被理想化为刚性和柔性组件。这个等效模型提供了一种简化的工具,可以预测充满液体的容器受到竖向地震作用时所产生的作用力。     

有多条轴对称焊接凹陷的钢圆柱薄壳在内压力和轴压力共同作用下的强度

钢筒仓中圆柱薄壳承受内压力和轴压力共同作用:在轴压和低内压作用下,壳可发生弹性失稳;在轴压和高内压作用下,壳可发生塑性破坏.内压轴压共同作用下的圆柱薄壳对几何缺陷比较敏感:单条轴对称焊接凹陷可使壳的承载力降低;而多条轴对称凹陷由于相邻凹陷的相互作用,可使壳的强度进一步降低;对于小间距的凹陷,这种相互作用更为明显.本文首次对有多条小间距轴对称凹陷轴压圆柱薄壳的整体结构在不同水平内压作用下的强度进行了有限元分析,并将计算结果与欧洲规范EC3的设计曲线进行比较,对EC3的设计曲线提出了修改意见,从而达到安全设计的目的.     

大矢跨比开孔单层球面网壳结构的抗振分析与设计

本结构一工程实例,采用子空间迭代法求出该网壳结构的前20阶自振频率和振型,分析了其振动规律;应用振型分解反应谱法和时程分析法分析了该网壳结构的地震反应;结合现行抗震设计规范对网壳结构进行了“二阶级”抗震验算。最后,本得出了一些结论工程界参考。     

Einsatz von multiplen Schwingungstilger‐Systemen an schlanken Fußgängerbrücken

The Application of Multiple Tuned Mass Damper Systems at slender footbridges. While for standard footbridge only a few vibration modes are within the critical footfall frequency range and hove to be considered for the dynamic design, lightweight structures dis‐play multiple modes in that frequency range. Furthermore the modal masses are very little so also the smaller load components for the excitation of higher harmonic vibration modes can become significant to assess the vibration susceptibility. Various observations have been made during experimental tests of these structures and will be introduced in this contribution using the example of a canopy walk structure and a stress ribbon bridge. To understand the observed effects at such continuous dynamic systems for pedestrian loading, numerical calculations have been performed for which a similar lightweight structure has been modelled and pedestrian loading was simulated with several footfall frequencies. Similar to the experimentally investigated structures it was found that the multimodal dynamic response of the bridges strongly depends on the pedestrian loading (footfall frequency). Experimental tests have shown, that the application of a Tuned Mass Damper System to dampen only the critical mode that is within the footfall frequency range is not sufficient to reduce the multi‐modal dynamic response of the lightweight bridge structures under pedestrian so the occurring accelerations remain below certain comfort levels. Therefore the concept of Multiple Tuned Mass Dampers was introduced to the bridge structure and its practicability was investigated.     

T-ring stiffened cone cylinder intersection under internal pressure

Cone–cylinder junctions are vastly used in the industries such as oil refineries and aeronautics. They can be seen in pressure vessels and piping such as tanks' roofs and pipes' reducers. When cone–cylinder junctions are subjected to the internal pressure, compression stresses are established near the joining point of the cone to cylinder and make the junction susceptible to non-symmetric buckling failure or axisymmetric failure. As it is practical to increase the shell wall thickness locally near the point of intersection, sometimes it is more convenient to attach a ring-beam exactly to the point of intersection. Only limited work has been done on the T-ring stiffened cone–cylinder junctions under internal pressure. In this study, experimental behavior along with numerical analysis of T-ring stiffened cone–cylinder intersection under internal pressure has been dealt and experimental results such as buckling mode and load are presented here and compared with numerical results. It can be seen that by wise consideration and manipulated use of material properties and geometric imperfections in nonlinear analysis, buckling mode and load resulted from non-linear analysis are compatible with that of experimental results. Two classes of non-linear analyses have been carried out and compared with each other, then it was inferred that even though pattern of geometrical imperfection is effective in determination of buckling modes, but in these kinds of structures it is not necessarily used for the analysis of buckling loads. Finally experimental results were compared with design proposals. It is shown that these proposals can conservatively predict the failure loads.     

Temperature-induced variations of measured modal frequencies of steel box girder for a long-span suspension bridge

This paper addresses the temperature-induced variations of measured modal frequencies of steel box girder for a suspension bridge using long-tem monitoring data. The output-only modal frequency identification of the bridge is effectively carried out using the Iterative Windowed Curve-fitting Method (IWCM) in the frequency-domain. The daily and seasonal correlations of frequency-temperature are investigated in detail and the analysis results reveal that: (i) the identified modal frequencies using IWCM provide an effective indication for changes of the bridge due to the ambient temperature variations; (ii) temperature is the critical source causing modal variability, and there is an overall decrease in modal frequency with temperature for all the identified modes; (iii) the random variations in measured modal frequencies mainly arise from the identification algorithm due to the nonstationary loadings, which can be effectively eliminated using multi-sample averaging technique; (iv) the daily averaged modal frequencies of vibration modes have remarkable seasonal correlations with the daily averaged temperature and the seasonal correlation models of frequency-temperature are suitable for structural damage warning if future seasonal correlation models deviate from these normal models.     

Elastic buckling of clothoidal–spherical shells under external pressure – theoretical study

The paper is devoted to a non-typical shape of a shell of revolution with positive Gaussian curvature. The meridian of the shell is a plane curve composed of a clothoid and a circular arc. Geometrical properties of the middle surface of the shell of revolution are presented. Pre-buckling state of the shell under uniform pressure is described analytically. The critical pressure and buckling modes for the shell are calculated with the use of the FEM (the ANSYS system). Post-buckling behaviour of the shells is shown. Results of analytical and numerical investigations are presented in tables and figures.