Vibrational energy flow analysis of penetration beam-plate coupled structures

This study concerns the transmission of vibrational energy through beam-plate junctions by energy flow analysis, which is an analytic tool for predicting the frequency averaged vibration response of built-up structures in the medium to high frequency ranges. A semi-infinite beam perpendicularly connected to an infinite plate is studied using the wave transmission approach. To calculate the power transmission and the reflection coefficients of the beam-plate junction, compatibility and equilibrium conditions are applied when each wave component is incident on the beam and plate, respectively. Power coefficients are calculated and plotted against frequencies for different dimensions and the directivity pattern of the scattered waves in the plate show close agreement with that of the rigid inclusion as the frequency increases. The results obtained are applied to the finite beam and the circular plate coupled structure, and the energy densities obtained from energy flow analysis show better agreement with analytic solution results as frequencies are increased.     

Vibrational energy flow models for out-of-plane waves in finite thin shell

In this paper, an approximate energy flow model for the out-of-plane vibration of a finite thin shell was developed. The derived energy governing equation for the model was expressed in terms of the time- and locally space-averaged far-field wave energy density which can be used as the main equation for the prediction of the out-of-plane structural vibration levels of the energy density and intensity in medium-to-high frequency ranges. The derived model can be applied to the vibration energy problems of a cylindrical shell, spherical shell and doubly-curved shell, whose radius of curvature in each direction is constant, regardless of the position, assuming that the in-plane motion is relatively small. To verify the results of the derived model, wave numbers were obtained using an energy flow analysis and classical analysis, such as the method using Donnell-Mushtari equations. For the case of various types of finite thin shell, the derived energy equations were applied. The results for the spatial distributions and levels of the energy density and intensity were compared with classical displacement solutions, according to the changes in the frequency and internal loss factor of the shell.     

筋肋增强薄壁圆筒有限元分析

镁合金薄壁结构在飞行器和航海器工程领域应用范围逐步扩展。针对一种筋肋增强镁合金薄壁圆筒结构试件,采用Solid Works Simulation有限元分析软件,数值模拟圆筒结构应力和变形分布及结构固有模态特性。结果表明在1~1.75 MPa外压载荷下,圆筒壳板最大等效应力和变形都发生在外止口临域单元框壳板中心部位,其值随外压载荷的变化与筒体试验有关结果符合较好,筋和肋对增强薄壁结构壳体刚性起主要作用。圆筒前十阶固有频率从683 Hz依次增加至1147 Hz。Simulation软件能够用于筒体结构的后续改进设计和深化研究使用。     

A laminated thin cylindrical shell under axisymmetric static loading

A model is used to discuss the behavior of a laminated shell in which the laminating mechanism is represented by springs which allow both separation and relative layeral motion of “slip” of the faces of the homogeneous isotropic layers. By varying the spring constants it is possible to determine the dependence of both the buckling load and the flexural response upon a wide range of conditions. It is the attempt here to use the most simple model possible which has physical relevance.     

Paradoxical buckling behaviour of a thin cylindrical shell under axial compression

The widely accepted theory of buckling of thin cylindrical shells under axial compressive loading emphasises the sensitivity of the buckling load to the presence of initial imperfections. These imperfections are conventionally taken to be minor geometric perturbations of a shell which is initially stress-free. The original aim of the present study was to investigate the effect on the buckling load of imperfections in the form of local initial stress, which are probably more typical of practice than purely geometric ones. Experiments were performed on a vertical “melinex” cylinder of diameter 0.9 m and height 0.7 m, with radius/thickness ratio 1800. The upper and lower edges of the cylinder were clamped to end discs by means of circumferential belts — an arrangement that allowed states of self-stress to be introduced to the shell readily by means of local “uplift” at the base. The upper disc was made sufficiently heavy to buckle the shell, and it was supported by a vertical central rod under screw control. Many buckling tests were performed. Surprisingly, the buckling loads were generally at the upper end of the range of fractions of the classical buckling load that have been found in many previous experimental studies. Even when the local uplift at the base caused a local “dimple” to be formed before the shell was loaded, the buckling load was relatively high. A surface-scanning apparatus allowed the geometric form of the shell to be monitored, and the progress of such a dimple to be followed; and it was found that a dimple generally grew in size and migrated in a stable fashion up the shell as the load increased, until a point was reached when unstable buckling occurred. These unexpected and paradoxical features of the behaviour of the experimental shell may be attributed to the particular boundary conditions of the shell, which provide in effect statically determinate support conditions. This study raises some new issues in the field of shell buckling, both for the understanding of buckling phenomena and for the rational design of shells by engineers against buckling.     

基于ANSYS的薄膜蒸发器筒节夹套参数化有限元分析

通过调用薄膜蒸发器三维零件实体造型设计参数以及本课题组开发的辅助设计系统中的物料特性数据,作为薄膜蒸发器筒节夹套应力分析的设计参数,采用Visual Basic对有限元软件ANSYS进行二次开发,实现筒节夹套的有限元建模、热应力耦合分析,实现了参数化设计与有限元分析的集成化,提高了设计效率与设计精度.     

Research on transmission paths of a coupled beam-cylindrical shell system by power flow analysis

A power flow analysis based on a substructure approach is performed to exhibit vibration transmission in a complex coupled beam-cylindrical shell system. The system is divided into a shell substructure and a beam substructure, which are coupled by three spring-dampers. The theoretical receptance function of each substructure with a free-free interface condition is formulated by modal analysis to describe the dynamical behavior. On the basis of the receptance functions of the two substructures as well as synthesis through the geometrical compatibility and force balance conditions at the coupling interfaces, the dynamic characteristics of the coupled system are calculated. Both the input and transmitted powers within the system are estimated, and the influences of the excitation locations, the stiffness and loss factor of the spring-dampers on the vibration transmission are investigated as well. This paper was recommended for publication in revised form by Associate Editor Eung-Soo Shin G.P. Feng received his Ph.D. from the School of Mechanical Engineering at Shanghai Jiao Tong University. His research interests include vibration analysis, control and sound radiation, etc. Z.Y. Zhang received his Ph.D. from the School of Mechanical Engineering at Shanghai Jiao Tong University. Dr. Zhang is currently a Professor at the School of Mechanical Engineering at Shanghai Jiao Tong University in Shanghai, China. Y. Chen received his Ph.D. from the School of Mechanical Engineering at Shanghai Jiao Tong University. His research interests include vibration and shock analysis. H.X. Hua received his Ph.D. at the University of Brussels in Belgium. Dr. Hua is currently a Professor and Doctoral Supervisor at the School of Mechanical Engineering at Shanghai Jiao Tong University in Shanghai, China. His research interests include modal parameter identification, and analysis of vibration and shock.     

A frequency response function-based damage identification method for cylindrical shell structures

In this paper, a structural damage identification method (SDIM) is developed for cylindrical shells and the numerically simulated damage identification tests are conducted to study the feasibility of the proposed SDIM. The SDIM is derived from the frequency response function solved from the structural dynamic equations of damaged cylindrical shells. A damage distribution function is used to represent the distribution and magnitudes of the local damages within a cylindrical shell. In contrast with most existing modal parameters-based SDIMs which require the modal parameters measured in both intact and damaged states, the present SDIM requires only the FRF-data measured in the damaged state. By virtue of utilizing FRF-data, one is able to make the inverse problem of damage identification well-posed by choosing as many sets of excitation frequency and FRF measurement point as needed to obtain a sufficient number of equations.     

Vibration analysis of submerged thin FGM cylindrical shells

This study gives a brief work on vibration characteristics of cylindrical shells submerged in an incompressible fluid. The shell is presumed to be structured from functionally graded material. The effect of the fluid is introduced by using the acoustic wave equation. Love’s first order thin shell theory is utilized in the shell dynamical equations. The problem is framed by combining shell dynamical equations with the acoustic wave equation. Fluid-loaded terms are associated with Hankel function of second kind. Wave propagation approach is employed to solve the shell problem. Some comparisons of numerical results are performed for the natural frequencies of simply supported-simply supported, clamped-clamped and clamped-simply supported boundary conditions of isotropic as well as functionally graded cylindrical shells to check the validity of the present approach. The influence of fluid on the submerged functionally graded cylindrical shells is noticed to be very pronounced.     

Frequency characteristics of a thin rotating cylindrical shell using the generalized differential quadrature method

In this paper, the generalized differential quadrature (GDQ) method is used for the first time to study the effects of boundary conditions on the frequency characteristics of a thin rotating cylindrical shell. The present analysis is based on Love-type shell theory and the governing equations of motion include the effects of initial hoop tension and the centrifugal and coriolis accelerations due to rotation. The displacement field is expressed as a product of unknown smooth continuous functions in the meridional direction and trigonometric functions along the circumferential direction so that the three-dimensional dynamic problem may be transformed mathematically into a one-dimensional problem. Based on this approach, the results are obtained for the effects of the boundary conditions on the frequency characteristics at different circumferential wave numbers and rotating speeds and various geometric properties; the effect of rotating speed on the relationship between frequency parameter and circumferential wave number is also discussed. To validate the accuracy and efficiency of the GDQ method, the results obtained are compared with those in the literature and very good agreement is achieved.     

Experimental study on the energy flow analysis of underwater vibration for the reinforced cylindrical structure

Energy flow analysis (EFA) can be used effectively to predict structural vibration in the medium-to-high frequency ranges. In this study, the energy flow finite element method (EFFEM), based on EFA, was used to predict the vibrations of a reinforced cylindrical structure in water. The predicted results of the vibrational energy density for the structure were compared with corresponding experimental results. The structure was divided into several subsystems in the experiment, with several accelerometers attached to each subsystem. The input power excited into the experimental structure was measured using an impedance-head adhered to an exciter. Measured input power was used to predict vibration of the reinforced cylindrical structure by EFFEM in water for comparing experimental and numerical results. A comparison between the experimental and predicted results for the vibrational energy density showed that EFFEM was an effective tool for predicting structural vibration.     

Vibrational energy flow models for the 1-D high damping system

Energy flow analysis (EFA) is developed to predict the vibrational energy density of system structures in the high frequency range. The traditional energy flow model has been used to predict energy density distributions only for low damping systems because the traditional energy flow model is derived with low damping assumption. In this paper, vibrational energy governing equations are derived without low damping assumption for a rod and a beam; the developed energy flow model can consider damping effect of high damping systems. The wavenumber obtained without approximation of the imaginary term is used to obtain the dissipated power, the relationship between time and space averaged energy density and intensity of structures. In the case of low damping, the derived energy governing equations are analogous to the traditional energy governing equations. To verify the validity of the developed energy flow models, various numerical analyses are performed for a rod, a beam and a coupled beam in the high damping system for several excitation frequencies. The developed EFA results are compared with the classical solutions, and correlations between the developed EFA results and the classical solutions are verified.     

Elastohydrodynamic analysis of a cylindrical journal bearing with a flexible bearing shell

The effect of the elastic deformation of a bearing shell was considered in the determination of the performance characteristics of a hydrodynamic journal bearing. The finite element method with an iteration scheme was employed to solve the Reynolds equation governing flow in the clearance space and the three-dimensional linear elasticity equations representing the displacement vector field in the bearing shell. For design convenience a nondimensional deformation coefficient ψ relating μ, E_m, U₀ , C, R_j and tis defined. The performance characteristics were obtained in terms of load-carrying capacity, fluid flow, power loss and attitude angle for an aspect ratio $\text{L}\text{D = 1}$, eccentricity ? = 0.6 and for a wide range of deformation coefficients. The results are compared for bearing materials having Poisson's ratio v equal to 0.3 and 0.4.     

Layer-wise finite element analysis of functionally graded cylindrical shell under dynamic load

In this paper, a layer-wise finite element formulation is developed for the analysis of a functionally graded material (FGM) cylindrical shell with finite length under dynamic load. For this purpose, FGM cylinder is divided into many sub-layers and then the general layerwise laminate theory is formulated by introducing piecewise continuous approximations through the thickness for each state In this model the radial displacement is approximated linearly through each “mathematical” layer. The properties are controlled by volume fraction that is an exponential function of radius. The governing equations are derived from virtual work statement and solved by finite element method. The main contribution of the present study is to develop a discrete layerwise finite element for a 2-dimensional thick FGM cylindrical shell. Results are obtained for the time history of the displacement and stress components with different exponent “n” of functionally graded material. In addition, natural frequency and mean velocity of the radial wave propagation for different exponent “n” of functionally graded material (FGM) are studied and compared with similar ones currently obtained for FGM cylindrical shell of infinite length.     

Large deflection of a heated cylindrical shell

The large deflection of a heated cylindrical shell is investigated and some numerical results are presented.     

Investigating elastic stability of cylindrical shell with an elastic core under axial compression by energy method

In this paper, the elastic axisymmetric buckling of a thin, isotropic and simply supported cylindrical shell with an elastic core under axial compression has been analyzed using energy method. The nonlinear strain-displacement relations in general cylindrical coordinates are simplified using Sanders kinematic relations (Sanders, 1963) for axial compression. Equilibrium equations are obtained by using minimum potential energy together with Euler equations applied for potential energy function in cylindrical shell. To acquire stability equation of cylindrical shell with an elastic core, minimum potential energy theory and Trefftz criteria are implemented. Stability and compatibility equations for an imperfect cylindrical shell with an elastic core are also obtained by the energy method, and the buckling analysis of shell is carried out using Galerkin method. Critical load curves versus the aspect ratio are obtained and analyzed for a cylindrical shell with an elastic core. It is concluded that the application of an elastic core increases elastic stability and significantly reduces the weight of cylindrical shells.     

Nonlinear finite element analysis of a laminated cylindrical shell with transverse matrix cracks

A clamped laminated cylindrical shell is presented to investigate nonlinear structural behavior involving geometrically nonlinear deformation. In the investigation, transverse matrix cracks are considered in the stiffness of the laminated cylindrical shell. Stiffness degradation is examined for several laminated angles and transverse crack density. Micro-mechanics theory on the composite material was used to derive the degraded stiffness of the laminated cylindrical shell due to the crack density. Iterative numerical scheme was developed to calculate the degraded composite stiffness which is a complicated relation with the crack density. A nonlinear finite element program was developed using 3-D degenerated shell element and the fist order shear deformation theory to consider the large deformation of the clamped laminated cylindrical shell. The updated Lagrangian method is used for nonlinear finite element analysis. Nonlinear structural responses of the laminated cylindrical shell were examined for various stacking sequences and crack density under transversely loaded pressure. Also, the effect of crack opening/closed was considered in the examination. Through this study, it is realized that the transverse matrix crack causes moderate stiffness reduction and affects the responses of the composite shell.     

圆柱形变节流面积缓冲结构的缓冲性能分析

通过对液压油缸缓冲结构特点和缓冲特性的分析总结,提出一种新型油缸缓冲结构——圆柱形变节流面积缓冲结构.对该缓冲类型的缓冲结构参数设计、仿真和对比试验,可使液压油缸缓冲性能接近理想的缓冲性能,从而减少对液压设备的冲击,增强设备的安全性、舒适性及可靠性.     

Assessment of shell theories for hybrid piezoelectric cylindrical shell under electromechanical load

The assessment of classical lamination shell theory and first-order shear deformation theory is presented for simply supported finite circular cylindrical hybrid shell with cross-ply composite laminate as elastic substrate under electromechanical static load. Navier-type solutions are obtained and used in threedimensional equilibrium equations and transverse strain—displacement relation to obtain transverse stress components and improved value of deflection. These solutions are assessed by comparison with the threedimensional solution. The error in the two-dimensional shell theories increases as the shell becomes thicker and it is more for the patch loads in comparison to the uniformly distributed and sinusoidal loads.