Radiation and vibrational properties of submerged stiffened cylindrical shells

The vibratory response of submerged cylindrical shells is investigated. The shell response is presented in terms of the spatial wave-number spectrum of the normal surface displacement. The power output of the vibrating shell into the fluid and the far-field radiation from the shell are presented as a function of the wave number of the exciting force. The effects of structural damping and stiffeners are also studied.     

Predicting transmission of structure-borne sound power from machines by including terminal cross-coupling

Structure-borne sound generated by audible vibration of machines in vehicles, equipment and house-hold appliances is often a major cause of noise. Such vibration of complex machines is mostly determined and quantified by measurements. It has been found that characterization of the vibratory source strength and the prediction of power transmission to a supporting structure or the machine casing itself can be greatly simplified if all mobility cross-terms and spatial cross-coupling of source velocities can be neglected in the analysis. In many cases this gives an acceptable engineering accuracy, especially at mid- and high-frequencies. For structurally compact machines, however, the influence of cross-coupling cannot always be ignored. The present paper addresses this problem and examines the transmission of structure-borne sound power by including spatial cross-coupling between pairs of translational terminals in a global plane. This paired or bi-coupled power transmission represents the simplest case of cross-coupling. The procedure and quality of the predicted transmission using this improved technique is demonstrated experimentally for an electrical motor unit with an integrated radial fan that was mounted resiliently in a vacuum cleaner casing. It is found that cross-coupling plays a significant role, but only at frequencies below 100 Hz for the examined system.     

Acoustic measurements and computational results on material specimens with harmonic variation of the cross section

The present work represents both an experimental and theoretical investigation of the behavior of finite cylindrical rods with harmonic variation of the cross section. The matrix method was used to compute the transfer power spectra of elastic rods with uniform circular cross section and of rods with harmonic variation of the cross section with distance. Theoretical and experimental results show that for a rod with periodical variation of the cross section, a new set of supplementary frequencies appear for which the transfer power coefficient has significant values, which are in relation with the space period of the inhomogeneity. Also, due to the radial component of the displacement certain modes are enhanced which satisfy boundary conditions on the surface and are obtained from the zeroes of Bessel functions.     

The measurement of structural mobilities of a circular cylindrical shell

Structural mobility is useful for the estimation of structural power flows in coupled systems. Although the methods of measuring structural mobilities are easily found for one-dimensional beam structures, few are available for cylindrical shells. In this paper, a new method is proposed for the measurement of the structural mobilities of a circular cylindrical shell. A point force excitation is used instead of circumferential modal forces which are difficult to implement in practice. This method utilizes the least squares technique to obtain the transfer function components of different circumferential modes from the measured data. Experiments were carried out on a circular cylindrical shell with different end conditions excited by a point force to verify the feasibility of this proposed method.     

Structural and acoustic responses of a fluid-loaded cylindrical hull with structural discontinuities

This paper studies the low frequency vibrational behaviour and radiated sound of a submarine hull under axial excitation. The submarine is modelled as a fluid-loaded cylindrical shell with internal bulkheads and ring-stiffeners and closed at each end by circular plates. A smeared approach is used to model the ring stiffeners. The external pressure acting on the hull due to the fluid loading is calculated using an infinite model and is shown to be a good approximation at low frequencies. The radiated sound pressure is obtained by considering the finite cylindrical hull to be extended by two semi-infinite rigid baffles. The sound pressure is then only due to the radial displacement of the cylindrical shell, without taking into account the scattering at the finite ends. The main aim of this paper is to observe the influence of the various complicating effects such as the bulkheads, ring-stiffeners and fluid loading on the structural and acoustic responses of the finite cylindrical shell. Results from the analytical models presented in this paper are compared to the computational results from finite element and boundary element models.     

Acoustic radiation from shear deformable stiffened laminated cylindrical shells

An analytical model of acoustic radiation from shear deformable laminated cylindrical shells with initial axial loadings and doubly periodic rings is presented. The shear deformation and rotary inertia of the rings are taken into account and the rings interact with the cylindrical shell only through the normal forces. The far-field sound pressure is found by using the Fourier wavenumber transform and stationary phase method. High frequency limitation issues of the first-order shear deformation theory are discussed and the effects of the second set of rings, axial initial loadings and multiple external loadings on the far-field acoustic radiation are explored. Further, the helical wave spectra of the radial displacement and sound pressure are used to study the vibrational and acoustic characteristics of the laminated shells. Above the ring frequency, the profile of the helical wave spectra of the far-field sound pressure induced by the cylindrical shell is an ellipse and the patterns of the helical wave spectra of the far-field sound pressure keep unchanged. Moreover, the ellipse distinguishes the supersonic wavenumbers and subsonic wavenumbers from the helical wave spectra of the radial displacement and surface sound pressure in the wavenumber domain. The bright spots and highlights of the helical wave spectra show that the corresponding waves are dominant.     

Analysis of the response of damped cylindrical shells carrying discontinuously constrained beam elements

A simple analysis is presented of the forced vibratory response of a cylindrical shell having a number of axial beams adhered to it by a viscoelastic material layer. The attached beams are identical, closely spaced and distributed around the full circumference of the shell. The excitation is a concentrated vibratory force acting radially at the mid-section on the surface of the shell. The end conditions of the shell and the attached beams are all assumed to be simply supported. The effects of the operational temperature and frequency on the viscoelastic material properties are considered. An experiment was conducted, for comparison, on a damped cylindrical shell suspended in air by lightweight elastic shock cords and driven at the mid-section by an electromechanical vibration shaker. Good correlations between the test data and analytical solutions were obtained over a wide range of frequencies.     

Space harmonic analysis of sound radiation from a submerged periodic ring-stiffened cylindrical shell

An analytical method is developed to study radiated sound power characteristics from an infinite submerged periodically stiffened cylindrical shell excited by a radial cosine harmonic line force. The harmonic motion of the shell and the pressure field in the fluid are described by Flügge shell equations and Helmholtz equation, respectively. By using periodic theory of space harmonic analysis, the response of the periodic structure to harmonic excitations has been obtained by expanding it in terms of a series of space harmonics. Radiated sound power on the shell wall along the axial direction and the influence of different parameters on the results are studied, respectively. A conclusion is drawn that the stiffeners have a great influence at low and high frequencies while have a slight influence at intermediate frequencies for low circumferential mode orders. The work will give some guidelines for noise reduction of this kind of shell.     

Response of an open curved thin shell to a random pressure field arising from a turbulent boundary layer

A method is presented to predict the root mean square displacement response of an open curved thin shell structure subjected to a turbulent boundary-layer-induced random pressure field. The basic formulation of the dynamic problem is an efficient approach combining classic thin shell theory and the finite element method, in which the finite elements are flat rectangular shell elements with five degrees of freedom per node. The displacement functions are derived from Sanders’ thin shell theory. A numerical approach is proposed to obtain the total root mean square displacements of an open curved thin structure in terms of the cross spectral density of random pressure fields. The cross spectral density of pressure fluctuations in the turbulent pressure field is described using the Corcos formulation. Exact integrations over surface and frequency lead to an expression for the total root mean square displacement response in terms of the characteristics of the structure and flow. An in-house program based on the presented method was developed. The total root mean square displacements of a curved thin blade subjected to turbulent boundary layers were calculated and illustrated as a function of free stream velocity and damping ratio. A numerical implementation for the vibration of a cylinder excited by fully developed turbulent boundary layer flow was presented. The results compared favorably with those obtained using software developed by Lakis and Païdoussis (J. Sound Vib. 25 (1972) 1–27) using cylindrical elements and a hybrid finite element method.     

Buckling of 2D-FG Cylindrical Shells under Combined External Pressure and Axial Compression

This paper presents the stability of two-dimensional functionally graded (2D-FG) cylindrical shells subjected to combined external pressure and axial compression loads, based on classical shell theory. The material properties of functionally graded cylindrical shell are graded in two directional (radial and axial) and determined by the rule of mixture. The Euler's equation is employed to derive the stability equations, which are solved by GDQ method to obtain the critical mechanical buckling loads of the 2D-FG cylindrical shells. The effects of shell geometry, the mechanical properties distribution in radial and axial direction on the critical buckling load are studied and compared with a cylindrical shell made of 1D-FGM. The numerical results reveal that the 2D-FGM has a significant effect on the critical buckling load.     

Existence of axisymmetric modes of thin cylindrical shells with axial displacement restraint

A necessary and sufficient condition is derived for the existence of the axisymmetric mode of cylindrical shells with a radial displacement having one half wave along the axis and axial displacement restrained at both ends. The condition is purely geometric and consists of an upper bound on the mean radius to thickness ratio for a given fixed value of the length to mean radius ratio, above which the mode with one half wave in radial displacement along the axis ceases to exist. The proof is based on enforcing two basic lemmas concerned with the simplicity of the eigenvalues of the shell and the uniform ordering of these eigenvalues with the number of nodes of their corresponding radial displacement eigenfunctions.     

A power transmissibility method for assessing the performance of vibration isolation of building services equipment

Force transmissibility is commonly adopted in building services engineering to assess the performance of vibration isolation. However, it neglects the effect of floor mobility on structure-borne sound power transmitted from a vibratory machine to the floor/roof and the interactions among several contact points between the vibratory machine and the floor/roof. The problem that motivated this study is the occasional occurrence of unsatisfactory performance of vibration isolators observed in building services engineering. This problem may be due to the over-simplification of the vibratory problem in the usual definition of the un-damped force transmissibility or isolation efficiency commonly used in engineering practice. In this paper, use of a “power transmissibility”, which includes the effect of floor mobility and the interaction of all dynamic forces transmitted to the floor through the vibration isolators, is proposed.     

压电管堆式宽带换能器*

研究了一种具有管状叠堆结构的圆管换能器,其敏感元件是由纵向极化压电陶瓷单元组成的薄壁管状压电叠堆,探讨利用管状叠堆纵向和径向振动耦合实现宽带发射。利用压电柱壳振动理论推导了管堆的频率方程,分析了换能器的纵向和径向模态的振动耦合特性。在理论分析的基础上利用有限元方法对换能器的带宽和发射电压响应进行优化并研制换能器样机。测试结果表明,纵向极化的管状压电叠堆结构具有良好的发射电压响应和宽带特性,与理论及仿真结果相符。     

Nonlinear vibrations of electroelastic shells with relatively large shear deformations

A set of two-dimensional nonlinear equations for thin electroelastic shells in vibrations with moderately large thickness-shear deformations are obtained from the variational formulation of the three-dimensional equations of nonlinear electroelasticity by expanding the mechanical displacement vector and the electric potential into power series in the shell thickness coordinate and retaining lower order terms. As an example, the equations are used to study nonlinear thickness-shear vibrations of a circular cylindrical shell driven by an electric voltage. Nonlinear amplitude-frequency behavior of electric current near strong resonance is obtained.     

径向声子晶体隔声特性*

该文构造了由两种匀质材料交替分布的径向声子晶体柱壳模型。首先,针对声波在其中的轴对称传播情况进行了理论分析,建立了声波由内向外传播的传递矩阵,进而导出了声压透射系数和隔声量表达式。采用数值分析的方法系统地讨论了径向声子晶体柱壳的隔声特性,并与单一材质柱壳的传播规律进行对比分析,其次,借助有限元仿真分析的手段对数值结果进行了验证。最后,详细分析了内外流体的特性阻抗对径向声子晶体柱壳隔声特性的影响,得到了相应的参数影响规律。研究表明,径向声子晶体柱壳存在声波带隙,导致其在带隙范围内的隔声效果远远优于单材质柱壳,并且该结构的固有特性突破了质量定律的限制;声波带隙内表面局域态现象出现与否由内外声场和结构场共同决定。     

受振颗粒“毛细”系统中的对流与有序化

将球形颗粒倒入内径较窄的管状容器时,管壁的曲率会对颗粒的堆积结构产生影响,存在壁效应. 实验表明通过连续的竖直方向的振动,壁效应可以被强化,颗粒可以经由对流由无序排列转变为稳定的同轴筒形“壳层”结构. 每一壳层内,颗粒是二维的六角密堆积, 在这一转变过程中,颗粒堆积率的径向分布由初始的衰减振荡转变为等幅振荡. 分析了堆积率的不均匀性及空气在对流中的作用,以及形成“壳层”结构的动力学过程,对“壳层”结构的稳定性亦进行了讨论. 关键词： 颗粒物质 对流 有序化 毛细     

Nonlinear vibrations of clamped-free circular cylindrical shells

Only experimental studies are available on large-amplitude vibrations of clamped-free shells. In the present study, large-amplitude nonlinear vibrations of clamped-free circular cylindrical shell are numerically investigated for the first time. Shells with perfect and imperfect shape are studied. The Sanders-Koiter nonlinear shell theory is used to calculate the elastic strain energy. Shell displacement fields (longitudinal, circumferential and radial) are expanded by means of a double mixed series, i.e. harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. All boundary conditions are satisfied. The system is discretized by using natural modes of the shell and Lagrange equations by an energy approach, retaining damping through Rayleigh's dissipation function. Different expansions involving from 18 to 52 generalized coordinates are used to study the convergence of the solution. The nonlinear equations of motion are numerically studied by using arclength continuation method and bifurcation analysis. Numerical responses to harmonic radial excitation in the spectral neighborhood of the lowest natural frequency are compared with experimental results available in literature. The effect of geometric imperfections and excitation amplitude are numerically investigated and fully explained.     

激光辐照转动充压圆柱壳体热力学效应

 采用有限元计算方法对激光辐照下转动充压壳体的热力学问题进行了较为全面的数值计算，获得了激光辐照下转动内压圆柱壳壁上的温升、应力、应变、位移分布等物理图像，为进一步分析转动充压圆柱壳体在激光辐照下的破坏与失效奠定了基础。提出的解决数值计算中移动热流载荷问题的双时间步长法，可以有效提高计算效率，同时提高计算精度。研究结果表明：对于给定的壳体结构，其损伤阈值时间主要取决于靶面激光强度与壳体旋转频率；在辐照过程中，损伤最先出现在最初受激光辐照的区域。     

Theory and experiments for large-amplitude vibrations of empty and fluid-filled circular cylindrical shells with imperfections

The large-amplitude response of perfect and imperfect, simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of some of the lowest natural frequencies is investigated. Donnell's non-linear shallow-shell theory is used and the solution is obtained by the Galerkin method. Several expansions involving 16 or more natural modes of the shell are used. The boundary conditions on the radial displacement and the continuity of circumferential displacement are exactly satisfied. The effect of internal quiescent, incompressible and inviscid fluid is investigated. The non-linear equations of motion are studied by using a code based on the arclength continuation method. A series of accurate experiments on forced vibrations of an empty and water-filled stainless-steel shell have been performed. Several modes have been intensively investigated for different vibration amplitudes. A closed loop control of the force excitation has been used. The actual geometry of the test shell has been measured and the geometric imperfections have been introduced in the theoretical model. Several interesting non-linear phenomena have been experimentally observed and numerically reproduced, such as softening-type non-linearity, different types of travelling wave response in the proximity of resonances, interaction among modes with different numbers of circumferential waves and amplitude-modulated response. For all the modes investigated, the theoretical and experimental results are in strong agreement.     

A study of the effect of inertia blocks on the stability of the vibratory system and the performance of vibration isolation

Resilient vibration isolators and inertia blocks are commonly used by building services engineers to isolate vibratory machines in buildings. They are selected in practice according to the force transmissibility method and some crude methods or the experience of building services engineers. These methods, however, can produce inaccurate predictions, and a power transmissibility method has recently been proposed to assess the performance of vibration isolation. In this paper, normalized average vibration velocities and overall rotational velocities are proposed to study the stability of the vibratory system. The result shows that the use of an inertia block primarily does not improve the performance of vibration isolation, but does increase the stability of the vibratory system regardless of whether the machine is of even or uneven mass distribution and whether it is driven by the vibratory force or the rocking moment.