Determination of dynamic characteristics of rectangular plates with cutouts using a finite difference formulation

The paper describes a method for the prediction of dynamic characteristics of rectangular plates with cutouts. The method is based on the use of variational principles in conjunction with finite difference technique. A concept of interlacing grids has been developed to express the strain energy of nodal subdomains into which the plate is divided. The use of this idea has been demonstrated in relation to internal and boundary nodes. Natural frequencies and corresponding mode shapes of rectangular plates with one and two cutouts have been predicted and experimentally verified.     

Frequency fine-tuning in Class IV flextensional transducers

Class IV flextensional transducers (FTs) are the best-known FTs in literature. These are light-weight projectors (compared to the conventional Tonpilz designs) with capability for high power delivery at low frequencies. The resonance frequencies of this type of transducers are known to be dominantly dependent on the characteristics of the outer shell than on the driver stack. Consequently, the method of achieving fine-tuning of the transducer by modifying the characteristics of the stack, as practiced in the case of Tonpilz designs, is not very effective. This paper describes a method for fine-tuning of the frequency of a Class IV FT, which involves only a modification of a pair of small components used for coupling the stack to the transducer. The effectiveness of the method is examined by finite element modelling using the package ATILA, in the case of a 3 kHz aluminium shell transducer. Experimental results are also presented.     

DYNAMIC STABILITY OF CURVED PANELS WITH CUTOUTS

The parametric instability behaviour of curved panels with cutouts subjected to in-plane static and periodic compressive edge loadings are studied using finite element analysis. The first order shear deformation theory is used to model the curved panels, considering the effects of transverse shear deformation and rotary inertia. The theory used is the extension of dynamic, shear deformable theory according to Sanders' first approximation for doubly curved shells, which can be reduced to Love's and Donnell's theories by means of tracers. The effects of static and dynamic load factors, geometry, boundary conditions and the cutout parameters on the principal instability regions of curved panels with cutouts are studied in detail using Bolotin's method. Quantitative results are presented to show the effects of shell geometry and load parameters on the stability boundaries. Results for plates are also presented as special cases and are compared with those available in the literature.     

Vibrations of circular cylindrical shells with cutouts

An experimental and analytical study was carried out to examine the effect of circular cutouts on the resonant frequencies of thin cylindrical shells. The experimental results were obtained from tests performed on clamped-free aluminum cylinders and clamped ring-stiffened tri-acetyl cellulose shells with a lap-joint seam. The analytical solution was a simplified Rayleigh-Ritz type approximation. For the beam type mode, the circular cutouts had a significant influence on the frequency. For the mode with higher numbers of circumferential waves, however, the cutouts had a relatively small effect on the frequency spectra.     

含玻璃微球的黏弹性复合材料覆盖层的水下吸声性能分析

水下吸声覆盖层对潜艇的隐身具有重要的意义, 因此得到了广泛的关注. 本文对含有玻璃微球的黏弹性复合材料覆盖层的水下吸声性能进行了理论分析. 采用等效参数法计算了玻璃微球的体积含量对复合材料的力学和声学性能的影响. 应用声波在多层介质中传播的一维模型, 计算了不同玻璃微球体积含量的单层复合材料覆盖层的吸声性能.结果表明, 增加玻璃微球的体积含量可以提高覆盖层的低频吸声性能, 但是其高频吸声性能降低.采用遗传算法对玻璃微球在覆盖层厚度方向上的体积含量分布进行优化. 优化的多层结构可以在一定的频带内改善覆盖层的表面与水的声阻抗匹配, 在保证覆盖层的高频吸声系数大于某一限值(0.7)的前提下, 提高其低频吸声性能.另外, 多层优化结构覆盖层不含宏观的空腔结构, 不影响覆盖层的耐压性能.其结构简单, 对制备工艺的要求不高.因此, 本文形成的理论方法适用于水下吸声覆盖层的设计. 关键词： 水下吸声 黏弹性复合材料 玻璃微球 遗传算法     

Dynamic behaviour of a cylindrical shell with a cutout

This paper presents the results of analytical and experimental investigations connected with the dynamic behaviour of a cylindrical shell with a rectangular cutout. The finite element method is used to predict the vibration frequencies and mode shapes. The resulting eigenvalue problems are solved by using a simultaneous iteration technique. The analytical study shows the influence of the cutout on the natural frequencies and mode shapes of the shell. The subtended angle of the cutout ranges from 40° to 120°. Experimental verification was performed on a machined mild steel shell having welded end rings bolted on to sturdy supports. A reasonably good agreement is obtained, with the discrepancies of the order of less than 10 %. The cutout is found to have very little influence on the natural frequencies.     

Current distribution and giant magnetoimpedance in composite wires with helical magnetic anisotropy

The giant magnetoimpedance effect in composite wires consisting of a non-magnetic inner core and soft magnetic shell is studied theoretically. It is assumed that the magnetic shell has a helical anisotropy. The current and field distributions in the composite wire are found by means of a simultaneous solution of Maxwell equations and the Landau–Lifshitz equation. The expressions for the diagonal and off-diagonal impedance are obtained for low and high frequencies. The dependences of the impedance on the anisotropy axis angle and the shell thickness are analyzed. Maximum field sensitivity is shown to correspond to the case of the circular anisotropy in the magnetic shell. It is demonstrated that the optimum shell thickness to obtain maximum impedance ratio is equal to the effective skin depth in the magnetic material.     

Smearing technique for vibration analysis of simply supported cross-stiffened and doubly curved thin rectangular shells

Plates stiffened with ribs can be modeled as equivalent homogeneous isotropic or orthotropic plates. Modeling such an equivalent smeared plate numerically, say, with the finite element method requires far less computer resources than modeling the complete stiffened plate. This may be important when a number of stiffened plates are combined in a complicated assembly composed of many plate panels. However, whereas the equivalent smeared plate technique is well established and recently improved for flat panels, there is no similar established technique for doubly curved stiffened shells. In this paper the improved smeared plate technique is combined with the equation of motion for a doubly curved thin rectangular shell, and a solution is offered for using the smearing technique for stiffened shell structures. The developed prediction technique is validated by comparing natural frequencies and mode shapes as well as forced responses from simulations based on the smeared theory with results from experiments with a doubly curved cross-stiffened shell. Moreover, natural frequencies of cross-stiffened panels determined by finite element simulations that include the exact cross-sectional geometries of panels with cross-stiffeners are compared with predictions based on the smeared theory for a range of different panel curvatures. Good agreement is found.     

Natural frequency split estimation for inextensional vibration of imperfect hemispherical shell

In this study, mathematical model of hemispherical shell is introduced using inextensional vibration mode shapes. Adopting energy equations, the natural frequency of the shell is determined by applying Rayleigh's energy method. Further, the vibration for imperfect shell is investigated with point mass elements representing imperfections on the structures. Also, the effects are considered via energy relations, and the split amount of the natural frequencies can be determined. Finally, the influences of point mass are presented by explicit functions for the split of the natural frequency and shifting angle of mode orientation. Based on the proposed model of imperfect shell with multiple point masses, the structure can be expressed as an equivalent single mass model.     

A spurious frequencies suppression method for optical frequency comb based microwave photonic filter

The traditional optical frequency comb (OFC) based microwave photonic filters (MPFs) are rigidly restricted to be operated in a single “Nyquist zone”, as varieties of spurious frequencies signals coexist in the output. Here, a method for spurious frequencies suppression in the OFC‐based MPF is proposed and experimentally demonstrated. The method is achieved by applying group velocity dispersion on the carrier combs to separate the filter transfer functions of the spurious frequencies from that of the input radio frequency signal. It is fairly simple and effective, and has no effect on the filter characteristic. With this method, the filter pass band can be freely tuned without the limitation of the “Nyquist zone”. It can be considered as a step forward for the practical application of the OFC‐based MPF.     

Axisymmetric vibrations of a viscous-fluid-filled piezoelectric spherical shell and the associated radiation of sound

Axisymmetric vibrations of a viscous-fluid-filled piezoelectric sphere, with radial polarization, submerged in a compressible viscous fluid medium are investigated. The oscillations are harmonically driven by an axisymmetrically applied electric potential difference across the surface of the shell. A theoretical formulation cast the piezoelectric shell problem into a corresponding problem of an elastic shell with the contribution of piezoelectricity confined to slightly modified in vacuum natural frequencies and their associated mode shapes. It is noted that the fluid inside the shell will have a dominating influence on the vibrational characteristics of the submerged shell. The circular components of the natural frequency spectra closely follow those of the fluid-filled shell in vacuo. Furthermore, the corresponding damping components of those natural frequencies are rather small, making acoustic radiation and under-damped oscillation possible for an infinite number of natural frequencies. The characteristics of natural frequencies are elucidated using a fluid-filled polyvinglindene fluoride (PVDF) shell submerged in both air and water as an example. It is found that the piezoelectric parameters that contribute to the shell's natural frequencies is of a small order for thin PVDF shells, and is thereby negligible. It is noted that, with the mechanical constant typically associated with piezoelectric materials, fluid viscosity could have a significant effect on some vibrations. In certain cases, a natural frequency associated with a minimum viscous damping and a maximum of total damping (indicating highly efficient acoustic radiation) is possible with such a frequency.The vibrational characteristics, fluid loading, and energy flow are evaluated for a fluid-filled PVDF shell submerged in air and water. The inclusion of fluid inside the shell is shown to produce various narrow band peaks responses, vibrational absorbing frequencies, and non-dissipating frequencies. Those vibrational characteristics could have many potential applications. For example, the interior fluid could offer the option of generating a desired narrow band near resonant sound radiation while keeping power dissipation due to fluid viscosity to a minimum. Those well-defined narrow band characteristics also open up possibilities of using a vibrating, fluid-filled shell as a micro scale sensor for sensing and detection applications.     

Effective medium theory applied to frequency selective surfaces on periodic substrates

We apply the effective medium theory combined with the conventional periodic method of moments （MoM） to analyze frequency selective surfaces （FSSs） on periodic and anisotropic substrates. Based on the effective medium theory, even periodic and anisotropic substrates can be considered homogeneous; thus, the Green’s function can be obtained. The resulting integral equation can then be solved by the MoM using rooftop basis functions and Galerkin testing functions. We analyze an example using this technique, and the numerical results agree with Fallahi’s full-vector semi-analytical method, showing an increasing difference between the results as the frequencies increase. These results show that the proposed method is effective for analyzing FSSs on periodic and anisotropic substrates.     

LOCALIZED FAMILIES OF BENDING WAVES IN A THIN MEDIUM-LENGTH CYLINDRICAL SHELL UNDER PRESSURE

The initial-boundary-value problem for the equations describing motion of a thin, medium-length, non-circular cylindrical shell is examined. The shell edges are not necessarily plane curves, with the conditions of a joint support, a rigid clamp or a free edge being considered as the boundary conditions. The shell is supposed to experience normal internal (or external) dynamic pressure which may be non-uniform in the circumferential direction. It is assumed that the initial displacements and velocities of the points at the shell middle surface are functions decreasing rapidly away from some generatrix. Using the complex WKB method the asymptotic solution of the governing equations is constructed by superimposing localized families (wave packets) of bending waves running in the circumferential direction. The dependence of frequencies, group velocities, amplitudes and other dynamic characteristics upon variable pressure and geometrical parameters of the shell are studied. As an example, the wave forms of motion of a circular cylindrical shell with sloping edges under growing dynamic pressure are considered. The effect of localization of bending vibrations near the longest generator as well as the effects of reflection, focusing and increasing amplitude in the running wave packets are revealed.     

Stresses in shell structures

In this paper the stresses obtained for various (thin) shell structures by using two types of doubly curved finite elements are compared with published information. One of the elements—a ring shell element—is designed to analyze axisymmetric structures such as cylinders and hyperboloids. The accuracy and convergence of this element is shown to be excellent. The other element—a quadrilateral shell element—is designed to calculate stresses, mode shapes and frequencies of axisymmetric structures as well as sections of shell structures. The quadrilateral element is more versatile than the ring element. However, it is found that the convergence of the ring element is superior to that of the quadrilateral element. The resonant stresses of a hyperboloidal shell structure have been presented, and, as far as the author is aware, a similar investigation has not previously been reported in the literature. Whilst the primary purpose of the paper is to examine the usefulness of the two doubly curved elements in the analysis of shell structures, the examples considered in the text are described in detail to facilitate comparative structures by future investigators.     

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.     

FREE VIBRATION OF A PARTIALLY LIQUID-FILLED AND SUBMERGED, HORIZONTAL CYLINDRICAL SHELL

The dynamic characteristics (i.e., natural frequencies and mode shapes) of a partially filled and/or submerged, horizontal cylindrical shell are examined. In this investigation, it is assumed that the fluid is ideal, and fluid forces are associated with inertial effects only: namely, the fluid pressure on the wetted surface of the structure is in phase with the structural acceleration. The in vacuo dynamic characteristics of the cylindrical shell are obtained using standard finite element software. In the “wet” part of the analysis, it is assumed that the shell structure preserves its in vacuo mode shapes when in contact with the contained and/or surrounding fluid and that each mode shape gives rise to a corresponding surface pressure distribution of the shell. The fluid-structure interaction effects are calculated in terms of generalized added masses, using a boundary integral equation method together with the method of images in order to impose an appropriate boundary condition on the free surface. To assess the influence of the contained and/or surrounding fluid on the dynamic behaviour of the shell structure, the wet natural frequencies and associated mode shapes were calculated and compared with available experimental measurements.     

A detailed investigation of the electronic properties of a multi-layer spherical quantum dot with a parabolic confinement

In this work, we aim a detailed investigation of the electronic properties of a spherical multi-layer quantum dot with and without a hydrogenic impurity. The structure is introduced in the form of core/shell/well/shell layers. The core and well layers are defined by the parabolic electronic potentials. We carry out the effect of the core radius and layer thickness on the energy levels, their wave functions, binding energies of the impurity and the probability distributions. In order to determine the sublevel eigenvalues and eigenfunctions, the Schrödinger equation is solved full numerically by shooting method in the frame of the effective mass approximation. The results are analyzed in detail as a function of the layer thicknesses and their probable physical reasons are tried to be explained. It is found that the electronic properties and impurity binding energies are strongly depending on the layer thicknesses.     

Axial acoustic radiation force on an elastic spherical shell near an impedance boundary for zero-order quasi-Bessel–Gauss beam

Shell structures have increasingly widespread applications in biomedical ultrasound fields such as contrast agents and drug delivery,which requires the precise prediction of the acoustic radiation force under various circumstances to improve the system efficiency.The acoustic radiation force exerted by a zero-order quasi-Bessel-Gauss beam on an elastic spherical shell near an impedance boundary is theoretically and numerically studied in this study.By means of the finite series method and the image theory,a zero-order quasi-Bessel-Gauss beam is expanded in terms of spherical harmonic functions,and the exact solution of the acoustic radiation force is derived based on the acoustic scattering theory.The acoustic radiation force function,which represents the radiation force per unit energy density and per unit cross-sectional surface,is especially investigated.Some simulated results for a polymethyl methacrylate shell and an aluminum shell are provided to illustrate the behavior of acoustic radiation force in this case.The simulated results show the oscillatory property and the negative radiation force caused by the impedance boundary.An appropriate relative thickness of the shell can generate sharp peaks for a polymethyl methacrylate shell.Strong radiation force can be obtained at small half-cone angles and the beam waist only affects the results at high frequencies.Considering that the quasi-Bessel-Gauss beam possesses both the energy focusing property and the non-diffracting advantage,this study is expected to be useful in the development of acoustic tweezers,contrast agent micro-shells,and drug delivery applications.     

Free vibrations of elastic circular toroidal shells

In this paper, the free vibrations of elastic in vacuo circular toroidal shells under different boundary conditions are studied using the linear Sanders thin shell theory. Beam functions are used to describe the motion along the meridional direction whilst trigonometric functions are used to represent the deformation of the cross section. It is shown that both the natural frequencies and the mode shapes can be accurately predicted as long as the employed beam functions satisfy the boundary conditions at the ends of the shells. The dependence of the free vibration characteristics of an elastic toroidal shell upon boundary conditions and toroidal to cross-sectional radius ratio is also illustrated and explained in this paper.     

AN ANALYTICAL APPROACH TO DETERMINING THE DYNAMIC CHARACTERISTICS OF A CYLINDRICAL SHELL WITH CLOSING CRACKS

The paper is devoted to developing mathematical models of the elastic oscillations of a cylindrical shell with surface closing cracks. The respective forms of shell vibrations have been chosen to represent various types of damage of the shell. In the case of dispersed and single-surface damage, the transverse shell vibrations are simulated. The cycle of vibrations is assumed to be subdivided into two parts, in one of them the damaged surface fibers are compressed so closing the cracks and negating their influence. For the second part, the cracks are open, so their influence is taken into account. The problem is solved in a piecewise linear with different frequencies and amplitudes at each vibrations cycle interval. The vibration parameters are calculated by means of Relay's energy conservation method and are represented by analytical expressions, the system being assumed to be conservative. The functions determining the vibration process are decomposed by a Fourier analysis using the averaged frequency, the coefficients of the resulting series being obtained as analytical expressions. Vibrodiagnostic functions, which enable the geometrical parameters of the cracks to be determined depending on the geometry of the shell and type of damage, have been plotted.