Helmholtz水声换能器弹性壁液腔谐振频率研究

针对传统Helmholtz水声换能器设计中刚性壁假设的局限性,将Helmholtz腔体的弹性计入到液腔谐振频率计算中,实现低频弹性Helmholtz水声换能器液腔谐振频率精确设计.基于细长圆柱壳腔体的低频集中参数模型,导出了腔体弹性引入的附加声阻抗表达式,得到了弹性壁条件下Helmholtz水声换能器等效电路图,给出了考虑了末端修正的弹性壁Helmholtz共振腔液腔谐振频率计算公式.利用ANSYS软件建立了算例模型,仿真分析了不同材质、半径、长度时的Helmholtz共振腔液腔谐振频率.结果对比表明弹性理论值与仿真值符合得很好,相比起传统的刚性壁理论计算结果,本文的弹性壁理论得出的液腔谐振频率值有所降低,与真实情况更加接近.本文的结论可以为精确设计低频弹性Helmholtz水声换能器提供理论支持.     

Analytical modeling of squeeze film damping for rectangular elastic plates using Green's functions

An analytical method for the solution of squeeze film damping based on Green's function to the nonlinear Reynolds equation considering an elastic plate is presented. This allows calculating the stiffness and damping forces rapidly for various boundary conditions. The elastic plate velocity is applied to the nonlinear Reynolds equation as a forcing term. The nonlinear Reynolds equation is divided into multiple linear nonhomogeneous Helmholtz equations, which then can be solvable using the presented approach. Approximate mode shapes of a rectangular elastic plate are used, enabling the calculation of the damping ratio and frequency shift for the linear case, as well as the complex resistant pressure, for both linear and nonlinear cases.     

Interaction of a plane progressive sound wave with a functionally graded spherical shell

An exact analysis is carried out to study interaction of a time-harmonic plane progressive sound field with a radially inhomogeneous thick-walled elastic isotropic spherical shell suspended in and filled with compressible ideal fluid mediums. Using the laminated approximation method, a modal state equation with variable coefficients is set up in terms of appropriate displacement and stress functions and their spherical harmonics. Taylor’s expansion theorem is then employed to obtain the solution to the modal state equation ultimately leading to calculation of a global transfer matrix. Numerical example is given for a water-submerged/air-filled Aluminum/Zirconia elastic spherical sandwich shell containing a functionally graded interlayer and subjected to an incident progressive plane sound wave. The mechanical properties of the interlayer are assumed to vary smoothly and continuously across the thickness with the change of volume concentration of its constituents. The effect of incident wave frequency, thickness and compositional gradient of the interlayer on the form function amplitude and the average radiation force acting on the composite shell are examined. Limiting cases are considered and fair agreements with well-known solutions are established.     

Formulas for the H/V ratio (ellipticity) of Rayleigh waves in orthotropic elastic half-spaces

ABSTRACT

This paper concerns the propagation of Rayleigh waves in compressible and incompressible orthotropic elastic half-spaces. The main aim of the paper is to derive formulas for the H/V ratio (ellipticity) of Rayleigh waves. First, the expression of the H/V ratio in terms of the Rayleigh wave velocity for compressible orthotropic elastic half-spaces is derived using the surface impedance matrix. From this expression and the secular equation of Rayleigh waves, the equation for the H/V ratio is obtained. It is a cubic equation. Employing the theory of cubic equations, the formula for the H/V ratio for compressible orthotropic elastic half-spaces has been derived. The H/V ratio formula for incompressible orthotropic elastic half-spaces has been obtained using the incompressible limit method. Since the H/V ratio of Rayleigh waves is a good tool for nondestructively evaluating mechanical properties of structures before and during loading, the obtained formulas will be very significant in practical applications.     

Instability of single-walled carbon nanotubes conveying Jeffrey fluid

We report instability of the single-walled carbon nanotubes(SWCNT) filled with non-Newtonian Jeffrey fluid.Our objective is to get the influences of relaxation time and retardation time of the Jeffrey fluid on the vibration frequency and the decaying rate of the amplitude of carbon nanotubes.An elastic Euler-Bernoulli beam model is used to describe vibrations and structural instability of the carbon nanotubes.A new vibration equation of an SWCNT conveying Jeffrey fluid is first derived by employing Euler-Bernoulli beam equation and Cauchy momentum equation taking constitutive relation of Jeffrey fluid into account.The complex vibrating frequencies of the SWCNT are computed by solving a cubic eigenvalue problem based upon differential quadrature method(DQM).It is interesting to find from computational results that retardation time has significant influences on the vibration frequency and the decaying rate of the amplitude.Especially,the vibration frequency decreases and critical velocity increases with the retardation time.That is to say,longer retardation time makes the SWCNT more stable.     

Generalization of the rotated parabolic equation to variable slopes

The rotated parabolic equation [J. Acoust. Soc. Am. 87, 1035-1037 (1990)] is generalized to problems involving ocean-sediment interfaces of variable slope. The approach is based on approximating a variable slope in terms of a series of constant slope regions. The original rotated parabolic equation algorithm is used to march the field through each region. An interpolation-extrapolation approach is used to generate a starting field at the beginning of each region beyond the one containing the source. For the elastic case, a series of operators is applied to rotate the dependent variable vector along with the coordinate system. The variable rotated parabolic equation should provide accurate solutions to a large class of range-dependent seismo-acoustics problems. For the fluid case, the accuracy of the approach is confirmed through comparisons with reference solutions. For the elastic case, variable rotated parabolic equation solutions are compared with energy-conserving and mapping solutions.     

Spatial resonance in a small artery excited by vibration input as a possible mechanism to cause hand–arm vascular disorders

Hand–arm vibration syndrome (HAVS) is collectively a vasospastic and neurodegenerative occupational disease. One of the major symptoms of HAVS is vibration white finger (VWF) caused by exaggerated vasoconstriction of the arteries and skin arterioles. While VWF is a very painful and costly occupational illness, its pathology has not been well understood. In this study a small artery is modeled as a fluid filled elastic tube whose diameter changes along the axial direction. Equations of motion are developed by considering interactions between the fluid, artery wall and soft-tissue bed. It is shown that the resulting wave equation is the same as that of the basilar membrane in the cochlea of mammals. Therefore, the artery system shows a spatial resonance as in the basilar membrane, which responds with the highest amplitude at the location determined by the vibration frequency. This implies that a long-term use of one type of tool will induce high-level stresses at a few identical locations of the artery that correspond to the major frequency components of the tool. Hardening and deterioration of the artery at these locations may be a possible cause of VWF.     

Elastic properties of composites: periodical homogenisation technique and experimental comparison using acoustic microscopy and resonant ultrasonic spectroscopy

The macroscopic elastic properties of two composites (Duralumin/air and Duralumin/tungsten carbide (WC)) have been calculated using periodical homogenisation methods and the elastic properties of each phase (measured by high frequency acoustic microscopy). In order to check the validity of such an approach, acoustical resonant spectroscopy has also been applied. Thanks to the comparison between the resonant frequencies predicted and measured, two major conclusions have been obtained: the homogenisation method is very accurate for the composite Duralumin/air, but not for the Duralumin/WC sample: the experimental results are not in very good agreement with the simulation. This result can be then explained by the major role of interfacial state between Duralumin and tungsten carbide.     

On the equilibrium equation for a generalized biological membrane energy by using a shape optimization approach

A mechanical equilibrium equation of a vesicle membrane under a generalized elastic bending energy is obtained in this paper. Moreover, the derivation of this equilibrium equation is based on some shape optimization tools. This approach is new and more concise than the tensorial tools used previously for this problem.     

A mapping approach for handling sloping interfaces

A mapping approach for handling sloping interfaces in parabolic equation solutions is developed and tested. At each range, the medium is rigidly translated vertically so that a sloping interface becomes horizontal. To simplify the approach, the slope is assumed to be small and the extra terms that arise in the wave equation under the mapping are neglected. The effects of these terms can be approximately accounted for by applying a leading-order correction to the phase. The mapping introduces variations in topography, which are relatively easy to handle for the case of a pressure-release boundary condition. The accuracy of the approach is demonstrated for problems involving fluid sediments. The approach should also be accurate for problems involving elastic sediments and should be useful for solving three-dimensional problems involving variable topography.     

Stationary shapes of deformable particles moving at low Reynolds numbers

We introduce an iterative solution scheme in order to calculate stationary shapes of deformable elastic capsules which are steadily moving through a viscous fluid at low Reynolds numbers. The iterative solution scheme couples hydrodynamic boundary integral methods and elastic shape equations to find the stationary axisymmetric shape and the velocity of an elastic capsule moving in a viscous fluid governed by the Stokes equation. We use this approach to systematically study dynamical shape transitions of capsules with Hookean stretching and bending energies and spherical resting shape sedimenting under the influence of gravity or centrifugal forces. We find three types of possible axisymmetric stationary shapes for sedimenting capsules with fixed volume: a pseudospherical state, a pear-shaped state, and buckled shapes. Capsule shapes are controlled by two dimensionless parameters, the Föppl-von-Kármán number characterizing the elastic properties and a Bond number characterizing the driving force. For increasing gravitational force the spherical shape transforms into a pear shape. For very large bending rigidity (very small Föppl-von-Kármán number) this transition is discontinuous with shape hysteresis. The corresponding transition line terminates, however, in a critical point, such that the discontinuous transition is not present at typical Föppl-von-Kármán numbers of synthetic capsules. In an additional bifurcation, buckled shapes occur upon increasing the gravitational force.     

Surface stress of curved solid-fluid interfaces

The effects of curvature on elastic deformations have been analysed. The work of stretching a spherical solid-fluid interface has been split into two contributions which allow one to define a tangential surface stress and a normal surface stress. It is shown that only the latter can be identified with the mechanical surface stress appearing in Laplace's equation. The Shuttleworth equation is modified to include the excess of volume deformation.     

Characteristics of wave propagation and energy distributions in cylindrical elastic shells filled with fluid

The dispersion behaviour and energy distributions of free waves in thin walled cylindrical elastic shells filled with fluid are investigated. Dispersion curves are presented for a range of parameters and the behaviour of individual branches is explained. A non-dimensional equation which determines the distribution of vibrational energy between the shell wall and the contained fluid is derived and its variation with frequency and material parameters is studied.     

Kinematic waves in a liquefied paste

Paste means a dense mass of small unconsolidated (i.e., not joined together) solid particles with the pore-spaces completely filled with either gas or liquid. Liquefaction, here, means the conversion of its nature from that of a solid to that of a fluid by the application of mechanical motion; it can have, individually, either industrial applications or catastrophic consequences. The range of volume concentrations of the solid is very narrow in the liquefied state, and the liquefaction process requires that the mechanical motions be of relatively large amplitude and low frequency. The actual mechanism of the process is obscure; one is postulated here. It involves kinematic travelling waves, one in each phase, that do not utilize elastic processes, the energy and pressure amplitudes being much less than elastic dilatational waves would entail. Coupling between the waves is by conservative (inertial) forces and the dilatational phenomenon in each arises from the longitudinal spacing of the particles. The mass of each particle is its virtual mass. A plane sinusoidal wave is considered and expressions for wave velocity, phase constant, stress and concentration (as well as quantities analogous to “elasticity” and “elastic condensation”) are deduced. Some measured values of wave velocity and pressure amplitudes are reported and discussed in the light of the hypothesis.     

磁流变液构成的类梯度结构振动传递特性

提出了一种磁流变液构成的类梯度结构,并通过理论建模、数值计算和实验研究了该结构的振动传递特性.磁流变液在磁场作用下具有液固转换的特殊理化性质,而液固转换过程就是磁流变液的振动传递阻抗变化过程.因此,基于磁流变液的这一特性,通过控制磁场,构建了类梯度结构.基于弹性波传递的一维波动方程,建立了垂直入射的弹性波在类梯度结构中传递的波动方程.然后,使用连续介质的离散化方法和传递矩阵法进行求解,得到振级落差的表达式,对其进行数值计算,分析类梯度结构的振级落差随弹性波频率和磁场强度的变化趋势.最后,对类梯度结构的振动传递特性进行了实验研究,分析了磁场强度对类梯度结构振动传递特性的影响.研究结果表明,与均匀场作用的磁流变液相比,类梯度结构对弹性波的衰减效果更好,且该结构具备良好的可调控特性.     

Molecular dynamics simulation study on mechanical responses of nanoindented monolayer-graphene-nanoribbon

We investigated the mechanical responses of the nanoindented graphene-nanoribbon (GNR)-resonator using classical molecular dynamics simulations. The nanoindented force in this work was applied to the GNR's local point and then, GNR-resonator's frequency could be tuned by a nanoindented depth. We found the hardening or the softening of the GNR during its nanoindented-deflections, and such properties were recognized by the shift of the resonance frequency. The linear elastic regime in low applied force is explicitly separated with the non-linear elastic regime in high applied force. In particular, at the threshold point, a very small change of the nanoindented depth can cause great change in the resonance frequency, and this property can enable the GNR to be applied to electromechanical relay switching devices and the quantum-computer in quantum-mechanical coupling as well as mass detectors, pressure sensors, accelerometers, and alarms.     

Nonlinear wave processes in porous waterlike media containing a system of capillaries partially filled with a viscous liquid

A nonlinear dynamic state equation of waterlike porous material that contains a system of cylindrical capillaries partially filled with viscous liquid was received. It is shown that an acoustic nonlinearity of such media contains the relaxation elastic and inelastic components due to the nonlinear dependence of the capillary and viscous pressure in fluid on the capillary diameter. For the medium, theoretical study of such nonlinear phenomena as generation of the second harmonic and a difference frequency wave, self-demodulation of high-frequency pulses as well as the change in the propagation velocity and absorption coefficient of a test wave being under an action of static loading have been carried out. The frequency dependences of medium nonlinearity parameters for these processes were determined.     

球形粒子在Bessel波束照射下的轴向辐射力计算和分析

通过声散射理论,将水中粒子的Bessel波束声散射场的分波序列(PWS)表达公式加以推广,进而推导出声辐射力的表达公式,获得了液体球及弹性球在Bessel波束下声辐射力的变化规律。通过观察不同散射角形态函数,可发现声辐射力的产生与粒子背向散射抑制程度有关。对于液体球粒子,球壳厚度及材料介质对粒子声辐射力有着重要的影响,同时Bessel波束波锥角越大,产生负声辐射力的可能性越大。对于弹性球和弹性单层壳粒子,声辐射力的产生与其本身的共振特征存在很大的关系。同时,通过改变球壳内介质及壳层厚度的方法,可增加产生的负声辐射力的频率范围及幅值强度.      

Acoustic Localization in Weakly Compressible Elastic Media Permeated with Air Bubbles

The propagation of longitudinal acoustic waves in weakly compressible elastic media permeated with air bubbles is investigated on the basis of the radial pulsation equation of a single bubble. The multiple scattering of waves in such media is rigorously described by using a self-consistent approach. Theoretical results show that there exists strong acoustic localization in a range of frequency slightly above the bubble resonance frequency, even for a very small volume fraction of bubbles. Further study reveals that the localization is in fact attributed to collection behaviour of bubbles, allowing for an efficient cancellation of propagating waves. This is essentially consistent with the known conclusions recently drawn for bubbly liquid by Kou et al. [2003 Appl. Phys. Left. 83 4247]