Hybrid finite element method applied to supersonic flutter of an empty or partially liquid-filled truncated conical shell

In this study, aeroelastic analysis of a truncated conical shell subjected to the external supersonic airflow is carried out. The structural model is based on a combination of linear Sanders thin shell theory and the classic finite element method. Linearized first-order potential (piston) theory with the curvature correction term is coupled with the structural model to account for pressure loading. The influence of stress stiffening due to internal or external pressure and axial compression is also taken into account. The fluid-filled effect is considered as a velocity potential variable at each node of the shell elements at the fluid-structure interface in terms of nodal elastic displacements. Aeroelastic equations using the hybrid finite element formulation are derived and solved numerically. The results are validated using numerical and theoretical data available in the literature. The analysis is accomplished for conical shells of different boundary conditions and cone angles. In all cases the conical shell loses its stability through coupled-mode flutter. This proposed hybrid finite element method can be used efficiently for design and analysis of conical shells employed in high speed aircraft structures.     

Vibro-acoustic design sensitivity analysis using the wave-based method

Conventional element-based methods, such as the finite element method (FEM) and boundary element method (BEM), require mesh refinements at higher frequencies in order to converge. Therefore, their applications are limited to low frequencies. Compared to element-based methods, the wave-based method (WBM) adopts exact solutions of the governing differential equation instead of simple polynomials to describe the dynamic response variables within the subdomains. As such, the WBM does not require a finer division of subdomains as the frequency increases in order to exhibit high computational efficiency. In this paper, the design sensitivity formulation of a semi-coupled structural-acoustic problem is implemented using the WBM. Here, the results of structural harmonic analyses are imported as the boundary conditions for the acoustic domain, which consists of multiple wave-based subdomains. The cross-sectional area of each beam element is considered as a sizing design variable. Then, the adjoint variable method (AVM) is used to efficiently compute the sensitivity. The adjoint variable is obtained from structural reanalysis using an adjoint load composed of the system matrix and an evaluation of the wave functions of each boundary. The proposed sensitivity formulation is subsequently applied to a two-dimensional (2D) vehicle model. Finally, the sensitivity results are compared to the finite difference sensitivity results, which show good agreement.     

Two-dimensional analysis of fluid motion in the cochlea resulting from compressional bone conduction

Fluid motion resulting from the compressional excitation of the cochlear capsule due to bone conduction is examined in this paper. Vibrations of the skull deform the shape of the cochlear capsule and give rise to motion the fluid. A two-dimensional channel having a height to length ratio equal to ε is used to model the cochlea. The cochlear pressure is expressed as an integral equation in the cochlear partition velocity. In the limit as ε approaches zero the integral equation is solved and the cochlear pressure is expressed as an asymptotic expansion in ε. Rapid spatial variation in the velocity of the cochlear partition requires one to treat high-order fluid modes within the cochlear fluid. Hence, evanescent pressure modes are included in the analysis. Asymmetry in the oval and the round window velocity is shown to give rise to a pressure gradient across the cochlear partition and basilar membrane displacement. The vibration amplitude of the cochlear partition is shown to depend on the value of the ratio of the oval and the round window impedance.     

Sharp interface immersed-boundary/level-set method for wave–body interactions

A sharp interface Cartesian grid method for the large-eddy simulation of two-phase turbulent flows interacting with moving bodies is presented. The overall approach uses a sharp interface immersed boundary formulation and a level-set/ghost–fluid method for solid–fluid and fluid–fluid interface treatments, respectively. A four-step fractional-step method is used for velocity–pressure coupling, and a Lagrangian dynamic Smagorinsky subgrid-scale model is adopted for large-eddy simulations. A simple contact angle boundary condition treatment that conforms to the immersed boundary formulation is developed. A variety of test cases of different scales ranging from bubble dynamics, water entry and exit, landslide-generated waves, to ship hydrodynamics are performed for validation. Extensions for high Reynolds number ship flows using wall-layer models are also considered.     

A SEMI-ANALYTICAL COUPLED FINITE ELEMENT FORMULATION FOR COMPOSITE SHELLS CONVEYING FLUIDS

A coupled formulation based on the semi-analytical finite element technique is developed for composite shells conveying fluid. The structural finite element formulation is from Ramasamy and Ganesan (1998 Computers and Structures70, 363-376), while the fluid part is modelled by the characteristic wave equation. The fluid part is modelled using a velocity potential formulation and the dynamic pressure acting on the walls is derived from Bernoulli's equation. Impermeability and dynamic condition are imposed on the fluid-structure interface. The finite element equations for the composite shell conveying fluid are validated using available results in the literature. A detailed parametric study is carried out for various boundary conditions as well as for different length-to-radius and radius-to-thickness ratios.     

A two-dimensional cochlear fluid model based on conformal mapping

Using conformal mapping, fluid motion inside the cochlear duct is derived from fluid motion in an infinite half plane. The cochlear duct is represented by a two-dimensional half-open box. Motion of the cochlear fluid creates a force acting on the cochlear partition, modeled by damped oscillators. The resulting equation is one-dimensional, more realistic, and can be handled more easily than existing ones derived by the method of images, making it useful for fast computations of physically plausible cochlear responses. Solving the equation of motion numerically, its ability to reproduce the essential features of cochlear partition motion is demonstrated. Because fluid coupling can be changed independently of any other physical parameter in this model, it allows the significance of hydrodynamic coupling of the cochlear partition to itself to be quantitatively studied. For the model parameters chosen, as hydrodynamic coupling is increased, the simple resonant frequency response becomes increasingly asymmetric. The stronger the hydrodynamic coupling is, the slower the velocity of the resulting traveling wave at the low frequency side is. The model's simplicity and straightforward mathematics make it useful for evaluating more complicated models and for education in hydrodynamics and biophysics of hearing.     

Dynamics of a rectangular plate resting on an elastic foundation and partially in contact with a quiescent fluid

In this study, a method of analysis is presented for investigating the effects of elastic foundation and fluid on the dynamic response characteristics (natural frequencies and associated mode shapes) of rectangular Kirchhoff plates. For the interaction of the Kirchhoff plate–Pasternak foundation, a mixed-type finite element formulation is employed by using the Gâteaux differential. The plate finite element adopted in this study is quadrilateral and isoparametric having four corner nodes, and at each node four degrees of freedom are present (one transverse displacement, two bending moments and one torsional moment). Therefore, a total number of 16 degrees-of-freedom are assigned to each element. A consistent mass formulation is used for the eigenvalue solution in the mixed finite element analysis. The plate structure considered is assumed clamped or simply supported along its edges and resting on a Pasternak foundation. Furthermore, the plate is fully or partially in contact with fresh water on its one side. For the calculation of the fluid–structure interaction effects (generalized fluid–structure interaction forces), a boundary element method is adopted together with the method of images in order to impose an appropriate boundary condition on the fluid's free surface. It is assumed that the fluid is ideal, i.e., inviscid, incompressible, and its motion is irrotational. It is also assumed that the plate–elastic foundation system vibrates in its in vacuo eigenmodes when it is in contact with fluid, and that each mode gives rise to a corresponding surface pressure distribution on the wetted surface of the structure. At the fluid–structure interface, continuity considerations require that the normal velocity of the fluid is equal to that of the structure. The normal velocities on the wetted surface of the structure are expressed in terms of the modal structural displacements, obtained from the finite element analysis. By using the boundary integral equation method the fluid pressure is eliminated from the problem, and the fluid–structure interaction forces are calculated in terms of the generalized hydrodynamic added mass coefficients (due to the inertial effect of fluid). To asses the influences of the elastic foundation and fluid on the dynamic behavior of the plate structure, the natural frequencies and associated mode shapes are presented. Furthermore, the influence of the submerging depth on the dynamic behavior is also investigated.     

Reduction of Numerical Oscillations in Simulating Moving-Boundary Problems by the Local DFD Method

In this work, the hybrid solution reconstruction formulation proposed by Luo et al. [H. Luo, H. Dai, P. F. de Sousa and B. Yin, On the numerical oscillation of the direct-forcing immersed-boundary method for moving boundaries, Computers & Fluids, 56 (2012), pp. 61–76] for the finite-difference discretization on Cartesian meshes is implemented in the finite-element framework of the local domain-free discretization (DFD) method to reduce the numerical oscillations in the simulation of moving-boundary flows. The reconstruction formulation is applied at fluid nodes in the immediate vicinity of the immersed boundary, which combines weightly the local DFD solution with the specific values obtained via an approximation of quadratic polynomial in the normal direction to the wall. The quadratic approximation is associated with the no-slip boundary condition and the local simplified momentum equation. The weighted factor suitable for unstructured triangular and tetrahedral meshes is constructed, which is related to the local mesh intervals near the immersed boundary and the distances from exterior dependent nodes to the boundary. Therefore, the reconstructed solution can account for the smooth movement of the immersed boundary. Several numerical experiments have been conducted for two- and three-dimensional moving-boundary flows. It is shown that the hybrid reconstruction approach can work well in the finite-element context and effectively reduce the numerical oscillations with little additional computational cost, and the spatial accuracy of the original local DFD method can also be preserved.     

Mechanical passive and active models of the human basilar membrane

Simple three-dimensional passive and active models of the human basilar membrane were built, solved using the Finite Element Method and tested. In the active model an active mechanism connected with electromotility of outer hair cells was included. In the active model the active mechanism was incorporated in the form of additional, local pressure load. In the passive model the active mechanism was neglected. Hydrodynamic coupling between the cochlear partition and cochlear fluid was excluded in both models. Geometrical and physical parameters of the model were chosen to be adequate to those of humans in the best possible way. However, some of these parameters had to be estimated. The models were tested by calculation of typical curves known from cochlear measurements performed mostly on animals. For the passive model a linear input-output function and very small values of the basilar membrane velocities were obtained. This behaviour is to be expected for the passive model and for the basilar membrane in the poor physiological condition. For the active model the compressed input-output functions, tuning curves, isointensity curves and reasonable BM velocities were obtained. Possible inadequacies, which could explain the differences between numerical results and measurements were described.     

Multi-focus design of underwater noise control linings based on finite element analysis

Varied, counter-demanding objectives in designing the underwater noise control linings are addressed using a finite element model based methodology. Four different kinds of designs are proposed to attend to diverse and conflicting requirements concerning echo reduction (ER) and transmission loss (TL) performance of these linings. In this regard a slightly modified hybrid type finite element based on the Pian and Tong (PT) formulation has been used to make the computational efforts less demanding as compared to the original one. The adequacy of this formulation has been shown by comparing its results with the analytical, finite element analysis based, and experimental results. Different unit cell representations for different types of distributions of air cavities on the linings are discussed with respect to their limitations and applicability. Effect of static pressure is studied by using a simplified technique which can be used to simulate deep sea testing environment. Performance variation of different designs is investigated under different water depths to study their applicability in such situations.     

A spatial template for the shape of tuning curves in the mammalian cochlea

The shape of the tuning curve of primary auditory neurons of four mammals is characterized using a simple exponential model. The regression analysis formalizes a distinction between the characteristic frequency of a neuron and its "nominal" characteristic frequency in cases of temporary threshold loss in high-frequency neurons. Second, the model offers a stronger quality test for sharpness of tuning than the Q10dB since it takes into account the threshold of the neuron at its characteristic frequency and its "characteristic place" of origin along the cochlear partition. Third, the model reveals that the low-frequency side of the tip segment of the tuning curve is bounded by a constraint or template which is most simply expressed in spatial terms. The template describes the basal-side boundary of an "excitatory region" whose length along the cochlear partition is proportional to the square root of the sound pressure. Tuning curve variability arises because biological dependencies influence the basic template. A "spatial-filter" hypothesis is developed and its generality is discussed, particularly in regard to the case of the acoustic "fovea" of the horseshoe bat. Finally, the possibility is discussed that the template possesses a simple physiological correlate in the form of a spatially localized region marked by a "dc" shift of the mean position of the basilar membrane which sets the sensitivity of the tuning mechanism [E.L. LePage, J. Acoust. Soc. Am. 82, 139-154 (1987)].     

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.     

A boundary element method for the calculation of noise barrier insertion loss in the presence of atmospheric turbulence

Atmospheric turbulence is an important factor that limits the amount of attenuation a barrier can provide in the outdoor environment. It is therefore important to develop a reliable method to predict its effect on barrier performance. The boundary element method (BEM) has been shown to be a very effective technique for predicting barrier insertion loss in the absence of turbulence. This paper develops a simple and efficient modification of the BEM formulation to predict the insertion loss of a barrier in the presence of atmospheric turbulence. The modification is based on two alternative methods: (1) random realisations of log-amplitude and phase fluctuations of boundary sources and (2) de-correlation of source coherence using the mutual coherence function (MCF). An investigation into the behaviours of these two methods is carried out and simplified forms of the methods developed. Some systematic differences between the predictions from the methods are found. When incorporated into the BEM formulation, the method of random realisations and the method of MCF de-correlation provide predictions that agree well with predictions by the parabolic equation method and by the scattering cross-section method on a variety of thin barrier configurations.     

Comparison of WKB and finite difference calculations for a two-dimensional cochlear model.

There are many points of uncertainty in the subject of cochlear models. In this paper only the question of efficient computing methods is addressed. For the cochlear model with a one-dimensional approximation for the fluid motion, Zweig, Lipes, and Pierce [J. Acoust. Soc. Am. 59, 975-982 (1976)] have shown that the WKB method agrees well with a direct numerical integration. For the two-dimensional fluid model, Neely [E.D. thesis, California Institute of Technology, Pasadena, CA (1977)] has shown that a direct finite difference solution is an order of magnitude faster than the integral equation approach used by Allen [J. Acoust. Soc. Am 61, 110-119 (1977)]. In the present work, a formal WKB solution is derived following Whitham [Linear and Nonlinear Waves (Wiley, New York, 1974)]. The advantage of this formulation is simplicity, but the disadvantage is that no error estimate is available. We find that the numerical results from the WKB solution agree well with those of Neely (1977), while the computer time is reduced by another order of magnitude. Thus, the WKB method seems to offer the satisfactory accuracy, efficiency, and flexibility for treating the more realistic cochlear models.     

Intensity-invariance of fine time structure in basilar-membrane click responses: implications for cochlear mechanics

Basilar-membrane and auditory-nerve responses to impulsive acoustic stimuli, whether measured directly in response to clicks or obtained indirectly using cross- or reverse-correlation and/or Fourier analysis, manifest a striking symmetry: near-invariance with stimulus intensity of the fine time structure of the response over almost the entire dynamic range of hearing. This paper explores the origin and implications of this symmetry for cochlear mechanics. Intensity-invariance is investigated by applying the EQ-NL theorem [de Boer, Aud. Neurosci. 3, 377-388 (1997)] to define a family of linear cochlear models in which the strength of the active force generators is controlled by a real-valued, intensity-dependent parameter, gamma (with 0 < or = gamma < or = 1). The invariance of fine time structure is conjectured to imply that as gamma is varied the poles of the admittance of the cochlear partition remain within relatively narrow bands of the complex plane oriented perpendicular to the real frequency axis. Physically, the conjecture implies that the local resonant frequencies of the cochlear partition are nearly independent of intensity. Cochlear-model responses, computed by extending the model obtained by solution of the inverse problem in squirrel monkey at low sound levels [Zweig, J. Acoust. Soc. Am. 89, 1229-1254 (1991)] with three different forms of the intensity dependence of the partition admittance, support the conjecture. Intensity-invariance of cochlear resonant frequencies is shown to be consistent with the well-known "half-octave shift," describing the shift with intensity in the peak (or best) frequency of the basilar-membrane frequency response. Shifts in best frequency do not arise locally, via changes in the underlying resonant frequencies of the partition, but globally through the intensity dependence of the driving pressure. Near-invariance of fine time structure places strong constraints on the mechanical effects of force generation by outer hair cells. In particular, the symmetry requires that the feedback forces generated by outer hair cells (OHCs) not significantly affect the natural resonant frequencies of the cochlear partition. These results contradict many, if not most, cochlear models, in which OHC forces produce significant changes in the reactance and resonant frequencies of the partition.     

Acoustic signature of a submarine hull under harmonic excitation

The structural and acoustic responses of a submarine under harmonic force excitation are presented. The submarine hull is modelled as a cylindrical shell with internal bulkheads and ring stiffeners. The cylindrical shell is closed by truncated conical shells, which in turn are closed at each end using circular plates. The entire structure is submerged in a heavy fluid medium. The structural responses of the submerged vessel are calculated by solving the cylindrical shell equations of motion using a wave approach and the conical shell equations with a power series solution. The far-field radiated sound pressure is then calculated by means of the Helmholtz integral. The contribution of the conical end closures on the radiated sound pressure for the lowest circumferential mode numbers is clearly observed. Results from the analytical model are compared with computational results from a fully coupled finite element/boundary element model.     

概率盒框架下混合认知不确定声场的响应预测

针对含概率盒-证据混合认知不确定参数声场的响应预测问题,提出了一种概率盒框架下的改进区间蒙特卡洛方法。该方法首先将混合认知不确定参数转换为纯概率盒形式,然后结合有限元方法推导出混合认知不确定声场的盖根鲍尔多项式代理模型,再采用蒙特卡洛方法求解代理模型得到声压响应。以含概率盒-证据混合认知不确定参数的二维管道声场模型和卡车乘客舱声腔模型为例,计算结果表明混合认知不确定参数影响下的声压响应为概率盒形式,其包括声压响应极值和相应的概率信息,并且所提方法较常规混合离散方法效率更优,较基于一阶摄动法的区间蒙特卡洛方法准确性更高。研究结果表明:所提方法可以有效预测混合认知不确定声场的声压响应,并可进行声学性能的风险和保守估计。      

Structural instability in fluid-structure systems under hydrodynamic shock conditions

The effects of non-linear fluid-structure interaction on the dynamic buckling of structures are investigated. In particular the structural buckling characteristics are studied for the case of a strong shock wave propagating through a fluid medium striking a structure. Non-linear terms are retained for both fluid and structural systems. A one-dimensional example consisting of a perfect gas-spring-mass system is solved for shock wave loading. Solutions are obtained by using the finite element method. The numerical methods utilized appear to be applicable to complex multi-dimensional systems. It is shown that in a non-linear fluid-structure interaction problem the incident pressure may be amplified significantly during reflection from a structure. Thus, an acoustic fluid model may be non-conservative for strong shock problems. Structures in a fluid will buckle at an incident pressure level which is much less than that which causes buckling in a vacuum.     

光滑粒子流体动力学方法固壁处理的一种新型排斥力模型

与传统网格法相比, 光滑粒子流体动力学方法不能直接施加壁面边界条件, 这就限制了该方法在工程中的应用.为此, 本文基于Galerkin加权余量法并结合传统排斥力方法, 推导出一种新的排斥力公式来施加壁面边界条件.该方法不含未知参数, 能在不减小边界粒子尺寸的情形下有效地防止流体粒子穿透壁面, 同时可避免邻近边界的流体粒子的速度及压力振荡. 分别通过静止液柱算例、液柱坍塌算例、容器中液体静止算例及溃坝算 例来验证本文方法的有效性, 并与传统边界处理方法进行对比, 结果表明: 本文方法克服了传统方法存在的缺陷, 是一种有效的固壁边界处理方法. 关键词： 光滑粒子流体动力学法 固壁边界 排斥力 加权余量法