Surface integral analogy approaches for predicting noise from 3D high-lift low-noise wings

Three surface integral approaches of the acoustic analogies are studied to predict the noise from three concep- tual configurations of three-dimensional high-lift low-noise wings. The approaches refer to the Kirchhoff method, the Ffowcs Williams and Hawkings （FW-H） method of the permeable integral surface and the Curle method that is known as a special case of the FW-H method. The first two approaches are used to compute the noise generated by the core flow region where the energetic structures exist. The last approach is adopted to predict the noise specially from the pressure perturbation on the wall. A new way to con- struct the integral surface that encloses the core region is proposed for the first two methods. Considering the local properties of the flow around the complex object-the actual wing with high-lift devices-the integral surface based on the vorticity is constructed to follow the flow structures. The surface location is discussed for the Kirchhoff method and the FW-H method because a common surface is used for them. The noise from the core flow region is studied on the basis of the dependent integral quantities, which are indicated by the Kirchhoff formulation and by the FW-H formulation. The role of each wall component on noise contribution is analyzed using the Curle formulation. Effects of the volume integral terms of Lighthill＇s stress tensors on the noise pre-diction are then evaluated by comparing the results of the Curle method with the other two methods.

Complementing the Lagrangian Density of the E. M. Field and the Surface Integral of the p-v Vector Product

Considering the Lagrangian density of the electromagnetic field, a 4 × 4 transformation matrix is found which can be used to include two of the symmetrized Maxwell’s equations as one of the Euler-Lagrange equations of the complete Lagrangian density. The 4 × 4 transformation matrix introduces newly defined vector products. In a Theorem the surface integral of one of the newly defined vector products is shown to be reduced to a line integral.

Boundedness of singular integrals along surfaces on Lebesgue spaces

In the paper, we establish the LP（Rn＋1）-boundedness for a class of singular integral operators associated to surfaces of revolution {（y,γ（｜y｜）, y ∈ Rn} with rough kernels. We also give several applications of this inequality.

THE CURVILINEARINTEGRAL PROBLEMS TO VELOCITY FIELD FOR DRAWING THROUGH PARABOLIC DIES

n this paper with Von Karmanis basic assumptions a kinematically admissible continuous velocity field has been established to drawing through parabolic dies (or called trumpet dies). Then by. using the curvilinear and the integral as a function of the upper limit an upper bound analytical solution of the drawing stress is obtained.

Machining the Integral Impeller and Blisk of Aero-Engines:A Review of Surface Finishing and Strengthening Technologies

The integral impeller and blisk of an aero-engine are high performance parts with complex structure and made of difficult-to-cut materials. The blade surfaces of the integral impeller and blisk are functional surfaces for power transmission, and their surface integrity has signif- icant effects on the aerodynamic efficiency and service life of an aero-engine. Thus, it is indispensable to finish and strengthen the blades before use. This paper presents a comprehensive literature review of studies on finishing and strengthening technologies for the impeller and blisk of aero-engines. The review includes independent and inte- grated finishing and strengthening technologies and dis- cusses advanced rotational abrasive flow machining with back-pressure used for finishing the integral impeller and blisk. A brief assessment of future research problems and directions is also presented.

ROUGH MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION ON PRODUCT DOMAINS

In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions on kernels. The main results essentially improve and extend some known results.

Rough singular integrals associated with surfaces of Van der Corput type

In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф（lul）u＇ ： u ε ]t^n} as well as the related maimal operators provided that the function Ф satisfies certain oscillatory integral estimates of Van der Corput type, and the integral kernels are given by the radial function h E ε△γ（R＋） for γ 〉 1 and the sphere function ΩεFβ（S^n-1） for someβ 〉 0 which is distinct from HI（Sn-1）.

SURFACE INTEGRAL OF THREE－DIMENSIONAL VELOCITY FIELD FOR SQUARE BAR DRAWING THROUGH CONICAL DIE

ＳＵＲＦＡＣＥＩＮＴＥＧＲＡＬＯＦＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＶＥＬＯＣＩＴＹＦＩＥＬＤＦＯＲＳＱＵＡＲＥＢＡＲＤＲＡＷＩＮＧＴＨＲＯＵＧＨＣＯＮＩＣＡＬＤＩＥ￥ＺｈａｏＤｅｗｅｎ；ＧｕｏＣｈａｎｇｗｕ；ＬｉｕＸｉａｎｇｈｕａ（ＲｏｌｌｉｎｇＴ...

Adaptive integral dynamic surface control based on fully tuned radial basis function neural network

An adaptive integral dynamic surface control approach based on fully tuned radial basis function neural network （FTRBFNN） is presented for a general class of strict-feedback nonlinear systems,which may possess a wide class of uncertainties that are not linearly parameterized and do not have any prior knowledge of the bounding functions.FTRBFNN is employed to approximate the uncertainty online,and a systematic framework for adaptive controller design is given by dynamic surface control. The control algorithm has two outstanding features,namely,the neural network regulates the weights,width and center of Gaussian function simultaneously,which ensures the control system has perfect ability of restraining different unknown uncertainties and the integral term of tracking error introduced in the control law can eliminate the static error of the closed loop system effectively. As a result,high control precision can be achieved.All signals in the closed loop system can be guaranteed bounded by Lyapunov approach.Finally,simulation results demonstrate the validity of the control approach.

Simplified permeable surface correction for frequency-domain Ffowcs Williams and Hawkings integrals

A simplified surface correction formulation is proposed to diminish the far-field spurious sound generated by the quadrupole source term in Ffowcs Williams and Hawkings(FW-H)integrals.The proposed formulation utilizes the far-field asymptotics of the Green’s function to simplify the computation of its high-order derivatives,which circumvents the difficulties reported in the original frequency-domain surface correction formulation.The proposed formulation has been validated by investigating the benchmark case of sound generated by a convecting vortex.The results show that the proposed formulation successfully eliminates the spurious sound.The applications of the proposed formulation to flows with some special parameters are also discussed.

Curve integral with path independent in orthogonal curvilinear coordinate system

It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or three dimensional rectangular coordinate systems. Firstly, according to the coordinate transformation, the condition that the line integral is the path independent in the polar coordinate system is obtained easily from the Green's theorem in two-dimensional rectangular coordinate system and the condition is extended to arbitrary two-dimension orthogonal curvilinear coordinates. Secondly, through the coordinate transformation relationship and the area projection method, the Stokes formula in three-dimensional rectangular coordinate system is promoted to the spherical coordinate system and cylindrical coordinate system, and the condition that the line integral is a path independent is obtained. Furthermore, the condition is extended to arbitrary three-dimension orthogonal curvilinear coordinates. Lastly, the conclusions are made.

CURVILINEAR INTEGRAL OF THE VELOCITY FIELD OF DRAWING AND EXTRUSION THROUGH ELLIPTIC DIE PROFILE

ＣＵＲＶＩＬＩＮＥＡＲＩＮＴＥＧＲＡＬＯＦＴＨＥＶＥＬＯＣＩＴＹＦＩＥＬＤＯＦＤＲＡＷＩＮＧＡＮＤＥＸＴＲＵＳＩＯＮＴＨＲＯＵＧＨＥＬＬＩＰＴＩＣＤＩＥＰＲＯＦＩＬＥ￥Ｚｈａｏ，Ｄｅｗｅｎ；Ｚｈａｏ，Ｈｏｎｇｊｉｎ；Ｗａｎｇ，Ｇｕｏｄｏｎｇ（Ｒｏｌｌ...

L^p Bounds for the Commutators of Rough Singular Integrals Associated with Surfaces of Revolution

In this paper, we establish the L^p （R-n＋1） boundedness for the commutators of singular integrals associated to surfaces of revolution, { （t,Ф （ ｜ t｜ ） ）： t ∈R^n }, with rough kernels Ω∈ L（IogL）^2（sn^-1）, if Ф（｜t｜） = ｜t｜.

L^p BOUNDS FOR SINGULAR INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION ON PRODUCT DOMAINS

In this paper, the authors establish Lp boundedness for several classes of multiple singular integrals along surfaces of revolution with kernels satisfying rather weak size condition. The results of the corresponding maximal truncated singular integrals are also obtained. The main results essentially improve and extend some known results.

Oscillatory Strongly Singular Integral Associated to the Convex Surfaces of Revolution

Here we consider the following strongly singular integral TΩ,γ,α,βf（x,t）=∫R^ne^i｜y｜^-βΩ（y/｜y｜）/｜y｜^n＋af（x-y,t-γ（｜y｜））dy, where Ω∈L^p（S^n-1）,p〉1,n〉1,α〉0 and γis convex on （0,∞）.We prove that there exists A（p,n） 〉 0 such that if β 〉 A（p,n） （1 ＋α）, then TΩ,γ,α,β is bounded from L^2 （R^n＋1） to itself and the constant is independent of γ Furthermore,when Ω∈ C^∞ （S^n-1 ）, we will show that TΩ,γ,α,β is bounded from L^2 （R^n＋l） to itself only if β〉 2α and the constant is independent of γ.

A Class of Singular Integral Operators Associated to Surfaces of Revolution

In this paper, the authors establish the Lp-mapping properties of a class of singular integral operators along surfaces of revolution with rough kernels. The size condition on the kernels is optimal and much weaker than that for the classical Calderon-Zygmund singular integral operators.

RELATIONSHIP BETWEEN J-INTEGRAL AND FRACTURE SURFACE AVERAGE PROFILE

To investigate the causes that led to the formation of cracks in materials, a novel method that only considered the fracture surfaces for determining the fracture toughness parameters of J-integral for plain strain was proposed The principle of the fracture-surface topography analysis （FRASTA） was used. In FRASTA, the fracture surfaces were scanned by laser microscope and the elevation data was recorded for analysis. The relationship between J-integral and fracture surface average profile for plain strain was deduced. It was also verified that the J-integral determined by the novel method and by the compliance method matches each other well.

Formation of integral fins function-surface by extrusion-ploughing process

An extrusion-ploughing process was presented to fabricate the integral fin function-surface. Cutting edge inclination angle and rake angle can be calculated from the tool’s geometry relationship. The description of fins’ geometry characters was standardized. The experiments show that, when the middle cutting edge’s inclination angle η is less than 35°, continuous fin will come out; when η is between 35° and 55°, the fins will be saw-tooth ones, and the fins will be torn when this angle is above 55°; when the extrusion angle θ is between 60° and 150°, the fins will appear, or else, the fins will be torn into chips from the base. Forming angle and clearance angle have little effect on fin’s formation. For continuous fin, its height is close to cutting depth when it is small, but it will become approximately constant as cutting depth grows; for saw-tooth fins, the width, the height, as well as the clearance will increase with the increase of cutting depth, but the increment of clearance is small; neither for continuous fin, nor for saw-tooth ones, cutting velocity has little influence on their structure parameters.

INTEGRAL SURFACES WITH VARIABLE INTEGRAL NEIGHBORS ON N-SIDED REGIONS

This paper presents a new approach to construct C1 continuous surfaces on N-sided regions. For C0 continuous surfaces on N-sided regions their smoothed surfaces are constructed by the integral smoothing operation with displaced integrals. The final smoothed surfaces are C1 continuous with the original surfaces on the boundary.