连续系统动态载荷识别的时域方法

本文提出连续系统动态载荷识别的一种时域方法.通过适当变换,将问题归结为求解Volterra型第一类积分方程.在一定的载荷假设条件下,用插值函数将积分方程离散化,即可获得动态载荷时间历程或分布形式的时域识别计算模式.采用数值解法进行的仿真实例及实梁试验表明,方法是有效的.     

A numerical model for determining the motion of a bubble close to a fixed rigid structure in a fluid

This paper is concerned with the problem of modelling the motion of a bubble close to a rigid structure in an infinite fluid. It is well known that the boundary integral method is a powerful technique for modelling the motion of a single bubble in a fluid. In this paper we shall present a modified boundary integral method for modelling the motion of a bubble close to a fixed finite rigid structure, and discuss a numerical scheme for solving the resulting integral equation for three-dimensional problems. Finally, we illustrate our method with some typical numerical results.     

Motion and force equilibrium of a local process (a soliton) in a continuous fluid medium

Consideration is given to the motion and force equilibrium of a local process (a soliton) in a continuous fluid medium. Integral characteristics of a soliton are introduced. An equation of motion, a global equation of force equilibrium, and equations of force equilibrium along individual axes are obtained that include the integral characteristics of a soliton. These equations are shown to permit direct evaluation of the interrelationship of the most important parameters of a local process based on generalized information on its structure. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 2, pp. 358–369, March–April, 2000.     

Elastic analysis of torsion crack problems of a bar with ring segment sections

In an earlier paper [6] we have studied the case of interaction of shear waves with a crack centrally situated in an infinite elastic strip; we, in this paper, extend the study to the case of two coplanar Griffith cracks. An integral transform method is used to find the solution of the equation of motion from the linear theory for a homogeneous, isotropic — elastic material. This method resolves the problem into an integral equation. It has been observed that shear waves with frequencies less than a parameter depending on the width of the wave guide can only propagate. The integral equation is solved numerically for a range of values of wave frequency, width of strip and the inter-crack distance. These solutions are used to calculate the dynamic stress intensity factor. The results are shown graphically.     

Interaction of shear waves with a griffith crack situated in an infinitely long elastic strip

This paper deals with the propagation of shear waves in a wave guide which is in the form of an infinite elastic strip with free lateral surfaces. This strip contains a Griffith crack. An integral transform method is used to find the solution of the equation of motion from the linear theory for a homogeneous, isotropic elastic material. This method reduces the problem into an integral equation. It has been observed that only shear waves with frequencies less than a parameter-value, depending on the width of the wave guide, can propagate. The integral equation is solved numerically for a range of values of wave frequency and the width of the strip. These solutions are used to calculate the dynamic stress intensity factor, displacement on the surface of the crack and crack energy. The results are shown graphically.     

The application of the boundary integral equations method to subsonic flow with circulation past thin airfoils in a wind tunnel

Summary In this paper we apply the direct boundary integral equations method to subsonic flow with circulation past a thin airfoil in a wind tunnel. A set of Green's functions for the equations of the velocity perturbation is deduced. These functions together with the non-linear limit condition imposed just on the surface profile lead to a Fredholm integral equation of the second kind over the profile only. The integral formulation has the advantage not to truncate the flow domain and to save computing effort when numerical solving is performed, due to the lack of the tunnel walls discretisation. In the case of the incompressible fluid we use the exact equations of motion, which implies a valid solution for any shape of the profile, being not necessarily thin. In the case of the compressible fluid we use the linearized motion equations, which implies a valid solution only for thin airfoils. The integral equation obtained on the surface, together with the circulation integral formula are solved via a collocation method. The numerical tests made for the circular obstacle show a very good agreement with the theory. The numerical experiments on the NACA-4412 profile were made in order to determine the tunnel and the compressibility effects being compared to the unbounded flow.     

A momentum integral solution for pulsatile flow in a rigid tube with and without longitudinal vibration

A momentum integral solution is obtained for fully developed pulsatile flow in a circular, rigid tube of infinite length. A fourth-order polynomial with unknown coefficients is used to represent the radial variation of axial velocity across the tube. Boundary conditions applied at the tube wall and the centerline give the velocity profile in terms of centerline velocity. The momentum integral equation then gives a differential equation for the centerline velocity; and complete solutions, including mass flow rate, are obtained for a sinusoidal pressure gradient, with and without a sinusoidal longitudinal wall velocity. Excellent agreement is found with Womersley's results for a stationary tube. For wall motion at the same frequency as the pressure gradient, both an increase in mass flow magnitude and an exact cancellation are found, depending on phasing. These results are used to discuss the application of momentum integral methods to pulsatile flows and possible fluid-dynamical aspects of cardiovascular behavior during whole-body vibration.     

Transient behavior of a few dies on an elastic half-space

Summary An asymptotic approach to dynamic interaction between a few distant dies and an elastic half-space is proposed. The transient motion of the dies under low-frequency vertical load is under consideration. The explicit expression for the fundamental singular solution of Lamb's problem is used to derive the boundary integral equation of contact. Then this equation is asymptotically simplified and solved numerically in combination with equations of motion of the dies.Equations obtained in the asymptotic limit describe both the die-medium dynamic interaction and the interaction between dies through the elastic medium. These equations take into account the energy dissipation phenomenon associated with energy transfer deep into the medium by outgoing elastic waves, of so called geometrical damping.Equations proposed are asymptotically correct within the corresponding range of parameters, as such improving the state-of-the-art.     

Boundary layer of non-Newtonian fluids obeying a rheological power law for arbitrary pressure gradients

The equations of the boundary layer associated with non-Newtonian fluids obeying a rheological power law are integrated by a semiintegral method based on the simultaneous solution of the linearized equation of motion and the integral relationship.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 3, pp. 398–404, March, 1971.     

The dynamical problem of a rectangular stamp moving on an elastic half plane

Summary In this work, the stresses under a rectangular rigid stamp moving on an elastic half plane are calculated. The boundary value problem has been formulated in the form of a singular integral equation whose unknown function is the stress distribution under the stamp. The solutions of the equation have been compared for the cases of absence or presence of friction and for the cases of motion or rest. The work is an extension of Muskhelishvili's results and differs numerically from these ones only when the speed of the stamp is comparable with the shear wave speed.     

Various integral equations for a single crack problem of elastic half-plane

Two kinds of the complex potentials used for the crack problem of the elastic half-plane are suggested. First one is based on the distribution of dislocation along a curve, and second one is based on the distribution of crack opening displacement along a curve. Depending on the use of the complex potentials and the right hand term in the integral equation, two types of the singular integral equation for a single crack problem of elastic half-plane are derived. Regularization of the suggested singular integral equations gives three types of the Fredholm integral equation for the relevant problem. The weaker singular integral equation and the hypersingular integral equation are also introduced. Seven types of the integral equation are finally obtainable. The relation between the kernels of the various integral equations is also discussed.     

The theory of oscillating thick wings in subsonic flow. Lifting line theory

Summary On the basis of the fundamental solutions method developped by the author in some previous papers, in this paper a theory of oscillating thick wings in subsonic flow is given. In this way the representation of the general solution for arbitrary wings and the integral equation of the problem are obtained. The known solutions for the stationary motion and the plane problem are regained as particular cases. General solutions and integral equations for the incompressible fluid and for the two and three dimensional motion at Mach number one are also put into evidence. In the last part of the paper the theory of oscillating lifting line is given.     

A new quadrature algorithm consisting of volume and integral domain corrections for two-dimensional peridynamic models

International Journal of Fracture - Peridynamic (PD) models using the equation of motion in the integral form are applied to describe the failure and damage of materials. At present, the most...     

The method of a small parameter in the classical Stefan problem

It is shown that the motion of a phase interface with relatively small perturbations of the boundary condition is described by the Volterra linear integral equation. The solution is investigated using a Laplace transformation.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 38, No. 2, pp. 329–335, February, 1980.     

A note on the impact response of a cracked orthotropic material

An approach involving potential functions is used to simplify the equations of motion for an Orthotropic material to an elementary differential equation whose solution may be used for a wide variety of problems in elastodynamics of Orthotropic materials. Solutions for the dynamic mode I and II stress intensity factors for a Griffith crack in an Orthotropic material are obtained. The new approach allows the stress intensity factors to be determined with a minimal use of integral transforms. The solutions for the stress intensity factors are shown to be the same as those obtained by previous researchers.     

Pressure and flow in fluid films constrained between translating and vibrating flexible surfaces

In this paper, the dynamic pressure and flow developed in a two-dimensional, viscous fluid film constrained between flexible surfaces are analyzed. The problem formulation assumes that the response of the flexible surface is governed by linear equations of motion, and the fluid motion is governed by linearized momentum equations including the unsteady inertia. Three states of the model are developed to describe the coupled fluid-structural response problem. The fluid dynamic pressure is derived in the frequency domain as a function of the fluid impedances and the surface transverse vibrations. The perturbed, coupled problem is described by an integral equation (in state vector form) that governs the coupled responses of the flexible surfaces. The integral equation is solved by a discretization method. The analysis is applied to a rigid slider bearing with a flexible, translating plate surface under the excitation of a harmonic point load. The accuracy of the discretization method is evaluated, and numerical results for the dynamic pressure and the plate response are presented.     

Internal diffusion in a biporous sorbent in the case of a rectangular sorption isotherm

Sorption in a sorbent of biporous structure is considered in the case of a limiting convex-rectangular— isotherm. An accurate integral equation for the sorption wave front is obtained. Asymptotic laws of front motion are found for small and large times.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 36, No. 3, pp. 522–527, March, 1979.     

Boundary element analysis of guided waves in a bar with an arbitrary cross-section

A boundary element method (BEM) is presented for analyzing the dispersion relation of guided waves in a bar with an arbitrary cross-section. A boundary integral equation for a harmonic motion in time and space is derived with respect to the boundary of the cross-section of the bar. By means of a collocation method, a homogeneous matrix equation which depends on the frequency and the wave number of the guided wave is obtained. The dispersion relation of guided waves is then obtained by finding nontrivial solutions of the matrix equation. The Newton's method is used to find the solution of the dispersion relation mode by mode for both propagating waves and nonpropagating waves. Numerical results are shown for a square bar, rectangular bars, and an L-shaped bar. Dispersive properties of guided waves in the bars are discussed in comparison with the results for Lamb modes in a 2D plate.     

The DRM sub-domain decomposition approach for two-dimensional thermal convection flow problems

This work presents a domain decomposition boundary integral equation method for the solution of the coupling of the momentum and energy equations governing the motion of a viscous fluid due to natural convection. The domain integrals in the proposed integral representation formula of both equations are transformed into surface integrals at the contour of each sub-region via the dual reciprocity method (DRM). Finally, some examples showing the accuracy, the efficiency and the flexibility of the proposed method are presented.     

On the calculation of boundary stresses with the Somigliana stress identity

The computation of boundary stresses by Boundary Element Method (BEM) is usually performed either by expressing the boundary tractions in a local co-ordinate system, calculating the remaining stresses by shape function differentiation and inserting into Hooke's law or recently also by solving the hypersingular integral equation for the stresses. While direct solution of the hypersingular integral equation, the so-called Somigliana stress identity, has been shown to be more reliable, the interpretation and numerical treatment of the hypersingularity causes a number of problems. In this paper, the limiting procedure in taking the load point to the boundary is carried out by leaving the boundary smooth and the contributions of all different types of singularities to the boundary integral equation are studied in detail. The hypersingular integral in the arising boundary integral equation is then reduced to a strongly singular one by considering a traction free rigid body motion. For the numerical treatment, an algorithm for multidimensional Cauchy Principal Value (CPV) integrals is extended that is applicable for the calculation of boundary stresses. Moreover, the shape of the surrounding of the singular point is studied in detail. A numerical example of elastostatics confirms the validity of the proposed method.