Ma Xingrui

Modal part analysis of slosh of the liquid in a cylindrical container in the case of small bond number

Reconstruction of liquid free slosh modes by curved quiet free surface was investigated in the case of small Bond number by means of modal part analysis method in this paper. It is shown that the curved liquid quiet free surface would couple the modes to form new eigen-modes while the orthogonality of the modes which participate the liquid slosh are given only by their Bessel modal parts and it would change their eigen-frequencies respectively while the orthogonality are given by their triangle function modal parts. By studying the laterally forced slosh of the liquid in a cylindrical container based on the new eigen-modes, a characteristic of modeschoosing was found.

Forces and Moments of the Liquid Finite Amplitude Sloshing in a Liquid-Solid Coupled System

Nonlinear coupling dynamics between a spring-mass system and a finite amplitude sloshing system with liquid in a cylindrical tank is investigated. Based on a group of nonlinear coupling equations of six degrees of freedoms, analytical formulae of forces and moments of the liquid large amplitude sloshing were obtained. Nonlinearity of the forces and moments of the sloshing was induced by integrating on final configuration of liquid sloshing and the nonlinear terms in the liquid pressure formula. The symmetry between the formula of Ox and Oy direction proves that the derivation is correct. According to the coupled mechanism, the formulae are available in other liquid-solid coupled systems. Simulations and corresponding experimental results are compared. It is shown that the forces and moments formulae by integrating on the final sloshing configuration are more reasonable. The omitted high-dimensional modal bases and high-order nonlinear terms and the complexity of sloshing damping are main sources of errors.

A METHOD OF INTERFACE INVERSION IN INHOMOGENEOUS MEDIA

First, an approximate solution of time domain interface scattering field is derived by extending the classical Born approximation in the problem of interface scattering. In accordance with the solution form, a projection density compensation (PDC) inversion method is developed according to the projection slice theorem, which is valid for the cases of inhomogeneous media and wave mode transformation. Finally, in the model of layered media, the calculation algorithm and the simulation inversion comparison results of point defect, crack, and crack on an interface, as well as the experiment method and results in the condition of acoustic wave, are given.

Interaction of axially symmetric waves with an annular crack in an infinitely long hollow cylinder

In this paper an analysis of the interaction of longitudinal waves with an annular crack in an infinitely long hollow cylinder is presented. Using Fourier sine and cosine as well as Hankel integral transforms, formal complete solutions to the governing equations are given. By means of Abel integral transform, the problem is reduced to the solution of a Fredholm integral equation of the second kind which is, then, solved numerically for a range of values of the frequencies of the incident waves. The numerical values of the dynamic stress intensity factor at the rim of the crack have been calculated.

Refined dynamic equations of thick beam bending

In this paper, based on the theory of refined dynamic equations of thick plates bending, applied the differential operator algebra and decomposition of operator spectra, the refined dynamic equation of the beam flexural motion is first obtained by using proper gauge conditions and satisfying the boundary conditions. The refined equation of beams is a fourth-order equation, which governs the generalized displacement functions W , F and f . The dispersion relations, which are from the given beam theory, Euler-Bernoulli beam and Timoshenko beam, respectively, are compared. The refined equations of thick beams and applicable condition are investigated and discussed. Since derivation of the refined dynamic equation is conducted without any assumptions, so the proposed equation of thick beam bending is exact, that can be used to analyze vibration of thick beams at the high frequency and to evaluate the applicable condition of the engineering beam theory.

A computational method for interval mixed variable energy matrices in precise integration

To solve the Riccati equation of LQ control problem, the computation of interval mixed variable energy matrices is the first step. Taylor expansion can be used to compute the matrices. According to the analogy between structural mechanics and optimal control and the mechanical implication of the matrices, a computational method using state transition matrix of differential equation was presented. Numerical examples are provided to show the effectiveness of the present approach.To solve the Riccati equation of LQ control problem, the computation of interval mixed variable energy matrices is the first step. Taylor expansion can be used to compute the matrices. According to the analogy between structural mechanics and optimal control and the mechanical implication of the matrices, a computational method using state transition matrix of differential equation was presented. Numerical examples are provided to show the effectiveness of the present approach.

Theory and algorithm of optimal control solution to dynamic system parameters identification (II) — Stochastic system parameters identification and application example

Based on the contents of part (I) and stochastic optimal control theory, the concept of optimal control solution to parameters identification of stochastic dynamic system is discussed at first. For the completeness of the theory developed in this paper and part (I), then the procedure of establishing Hamilton-Jacobi-Bellman (HJB) equations of parameters identification problem is presented. And then, parameters identification algorithm of stochastic dynamic system is introduced. At last, an application example-local nonlinear parameters identification of dynamic system is presented.

ON THE STRESS CONCENTRATION IN THICK CYLINDRICAL .SHELLS WITH AN ARBITRARY CUTOUT

In this paper, based on the theory of thick shells including effects of transverse shear deformations, a complex variables analytic method to solve stress concentrations in circular cylindrical shells with a small cutout is established. A general solution and expression satisfying the boundary conditions on the edge of arbitrary cutouts are obtained. The stress problem can be reduced to the solution of an infinite algebraic equation series, and can be normalized by means of this method. Numerical results for stress concentration factors of the shell with a small circular and elliptic cutout are presented.

Dynamics of constrained mechanical systems and its application in robotics-implementation

Abstract In this paper, based on the orthogonality of the tangent space and normal space, the construction of the constrained system was studied and two implemental methods were proposed. These two methods make full use of recursive processes which reflect the hierarchical nature of the structure of the constrained system. Every recursive step has been standardized and the complexity in the dynamic analytical modelling and analysis has been greatly reduced. A hand-like multibody system is taken as an example to illustrate the usefulness and effectiveness of the methods proposed in this paper.

Impact response of a finite interface crack with adhesive tips

Of considerable importance in structural analysis is the transient response of a flaw to a time dependent stress field. A number of papers on the area of dynamic crack analysis have been reviewed in [ 1]. The impact response of a finite crack in plane extension has been considered in a paper by Sih and Embley [2]. Impact response of the interface crack is, however, a very complex problem due to the strong discontinuity of the material constants. The general elasticity solutions, that have been worked out for such a crack, involve oscillatory singularities which lead to wrinkling of the crack and overlapping of the materials [3]. These unreasonable phenomena have bothered scholars and research workers for a long time. In 1977, Comninou [4] proposed a frictionless contact model and solved the relevant static problem. The size of the contact region that is worked out according to the model is, however, too small to be acceptable to the assumption of continuum mechanics. In 1978, J.D. Achenbach [5] proposed another model which assumed that the crack faces are in adhesive contact near the tips. He solved the static problem and obtained some excellent results. The scattering of steady elastic waves by this kind of crack has been considered in a paper by Zhou Zhengong [6], and Rice [7] has further considered static contacting problems of the interface crack.