A Singular Perturbation Method for Parametric Investigation on J-lay Installation of Deepwater Pipelines

The maximum bending moment or curvature in the neighborhood of the touch down point （TDP） and the maximum tension at the top are two key parameters to be controlled during deepwater J-lay installation in order to ensure the safety of the pipe-laying operation and the normal operation of the pipelines. In this paper, the non-linear governing differential equation for getting the two parameters during J-lay installation is proposed and solved by use of singular perturbation technique, from which the asymptotic expression of stiffened catenary is obtained and the theoretical expression of its static geometric configuration as well as axial tension and bending moment is derived. Finite element results are applied to verify this method. Parametric investigation is conducted to analyze the influences of the seabed slope, unit weight, flexural stiffness, water depth, and the pipe-laying tower angle on the maximum tension and moment of pipeline by this method, and the results show how to control the installation process by changing individual parameters.

Determination of Heroin Based on Analyte Pulse Perturbation to an Oscillating Chemical Reaction

A new analytical method is proposed for the determination of heroin based on a sequential perturbation caused by trace amounts of heroin in the Cu(Ⅱ)-catalyzed oscillating reaction between hydrogen peroxide and sodium thiocyanate in an alkaline medium with the aid of a continuous-flow stirred tank reactor(CSTR). The method relies on the linear relationship between the change in oscillation period of the system and the concentration of heroin, with a detecting limit of 4.0×10^(-7) mol/L. The calibration curve fits a linear equation very well when the concentration of heroin is in the range of 2.0×10^(-6)_1.2×10^(-5) mol/L(r=0.9971). This method features good precision(RSD=0.98%). The influences of temperature, injection point, flow rate and reaction variables on the oscillation period were investigated in detail and a possible mechanism of the performance of heroin in the Cu(Ⅱ)-catalyzed oscillating reaction system is also discussed. The proposed method opens a new avenue for the determination of heroin.

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

The finite_element_displacement_perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first_order perturbation solution (the linear solution)of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others.It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonlinear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate,and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C_shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nonlinear solution they vary with respect to the convolutions of the bellows. Yet for most bellows, the linear solutions are valid in practice.

Perturbation Analysis of the Attached Water Mass Effect on Offshore Platform Dynamic Response

Theoretically speaking, it is impossible to make the differential equation of motion uncoupled for the natural modes of a system in consideration of the attached water. The hydro-elastic structure is equal to the non-proportional damping system. In this paper a perturbation analysis method is put forward. The structure motion equation is strictly solved mathematically, and the non-proportional damping problem is transformed into a series of proportional damping ones in the superposition form. The paper also presents the calculation formula of the dynamic response of the structure being subjected to harmonic and arbitrary load. The convergence of the proposed method is also studied in this paper, and the corresponding convergence conditions are given. Finally, the proposed method is used to analyze the displacement response of a real offshore platform. The calculation results show that this method has the characteristics of high accuracy and fast convergence.

PERTURBATION SOLUTION FOR THERMAL EXPANSION BUCKLING OF NO EXPANSION JOINT SLOPE PAVEMENT PLATE

The mechanical mechanism of thermal expansion buckling of no expansion joint slope pavement undergoing the action of a temperature field was analyzed. By using the regular perturbation method, the formula of perturbation solution for this problem was derived, the relationship between critical laying temperature difference of slope pavement and of level straight pavement was studied, and the unified solution as well as its numerical results was also obtained. In terms of this research, the reasonable laying temperature of no expansion joint slope pavement was given.

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

In order to analyze bellows effectively and practically, the finite_element_displacement_perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba_ tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root_mean_square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander's nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.

PERTURBATION FORMULATION OF CONTINUATION METHOD INCLUDING LIMIT AND BIFURCATION POINTS

This paper gives the perturbation formulation of continuation method for nonlinear equations. Emphasis is laid on the discussion of searching for the singular points on the equilibrium path and of tracing the paths over the limit or bifurcation points. The method is applied to buckling analysis of thin shells. The pre-and post-buckling equilibrium paths and deflections can be obtained, which are illustrated in examples of buckling analysis of cylindrical and toroidal shells.

MATRIX PERTURBATION METHOD FOR THE VIBRATION PROBLEM OF STRUCTURES WITH INTERVAL PARAMETERS

When the parameters of structures are uncertain, the structural natural frequencies become uncertain. The interval parameters description, i.e. the unknown-but bounded parameters description is one of the methods to study the uncertainty. In this paper, the vibration problem of structure with interval parameters was studied, and the eigenvalue problem of the structures with interval parameters was transferred into two different eigenvalue problems. The perturbation method was applied to the vibration problem of the structures with interval parameters. The numerical results show that the proposed method is sufficiently accurate and needs less computational efforts.

基于四元数误差模型的捷联惯导系统对准方法(英文)

The widely used conventional linearized error models or perturbation models are not effective to represent the nonlinear characteristics of SINS error propagation with large attitude errors. Error equations in terms of quaternion error are derived, and extended Kalman filter techniques are used to solve the in-flight alignment problems. In the case of small attitude errors, the nonlinear models can be reduced to conventional phi-angle models. The simulation results show that the proposed error models may improve the performance of alignment.

Small scale effects on buckling and postbuckling behaviors of axially loaded FGM nanoshells based on nonlocal strain gradient elasticity theory

By means of a comprehensive theory of elasticity, namely, a nonlocal strain gradient continuum theory, size-dependent nonlinear axial instability characteristics of cylindrical nanoshells made of functionally graded material(FGM) are examined. To take small scale effects into consideration in a more accurate way, a nonlocal stress field parameter and an internal length scale parameter are incorporated simultaneously into an exponential shear deformation shell theory. The variation of material properties associated with FGM nanoshells is supposed along the shell thickness, and it is modeled based on the Mori-Tanaka homogenization scheme. With a boundary layer theory of shell buckling and a perturbation-based solving process, the nonlocal strain gradient load-deflection and load-shortening stability paths are derived explicitly. It is observed that the strain gradient size effect causes to the increases of both the critical axial buckling load and the width of snap-through phenomenon related to the postbuckling regime, while the nonlocal size dependency leads to the decreases of them. Moreover, the influence of the nonlocal type of small scale effect on the axial instability characteristics of FGM nanoshells is more than that of the strain gradient one.

BUCKLING AND POSTBUCKLING OF LAMINATED THIN CYLINDRICAL SHELLS UNDER HYGROTHERMAL ENVIRONMENTS

The influence of hygrothermal effects on the buckling and postbuckling of composite laminated cylindrical shells subjected to axial compression is investigated using a micro-to-macro-mechanical analytical model. The material properties of the composite are affected hy the variation of temperature and moisture, and are hosed on a micromechanical model of a laminate. The governing equations are based on the classical laminated shell theory, and including hygrothermal effects. The nonlinear prebuckling deformations and initial geometric imperfections of the shell were both taken into account. A boundary layer theory of shell buckling was extended to the case of laminated cylindrical shells under hygrothermal environments, and a singular peturbation technique was employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical shells under different sets of environmental conditions. The influences played by temperature rise, the degree of moisture concentration, fiber volume fraction, shell geometric parameter, total number of plies, stacking sequences and initial geometric imperfections are studied.

NONLINEAR BENDING OF SIMPLY SUPPORTED RECTANGULAR SANDWICH PLATES

The fundamental equations and boundary conditions of the nonlinear bending theory for a rectangular sandwich plate with a soft core were derived by using the method of calculus of variations. Then the nonlinear bending for a simply supported rectangular sandwich plate under the uniform lateral load was investigated by using the perturbation method. As a result, a quite accurate analytic solution was obtained.

Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source

An exact and a numerical solutions to the problem of a steady mixed convective MHD flow of an incompressible viscous electrically conducting fluid past an infinite vertical porous plate with combined heat and mass transfer are presented.A uniform magnetic field is assumed to be applied transversely to the direction of the flow with the consideration of the induced magnetic field with viscous and magnetic dissipations of energy.The porous plate is subjected to a constant suction velocity as well as a uniform mixed stream velocity.The governing equations are solved by the perturbation technique and a numerical method.The analytical expressions for the velocity field,the temperature field,the induced magnetic field,the skin-friction,and the rate of heat transfer at the plate are obtained.The numerical results are demonstrated graphically for various values of the parameters involved in the problem.The effects of the Hartmann number,the chemical reaction parameter,the magnetic Prandtl number,and the other parameters involved in the velocity field,the temperature field,the concentration field,and the induced magnetic field from the plate to the fluid are discussed.An increase in the heat source/sink or the Eckert number is found to strongly enhance the fluid velocity values.The induced magnetic field along the x-direction increases with the increase in the Hartmann number,the magnetic Prandtl number,the heat source/sink,and the viscous dissipation.It is found that the flow velocity,the fluid temperature,and the induced magnetic field decrease with the increase in the destructive chemical reaction.Applications of the study arise in the thermal plasma reactor modelling,the electromagnetic induction,the magnetohydrodynamic transport phenomena in chromatographic systems,and the magnetic field control of materials processing.

Postbuckling of Imperfect Stiffened Cylindrical Shells Under Combined External Liquid Pressure and Axial Compression

posthuckling analysis is presented for the stilTened cylindrical shell of finite length subjected to combined loading of external liquid pressure and axial compression. The formulations are based on a boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, nonlinear large deflections in the postbuckling range and initial geometrical imperfections of the shell. The 'smeared stifl'cner' approach is adopted for the stiffencrs. In the analysis a singular perturbation technique is used (o determine the interactive buckling loads and the postbuckling paths. Numerical examples cover the performance of perfect and imperfect, stringer and ring stiffened cylindrical shells. Typical results arc presented in the dimcnsionless graphical form.

AXISYMMETRIC FLOW THROUGH A PERMEABLE NEAR-SPHERE

An analytical approach is described for the axisymmetric flow through a permeable near-sphere with a modification to boundary conditions in order to account permeability. The Stokes equation was solved by a regular perturbation technique up to the second order correction in epsilon representing the deviation from the radius of nondeformed sphere. The drag and the flow rate were calculated and the results were evaluated from the point of geometry and the permeability of the surface. An attempt also was made to apply the theory to the filter feeding problem. The filter appendages of small ecologically important aquatic organisms were modeled as axisymmetric permeable bodies, therefore a rough model for this problem was considered here as an oblate spheroid or near-sphere.

Noise analysis for sensitivity-based structural damage detection

As vibration-based structural damage detection methods are easily affected by environmental noise, a new statistie-based noise analysis method is proposed together with the Monte Carlo technique to investigate the influence of experimental noise of modal data on sensitivity-based damage detection methods. Different from the com- monly used random perturbation technique, the proposed technique is deduced directly by Moore-Pen＂ose generalized inverse of the sensitivity matrix, which does not only make the analysis process more efficient but also can analyze the influence of noise on both frequencies and mode shapes for three commonly used sensitivity-based damage detection methods in a similar way. A one-story portal frame is adopted to evaluate the efficiency of the proposed noise analysis technique.

APPLICATION OF THE MODIFIED METHOD OF MULTIPLE SCALES TO SOLVING THE PROBLEM OF A THIN CLAMPED CIRCULAR PLATE OF A VERY LARGE DEFLECTION

In this paper, the asymptotic behaviour of the solution to the problem of a thin clamped circular plate under uniform normal pressure at very large deflection was restudied by means of the modified method of multiple scales. The result presented herein is in good agreement with the one obtained by Professor Chien Wei-Zang who first proposed the method of composite expansions to solve this problem. However, the modified method of multiple scale seems to be simpler than the one in former method, and several computational errors in former method were corrected.

NONLINEAR VIBRATION AND THERMAL-BUCKLING OF A HEATED ANNULAR PLATE WITH A RIGID MASS

On the basis of Hamilton's principle and dynamic version of von Karman's equations, the nonlinear vibration and thermal-buckling of a uniformly heated isotropic annular plate with a completely clamped outer edge and a fixed rigid mass along the inner edge are studied. By parametric perturbation and numerical differentiation, the nonlinear response of the plate-mass system and the critical temperature in the mid-plane at which the plate is in buckled state are obtained. Some meaningful characteristic curves and data tables are given.

ELAPSED TIME OF PERIODIC MOTION WITH NEGATIVE DAMPING

An initially periodic motion is gradually raised out of the potential well by the effect of negative damping. The elapsed time when the motion ceases to be periodic is obtained by multiple variable expansions. An example of a strictly nonlinear system shows the result has a good approximation and is easy to calculate.

Internal resonance of an axially transporting beam with a two-frequency parametric excitation

This paper investigates the transverse 3:1 internal resonance of an axially transporting nonlinear viscoelastic Euler-Bernoulli beam with a two-frequency parametric excitation caused by a speed perturbation.The Kelvin-Voigt model is introduced to describe the viscoelastic characteristics of the axially transporting beam.The governing equation and the associated boundary conditions are obtained by Newton’s second law.The method of multiple scales is utilized to obtain the steady-state responses.The RouthHurwitz criterion is used to determine the stabilities and bifurcations of the steady-state responses.The effects of the material viscoelastic coefficient on the dynamics of the transporting beam are studied in detail by a series of numerical demonstrations.Interesting phenomena of the steady-state responses are revealed in the 3:1 internal resonance and two-frequency parametric excitation.The approximate analytical method is validated via a differential quadrature method.